Introduction text
Elementa 1 Workshop of the Future – 1800
Anyone familiar with the laws of nature can deliberately exploit natural processes for the benefit of mankind. This was the modern understanding of science that emerged in the 17th century.
Man as master and owner of Nature: this was René Descartes' vision. And the English philosopher Francis Bacon coined the slogan 'knowledge itself is power'.
Mathematics was considered the organising principle of a world created by God according to size, number and weight. Therefore Nature was studied experimentally, by measurement, counting, and weighing, and its laws were formulated in mathematical terms.
Mechanics was the universal science that applied to processes in the heavens as well as on earth. It was the basis for the newly emerging mechanical and structural sciences that combined theory and practice and whose methods of calculation are still in use today.
Anyone hoping to understand the highly technical world of today should take a look at the creative workshops of a revolutionary time when the scientific and technical foundations of our modern world were laid. Station text
Use of natural forces Machines to make physical work easier
In ancient Greek and Roman times, simple machines such as the lever, wedge, screw, winch and pulley were used to boost the muscle power of man and beast.
For centuries, natural sources of energy such as wind and water have powered mills of all kinds, widely used in Europe since the Middle Ages.
Engineers and natural scientists analyzed the function of these basic machines in the 17th and 18th centuries. Using the laws of mechanics and by doing experiments, they studied how the efficiency of traditional energy use could be improved.
They also discovered new ways of using the forces of nature. Experiments on the function of atmospheric air pressure, fire and steam culminated in the development of the steam engine, the main prime mover of the industrial age. 1 2 Can pulleys make things easier What‘s happening here? for me? The greater the number of sections of rope that Use the different systems of pulleys to raise the support the load, the less hard you have to pull. same amount of weight. Do you have to pull But what you save in effort, you have to pay back by pulling a greater length of rope through the
Pulley harder in some cases than others? Do you have to pull different lengths of rope through the pulley pulley system. systems? In general: machines don’t save you mechanical work. Any reduction in force must be balanced by having to pull/push through a greater distance. 3 A closer look A B
The product of the pulling force and the length of rope pulled through the pulley system always remains constant. In physics it’s called “mechanical work”. This rule applies to all machines – like levers and gears – and is called the „golden rule of mechanics“:
The product of force and distance always remains constant.
The force that you need to apply to the rope is determined by the number of sections of rope that support the load.
Example A: The load is suspended from 4 sections of rope. This means you only have to pull with ¼ of the load’s weight to lift it. However, the length of rope that you have to pull through the pulley system is four times as long as the distance moved by the load.
Example B: When you pull yourself up, your weight is carried by two sections of rope - the section you pull on also bears weight. So you only need to pull with half your own weight. But twice as much rope will pass through your hands as the distance (height) by which you raise yourself. tage that it can lift the car much more quickly. very quickly. Acrane with amotor has the advan very slowly while you have to pull on the rope lift acar. The disadvantage is that the car will rise With asystem of enough pulleys, you can easily cranes. shops. They are acheap alternative to motorized Hand-operated pulleys are also still used in work sail) on sailboats is still rigged using apulley. The boom (the horizontal spar beneath the tric winch is quadrupled by asystem of pulleys. example of this principle. The force from elec its which was used to set up the exhibition, is an er of man and machine. The crane on this floor, are still used today to reinforce the pulling pow Pulleys have been used since ancient times. They Why, what,wherefore? 4 - - - - schaften. 1724schaften. Wissen Mechanischer Grundes des Schau-Platz Generale. Machinarum TheatrumJakob Leupold: -
01.06.2013 TECHNOSEUM Pulley 1 3 Play Master Builder! A closer look
Hang the building blocks on the crane In this model, the treadmill is replaced by a hand- hook. Turn the wheel to raise and wheel. lower the blocks. You can also turn the whole crane. You To lift the “stone“ 1 m, the rope has to be wound could build a wall, for example. up 1 m. This needs 4 revolutions of the rope drum; the rim of the handwheel travels a distance of approximately 12 m.
The “golden rule of mechanics“ also applies in this case: the product of force and distance is always equal; the less force used, the longer the distance Model Crane that has to be traveled.
2 What‘s happening here?
Much like with the treadmill crane, the load is lifted using a transmission system.
As you turn the handwheel, the rope winds onto the axle and lifts the stone. Pulley Treadmill crane Find out more: Mannheim armoury, the current Zeughaus, in C5. than our model, was used in the 1770‘s to build the A crane of this type, and around five times larger was known as the “Large French Crane“. century German on books mechanical science, it This model is based on acrane from France. In 18th Why, what,wherefore? 4 Plans drawing for crane: the model by F. Denis, around 1777
01.06.2013 TECHNOSEUM Model Crane 1 2 Can you lift 275 kg? What‘s happening here?
Please ask a TECHNOscout to unlock the crane! If you stand still, directly under the shaft, Step into the wheel and follow the instructions the treadmill does not move. as you walk. Be careful! What direction do you have to walk to raise the However, once you start walking “uphill” on the stone? correct side, the wheel turns, the gears start tur- ning, the rope is wound up, and you lift the stone, even though at 275 kg it weighs much more than you do (you are probably not strong enough to pick it up). However, you have to walk 50 m in the wheel to lift the stone 1 m. Ask a TECHNOscout!
Treadmill Crane Treadmill A 3 Axle A closer look
When you stand under the axle your weight W acts directly W through the axle pivot and doesn’t produce a turning mo- ment, so the wheel stays still. Figure A As you walk „uphill“ in the wheel, the force W shifts and B acts with a moment arm h to give a turning moment W · h . Figure B h To raise the stone 1 m, 1 m of rope must be wound up. To wind the rope 1 m, the drum and the large gearwheel need to turn 0.877 times. The small gearwheel and treadmill have to turn 4.5 times as far, making just under 4 complete turns (3.95 to be exact). W
The distance that you walk in the treadmill is equal to 4 times the circumference of the treadmill: almost 50 m (49.62m to be exact).
The “golden rule of mechanics“ also applies in this case: the product of force and distance is always the same; the less force you have to use, the greater the distance through which you have to push. Model craneModel Pulley more: out Find capable of lifting larger and larger loads. cranes have been built from iron and steel and are cargo, and parts machines increased. Since then, century, the amount of merchandise and weight of With the advent of industrialization in the 18th gearwheels. of complex in design with swiveling jibs and systems those used in ancient times, but were often more dern Period were not very different in principle from The cranes of the Middle Ages and the Early Mo pulleys. multiple of systems times. Gearwheels were known, but cranes used Treadmills were commonly used in cranes in ancient or to load ships. aqueducts, and temples such as structures were used in ancient times to build large Cranes (machines used to lift heavy loads) Why, what,wherefore? 4 - Heb-Zeuge. 1725Heb-Zeuge. TheatrumJakob Machinarum. der Leupold: Schau-Platz Zeuge. 1725 TheatrumJakob Machinarum. Heb- der Leupold: Schau-Platz for of the the reproduction treadmillModel crane from
01.06.2013 TECHNOSEUM Treadmill Crane Waterwheels Undershot and overshot wheels
How can we harness the force of water?
Press the start button and see how the water drives the two waterwheels. On the left is an undershot wheel, on the right is an overshot wheel.
What's happening here?
The water is pumped up through the column in the middle. It flows equally to both sides to the waterwheels.
The undershot wheel on the left is turned by the force of running water on the blades at the bottom. The overshot wheel on the right is turned by water falling onto the blades from above.
The spring balance on each waterwheel shows the wheel’s turning moment. The number of revolutions and power output are shown on the digital display. Change the loading of the wheels by turning the knobs.
Find the speed at which the wheels produce the most power. You’ll discover that the maximum power output of the overshot wheel is greater than that of the undershot wheel.
A closer look
The water supplies the same amount of energy to both wheels, but the energy is exploited very differently. With the overshot wheel, the potential energy of the water is used directly: the water fills the buckets around the wheel's circumference, and the weight of the water drives the wheel round.
The overshot wheel could theoretically use all of the energy of the water, but only if the wheel turns so slowly that the water escapes from the buckets at the bottom without any significant kinetic energy (energy of movement). In practice, up to two thirds of the water's energy can be put to actual use.
With an undershot wheel, the potential energy of the water is converted into kinetic (movement) energy before the water strikes the wheel: this occurs at the outlet of the water column. The impact of the moving water against the blades creates the force that drives the wheel.
But the water can never deliver its entire energy to the undershot wheel. As it flows away, it flows at the speed of the rim of the wheel and so carries away unused kinetic energy.
The best wheel rim speed is half the water's approach speed. But even then theoretically only half of the water’s energy can be exploited. In practice, only about one third can be used.
Why, what, wherefore?
John Smeaton (1724-1792) used a similar setup in his experiments with overshot and undershot waterwheels. He published his findings in the Philosophical Transactions of the Royal Society in 1759.
Smeaton's test model, here set up as an undershot wheel. The dotted line in the drawing on the right shows the water channel for the experiment with the overshot wheel. Smeaton measured the work performed by the wheels using a pulley and weights. (An experimental enquiry concerning the natural powers of water and wind to turn mills and other machines depending on circular motion. In: Philosophical Transactions of the Royal Society. Vol. 51, 1759-1760, p.100-174).
Smeaton's experiments on model water wheels revealed that overshot water wheels are twice as efficient as undershot wheels. Overshot wheels can convert around two thirds of the water's energy, but undershot wheels only one third. These values apply for well-built water wheels with straight paddles.
Otto von Guericke Experiments with a vacuum
During the Renaissance, a question was discussed that had been raised in ancient times: can a vacuum exist in nature?
An important contribution to the discussion was provided by Otto von Guericke, the mayor of Magdeburg, with his experiments on air pressure and the vacuum.
He demonstrated his famous Magdeburg hemispheres in 1656: the power of 16 horses was not enough to pull apart the two halves of a split copper sphere from which the air had been removed.
Guericke then used a type of crane to demonstrate that atmospheric pressure could lift around 1300 kg when it pushed a piston into an evacuated cylinder.
Guericke's approach is a vivid example of the new, experimental natural sciences that started to change the views of the Christian western world beginning in the 16th century. Guericke demonstrated how scientific findings that were gained experimentally could be used technically.
In doing this he opened up new ways to make powered machines. The principle of using the pressure of atmospheric air, and later the pressure of steam or combustion gases, has been widely used since the 18th century in steam engines and internal combustion engines.
Otto von Guericke: Experimenta Nova (ut vocantur) Magdeburgica de Vacuo Spatio. 1672 [New (so-called) Magdeburg Experiments on the Vacuum]
Guericke's Crane
Can air be used to lift loads? Close the yellow and red valves (each lever must be at right angles to the pipe). Pump the air out of the black container.
Open the red valve (move the lever parallel to the pipe). What happens to the piston, the cable and the load platform?
Now open the yellow valve to allow air to flow back into the black container, the air lines and the cylinder.
What's happening here?
When the air has been removed from the black container, there is low pressure inside it. In the cylinder, however, the air pressure is the same as in the surrounding air. If the container and cylinder are connected, air flows out of the cylinder into the black container and equalizes the pressure.
The common internal pressure is now lower than the surrounding air pressure. The outside air pressure pushes the piston down and lifts the load. The Earth's atmosphere does the work!
A closer look
The air pressure exerted on the Earth's surface and on all things on it is equivalent to a force of 100,000 N (newton) per 1 m²
This pressure is equivalent to 1 bar or 100 kilopascal.
Air pressure acts equally on the inside and outside of open containers: the walls are thus not subject to stress.
If the air is pumped out of a closed container, a difference in pressure is produced. The air pressure inside is reduced and can no longer fully support the walls against the pressure from the outside. The forces that are produced can deform the wall or even destroy it. This effect occurs, for example, when a TV picture tube implodes.
The piston that moves in the cylinder is effectively a piece of wall that can move. It is held by the cable and the counterweight attached to it.
How does a suction cup work?
Press the suction cup onto the mirror. Then see how strongly it holds.
Press the two suction cups against each other and then try to pull them apart.
Careful: the handles of the suction cups can come off!
What's happening here?
When you press the suction cup onto the mirror, you push the air out of it. When you then pull on the handle, a partial vacuum is created under the plunger. Atmospheric air presses against the plunger and "fastens" the suction cup to the mirror. A suction cup cannot work in a vacuum. You will never see an astronaut holding onto the outside of the International Space Shuttle with suction cups.
A closer Look The force on the suction cup depends on the outside air pressure. It can be calculated using the following formula: force (F) = air pressure (p) x area (A)
Air pressure at sea level is on average 1013 mbar (millibar) or 101300 N (newton) per m² and the area under the suction cup is 0.0113 m².
If a complete vacuum was actually created under the suction cup, you would need a force equivalent to 117 kg to pull it off the mirror.
Why, what, wherefore?
Guericke impressively demonstrated the force of atmospheric pressure in his famous demonstration with the Magdeburg hemispheres. Like two suction cups, they were held together solely by the pressure of the surrounding air after he evacuated the air from inside them with an air pump.
You can reproduce the experiment by pressing the two suction cups together and finding a partner to pull against. Your partner in the experiment now opposes your pull - they are doing what the mirror did earlier.
Instead of 16 horses, Guericke would only have needed half that number for his experiment if he had simply tied one of the hemispheres to a tree trunk. But the demonstration would not have been as dramatic.
It's hard to imagine our daily lives without suction cups. Whether as towel holders or to attach a stuffed animal to a car windshield or to lift large panes of glass - they do many useful jobs for us with the help of partial vacuums.
1 3 How much pressure can you A closer look
produce when you blow into a This apparatus measures the pressure of your breath in mbar straw? (millibar). The formula for the hydrostatic pressure of water in the pipe is: Take a fresh straw from the dispenser, insert it into the metal support, and blow as hard as you can. pressure (P) = density (ρ) · gravitational acceleration (g) · height (h) The height of colored water in the pipe shows how or: P = ρ · g · h much pressure you generate. The diameter of the pipe doesn‘t come into it at all! We can now calculate what height of water in the pipe is equivalent to 1 mbar of pressure. First, we need to convert the unit mbar into Pa (pascal).
Exhaled Air
1 mbar = 100 Pa = 100 N (Newton) m 2
P Thus: h = ρ · g = 1,02 cm
This means when the pressure of your breath is 100 mbar, the water in the pipe rises by 1.02 m. 2 What‘s happening here?
The pressure of your breath pushes the colored wa- ter out of the container and into the pipe. The higher the water rises, the greater the pressure it produces because of its weight.
At some point, the pressure of the water is equal to pressure of your breath, and the water stops rising. Now you can read off the pressure. 4 What‘s happening here?
Air pressure at sea level is 1013 mbar on average. This is equivalent to a water level in the pipe of 10.33 m.
The pressure in a car tire, for example, is 2 bar. This would be equal to a water level of 20.40 m, and the pipe would have to be twice as high as a two-storey house. Exhaled Air 01.06.2013 TECHNOSEUM 01.06.2013
Station text
Mechanization of the world view The world as a clock
The laws of mechanics are universal: they apply in the heavens as well as on the Earth. This was the fundamental insight of natural sciences in the modern age.
A stone falling to the ground and the heavenly bodies moving in space follow the same laws of nature, formulated by Galileo Galilei and Isaac Newton in the 17th century.
The entire cosmos was viewed as a divine clock movement. Its pointer, for telling the time, is the moving shadow on a sundial. The mechanical clock reproduces the course of the stars across the sky and converts them into the movement of its hands.
This is how the earthly mechanical clock became a mechanical image of the grand heavenly machine and influenced the mechanistic world view of the modern age: the concept of the world as a clock.
1 3 Feather or ball? Which will drop A closer look faster in a vacuum? When the tube is full of air, the ball drops faster Press the green button to let air into the drop tube. than the feather because it has a much lower air Turn the tube over and watch how the feather and resistance than the feather, because of its shape. ball drop. Now press the red button. The air is now being However, when air is pumped out of the tube, sucked out of the tube. there is no air resistance: the different shapes Free Fall Wait until the pressure reading has reached its of the ball and feather no longer affect how fast lowest value. they fall. Turn the tube over again and watch how the feather and ball drop. Only gravitational forces and inertial forces now have an effect. Greater gravitational force acts on the heavier ball, but a correspondingly greater inertia opposes the acceleration. The opposite is true for the feather: the gravitational force is lower, but so is the inertia to be overcome.
This is the reason why the ball and feather fall at the same rate in a tube from which air has been removed. According to the laws of free fall in a 2 vacuum, the acceleration of both objects in the Earth‘s gravitational field is 9.81 m/s². What‘s happening here?
When there is air in the tube, the feather and ball drop as we would expect them to: the ball falls much faster than the feather.
When almost all of the air is pumped out of the tube, the feather and ball drop at almost the same rate. sistance all bodies would fall with the same speed.“ conclusion that in amedium totally devoid of re and found: “Having observed this, Icame to the Demonstrations“ Mathematical and “Discourses Galileo described this proposition in 1638 in his speed. the in differences smaller the most at the same rate. The lighter the medium, the however, floats. In air, gold, lead and wood fall al sink, although the lead sinks more slowly. Wood, rise to the surface and float. In water, gold and lead Only the gold sinks in mercury; the lead and wood density such as mercury, water and air? lead and wood are dropped into media of different what happens when heavy bodies made of gold, One of the things he reflected on was: deduction. and thought experiments of means by the equations of free fall (which are still valid today) of Pisa, as is often said. Instead, Galileo formulated on the law of falling bodies from the Leaning Tower Galileo Galilei (1564-1642) did not do experiments Why, what,wherefore? 4 - - Inclined Plane Find out more: of lead down the evacuated tube. tead of apiece of wool and awooden ball instead feather ins a dropped we though even doubters, Maybe our experiment would have convinced the bit of lead...“ were possible, apiece of wool could fall as fast as a that even in avacuum, if motion in such aplace Galileo’s claim overconfident: ”I shall never believe His opponent in the fictitious debate considered -
01.06.2013 TECHNOSEUM Free Fall 1 3 Is the ball speeding up? A closer look
Place the ball into the start position in the groove at The ball rolls down the groove because the force of gravity the top left. Press the green start button. acts on it. Yet only part of the full force of gravity acts to The ball is released and rolls down the groove. accelerate the rolling ball. The smaller the angle of the slope, the less force acts in the downhill direction, and the slower the acceleration of the ball.
We can think of the ball’s rolling motion as a slow falling motion and use it to study the laws of falling bodies. The basic connections between acceleration, speed, distance and time are the same in free fall as for a ball rolling down an inclined plane, but measurements are easier to make on the inclined plane.
The accelerating force is constant and so the acceleration is Inclined plane also constant, at around 0.35 m/s² on this slope. Accelerati- on in free fall would be around 28 times higher: 9.81 m/s². 2 The speed-time graph and the distance-time graph clearly show how in free fall the velocity increases linearly with time, but the distance is proportional to the square of the time. What's happening here?
A timer starts as soon as the ball is released. Whenever the ball passes one of the measuring points along the groove, the time is measured and displayed in the table on the monitor.
Once the ball has reached the bottom, the values in the table are converted into two diagrams: the distance-time graph and the speed-time graph.
The speed-time curve clearly shows what you’d expect by watching the rolling motion: the ball speeds up as it rolls. rate. rate. incorrect. The result is: all bodies fall at the same different weight fall at different speeds must be each other. The assumption that bodies of a contradict they but logical, alternativesBoth seem body did alone because together they are heavier? heavier than the faster together drop they would lighter body slows down the heavier body? Or Would an average speed be reached because the together? How fast would they drop if they were tied would fall faster than the smaller and lighter body. Let‘s assume that the larger and heavier body together? tied once same material are dropped –once separately and what happens if different two bodies made of the Benedetti, amathematician who died in 1590: reflectedHe on the thought experiment of deduction. and experiments (which are still valid today) by means of thought Galileo formulated the equations of free fall Leaning Tower of Pisa, as is often said. Instead, ments on the law of falling bodies from the Galileo Galilei (1564-1642) did not do his experi Why, what,wherefore? 4 - Free fall Free more: out Find ran out of acontainer was the measure of time. clock to measure the time: the weight of water that measuring slowed-down free fall. used He awater experiments with the inclined plane, specifically by had the equations, he tested their accuracy in equations of the laws of falling bodies. Once he Galileo‘s reasoning led him to the mathematical
01.06.2013 TECHNOSEUM Inclined plane 1 3 Is there such a thing as perpetual A closer look motion? What you see here is a demonstration of Newton‘s Gently push the disks and watch them slowly move. law of inertia:
“Every body continues in a state of rest or uniform motion in a straight line unless acted upon by an external impressed force. An external force is any effort directed against the body that changes its state either from one of rest or from uniform moti- on in a straight line.“
By using air cushion technology in this experiment, we reduce friction so much that the disk’s motion
Newton's Law 2 comes very close to the Newtonian ideal of uniform motion without an external force, in this case wi- What‘s happening here? thout the action of a frictional force.
The disks glide on an “air cushion“ over the surface, hardly seeming to slow down at all. They hit the edge, bounce and continue moving at a constant speed until they run into another edge or another disk. Eventually they come to a halt, because al- though friction has been minimised there are still small braking forces acting on them. view. also the basis for the mechanization of the world fundamental insight of modern natural science and nition of the universal validity of these laws was the laws of mechanics that apply on the Earth. Recog The celestial bodies were thus subject to the same Sun. the Moon around the Earth and of the planets around to the Earth‘s surface as well as the orbits of the and inertia determine both the free fall of astone gravity. And he was able to prove that gravitation under the influence of external forces such as inertia, but he also described the motion of bodies In this work, Newton not only formulated his law of advent of Einstein‘s of Theory Relativity. valid until the beginning of the 20th century and the 1687. It established classical mechanics. It remained in Philosophy) Natural of Principles (Mathematical mathematica“ naturalis principia “Philosophiae work Isaac Newton (1643 –1727) published his greatest Why, what,wherefore? 4 -
01.06.2013 TECHNOSEUM Newton's Law 1 2 How can I tell the time by the What's happening here? position of the sun? The light falls onto a scale with two hour markings: 2 10 Turn the small hole in the middle ring to the first one for the morning and one for the afternoon. letter of the current month on the scale. To be able to tell the time, you need to know whether it is morning or afternoon.
J F M A M J
D N O S A
Ring Sundial J 3 A closer look
Hold the small ring and let the large ring hang ver- The height of the sun above the horizon depends on the tically. Point it at the artificial sun in the upper right time of day. This can be used to tell the time. But the corner so that a beam of light passes through the sun is as high in the sky at 10 in the morning as it is at 2 small hole onto the inside of the ring. in the afternoon, because its motion is symmetric about its highest point at 12 noon. When reading off the time from this instrument, you have to know whether it is morning or afternoon.
But the sun’s height above the horizon also depends on the season: in winter it travels on a lower path than in the summer. This is why the height of the small hole must be set to the right month using the rotating ring.
The height of the sun also depends on the geographic la- titude. In Mannheim, for example, the sun is much lower in the sky than at the Equator. Ring sundials have to be designed for a specific latitude. Mannheim, for examp- le, is located between the 49th and the 50th degree of 2 10 latitude.
J F M A M J
D N O S A J Germany in 1893. European Time CET (CET). was introduced in standard times in countries, or even Central place had own its time, and there were no towers. Before the railways were built, every Sextants were used to set clocks in clock the help of solar altitude tables. could be used to find the exact local time with height of the sun above the horizon, and Solar sextants were used to measure the time. the of determination accurate was used well into the 19th century for sundial, to tell the time by the sun‘s altitude, the 19th century. The principle behind the ring They were commonly used from the 15th to Ring sundials are astronomical instruments. Why, what,wherefore? 4 1987/0860) early 19th EVZ: century (TECHNOSEUM, Brandegger, Ellwangen, A. J. sextant, Solar schichte) und TechnikgeKassel, Museum für Astronomie Ring sundial, around 1760 (Staatliche Museen -
01.06.2013 TECHNOSEUM Ring Sundial 1 What decides how fast a pendulum swings?
The weight? The width of the swing? The length? Try all three options: • Let the different weights swing. • Select different widths of swing. • Change the length of the pendulum by moving the cross bar. Compare the time it takes to complete a full swing Pendulum using the stopwatch. What do you find? 2 3 What's happening here? A closer look
The time it takes for the pendulum to complete a full swing The physical observations correspond closely to an ideal pen- from one side to the other and back is called the period. dulum: the so-called mathematical pendulum. In the mathe- It depends on the length of the pendulum. The longer the matical pendulum, the entire swinging mass is concentrated pendulum, the longer its period. in the suspended weight: the weight of the rope and the size of the suspended weight are neglected. Find the length at which the pendulum takes exactly one second to do half a swing, that is, from one pass through If a pendulum like the one in our experiment comes close to the middle to the next. this ideal, its period at amplitudes (widths) of less than about Count a number of passes every time you adjust the length 30° depends only on its length: the longer the pendulum, and compare your count to the seconds display on the stop- the greater its period. watch. If a clock runs fast (gains), you need to move the pendulum You can use the tower clock movement next to you for help: weight down: the pendulum is thus longer, it swings more it ticks once every second. slowly, and so the clock also runs more slowly. If a clock is too slow (losing time), the solution is the opposi- The greater the number of swings that you count and te: move the pendulum weight up to shorten the pendulum compare (e.g. ten swings), the better you can check whether and make the clock run more quickly. you have found the right length. The seconds pendulum is 99.4 cm (39 inches), approx. 1 m long. times over.times surpassed the accuracy of pendulum clocks many quartz clocks, and then in the 1950's atomic clocks, a second per day. It was not until the 1940's that 20th century, to less than afew thousandths of Their accuracy continued to improve well into the observations. astronomical Pendulum clocks were vital control devices for rapidly improved to within 1second per day. Christiaan Huygens (1629 – 1695) that accuracy in 1657 by the Dutch mathematician and physicist introduction of the pendulum as aspeed regulator about 15 minutes per day. It was not until the Early mechanical clocks were were accurate to units. countable mechanical division of time into ever smaller principle that is still in use today: the regular The mechanical clock introduced anew technical world in the modern age. “world as aclock“ in the mechanistic view of the “celestial machine“, it shaped the idea of the of civilization. an earthly As image of the great – an innovation of great importance in the history pendulum, invented a was without still but pement Around 1300, the mechanical clock, with an esca Why, what,wherefore? 4 - lum clock, patented 1657. patented clock, lum pendu his of Illustration 1658. Horologium. Huygens: Christiaan Technikgeschichte)und (Staatliche Kassel, Museum für Museen Astronomie and foliot, still nopendulum, 15th/16th century Wrought-iron tower mechanical clock with escapement - 1983/0046-92) EVZ: (TECHNOSEUM, Stübner, Glashütte, 1928 Paulberg Observatory, clock from the Heidel pendulum Precision -
01.06.2013 TECHNOSEUM Pendulum
Station text
Study of the movement of celestial objects Astronomy at the Mannheim Observatory
Measuring and mathematics are the basis of astronomy, the science of the heavens. Around 1600, Johannes Kepler was able to mathematically formulate his laws of planetary motion about the Sun, on the basis of accurate astronomical observations.
With the invention of the telescope by Kepler, Galileo, and Newton, the building of observatories boomed. They were used for the accurate observation of phenomena and events in space as well as for astronomical timekeeping.
Modeled on the great observatories in Paris, Copenhagen, and Petersburg, an observatory was also founded in Mannheim in 1774 with the elector's support.
Its first director, Christian Mayer, had an excellent reputation among experts due to his observations of fixed stars and his discovery of more than 100 double stars.
1 3 How can I find a star? A closer look
1. Select one of the dots marked with a drawing The position of a star is determined by two angles: the pin on the star map – a star. horizontal angle (azimuth) tells us how far left or right from 2. Turn the brass ruler until it lines up with your south the star is located; the vertical angle (altitude) tells us how high it is above the horizon. chosen dot and read off the degree-value of the dot from the ruler (0 to 75°). These two angles correspond to the rotation of the brass 3. Adjust the telescope to this degree-value on the ruler and the tilt of the telescope on the “star seeker“. The (+)- scale by tilting it up and down. Don't turn starry sky and star chart are thus related in such a way that the brass ruler. the stars and their images on the chart can be uniquely 4. Look through the eyepiece. If everything is linked. We just need to make sure that the plane of the start chart is parallel to the plane of the Equator, that is, tilted Star Seeker Star correct, you now see a “star“ (golden ball). according to the latitude of the place where it’s being used.
Finding the positions of stars actually works in both direc- tions. If, as in our experiment, a star on the chart is chosen, it can be found in the sky. Alternatively, if the instrument is aligned to a star in the sky, the star can be identified on the chart.
Unlike the reproduction here, the star chart in the original star seeker (in the display case opposite) can be turned. When observing the stars, the daily apparent rotation of the starry sky around the Earth must be taken into considerati- on; this is actually the rotation of the Earth. The horizontal angle constantly changes due to this rotation. The star chart is always turned to the exact time to compensate for the Earth‘s rotation.
Since here in the exhibition the positions of the “stars“ do not change during the day, a simplified replica with fixed star chart works fine. 2 What's happening here?
By turning and tilting the telescope, a unique correspondence is produced between the stars in the sky and their image on the chart. identify them on charts. on them identify amateurs the means to findstars in the heavens or With his “star seeker”, he also gave educated throughout Europe. were sold to courts, observatories and academies that instruments optical and geodetic scientific, mous instrument maker from Augsburg. built He Georg Friedrich Brander (1713 –1783) was afa Why, what,wherefore? 4 -
01.06.2013 TECHNOSEUM Star Seeker 1 2 ... and is but full and fair What's happening here?
Move the lever counter-clockwise. Viewed from the Earth, the illuminated part of the As you do, look over the handle to the model Moon constantly changes its shape and size as the Moon. Moon moves.
See how the light from the Sun lamp lights up the When the Moon is directly in front of the Sun, none surface of the model Moon. of the parts that we can see are illuminated, and we cannot see the Moon.
When the Moon is directly opposite the Sun, all of the parts that we can see are illuminated.
Between these two positions, more or less of the Moon’s visible surface is illuminated.
Sun Moon 3 A closer look Earth
The Phases of the moon the of Phases The What you see on a small scale here can also be observed night after night in the sky.
During a cycle of about 29.5 days the Moon travels around the Earth and passes through different phases:
New moon, waxing moon, full moon, waning moon, new moon. 01.06.2013 TECHNOSEUM The Phases of the moon
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Reflections of reality The laws of geometrical optics
Light is the foundation of all visual perception. Next to mechanics, the experimental study of light was a fundamental field of research at the beginning of modern science and technology.
Artists and engineers of the Renaissance had already begun using the laws of geometrical optics to create pictures in perspective.
The study of the refraction of light, its reflection, and the splitting of white light into the colors of the spectrum led to the development of microscopes, reflecting telescopes and refracting telescopes.
These inventions revolutionized the possibilities of visual perception. The huge and the tiny were revealed to the human eye for the first time: the expanse and diversity of the starry sky as well as the elementary components of organic life: cells.
1 2 How does a telescope work? What's happening here?
Look through the telescope. Flip up the round frosted-glass disk, a projection screen, Try the different options: using the red lever. You should now see the object that you with the frosted-glass disk up or down were looking at on it. You should be able to see it easily without the magnifying glass. (use the red lever), with or without the magnifying glass (on the chains). Bring the image into focus by moving the two red handles. Again, you don‘t need the magnifying glass. Use the red handles on the left and right sides of the tube to bring the image into focus. Don’t worry that this image is flipped both top to bottom and left to right. What setting gives you the sharpest enlarged image? Now look at the image through the magnifying glass han- ging from the two chains. You should now see it enlarged.
Flip the disk down by turning the handle. Through the mag- nifying glass you can now see the same image at the same 3 magnification, but much more clearly. A closer look Objective lens Optical axis Light path Keplerian Telescope Keplerian Inside the tube is a convex lens, the objective lens, with a Magnifying glass (eyepiece lens) focal length of 500 mm. The other small convex lens, the eyepiece lens in front of the projection screen, has a focal length of 50 mm and acts like a magnifying glass.
The magnification achieved by these lens combinations is produced as follows: the focal length of the objective lens is divided by that of the eyepiece lens. In this case, we get a Image plane 10-fold magnification. Position of the groundglass disk This magnification does not depend on whether the fros- Keplerian Telescope ted-glass disk is up or down. The disk is only there to show how a telescope works. It demonstrates that at the focal plane of the objective lens where the rays of light cross, an image is produced – in mid-air.
This image can be made visible with the frosted-glass disk. However, you can also see the image directly through the magnifying eyepiece lens, as you would in a telescope, without holding the ground-glass disk in the light path. This produces a brighter and more brilliant image. rectness of the heliocentric the of view. world rectness previous world view and were evidence of the cor similar to the Moon –all discoveries that shook the moons orbit Jupiter, and that Venus had phases there were mountains like those on Earth, that four consisted of amultitude of stars, that on the Moon Pointing it to the sky, he saw that the Milky Way convex objective lens and aconcave eyepiece lens. Galilei built asmall refracting telescope with a The Italian mathematician and physicist Galileo experiment station shows how it works. Keplerian telescope. It’s arefracting telescope. This pe apparatus with convex two lenses known as the Johannes Kepler (1571 –1630) designed atelesco view. heliocentric (Sun-centred) planets revolve around the Sun. This was called the the Sun that is at the center of the Universe. All the he revived an earlier idea: it’s not the Earth, but Copernicus. At the beginning of the 16th century, it became possible to test the theory of Nicolaus spectacle-maker Hans Lippershey (around 1608), With the invention of the telescope by Dutch concave mirror. with aconvex lens and reflecting telescopes with a maintwo of types telescope: refracting telescopes remote objects, or even stars and planets. There are A telescope is an optical instrument used to observe Why, what,wherefore? 4 - - Prisms and Lenses and Prisms more: out Find rehabilitated, by Pope John Paul II. the heliocentric theory. Only in 1992 was Galileo tion of the Scriptures, it was impossible to suppress withdraw his claims due to their blatant contradic Although the Catholic Church forced Galileo to -
01.06.2013 TECHNOSEUM Keplerian Telescope 1 3 What do prisms and lenses do to A closer look rays of light? A beam of white light consists of many rays of light of diffe- rent colors (i.e. light of different wavelengths). Place the prism into the beam of light. Move it back and forth, and turn it. When a light beam strikes a prism, three things happen: Try the same thing with the lenses. 1. Part of the beam is reflected by the glass/air surfaces as Which lens focuses the light, and which one it enters and leaves the prism. spreads the light out? Now line up the lenses and 2. The beam is refracted by both surfaces and bent to prism one behind the other in the beam of light. wards the thicker end of the prism. 3. In the process, it is split up into separate coloured beams. Ideally, a spectrum with the colors of the rainbow is produced.
You can think of a lens as being made of many segments of a prism. In concave (hollow) lenses, the arrangement of these segments makes rays diverge, in convex (crowned) 2 lenses the arrangement of the segments makes the light rays converge.
A spectrum of colors is also produced by lenses, causing
Prisms and Lenses and Prisms What's happening here? colored fringes, which spoil the images in optical instru- The prism bends the rays and produces a spot of ments. This lens error is known as chromatic aberration. light with colorful edges on the side wall.
The convex (crowned) lens (Fig. A) concentrates, or converges, the rays; the concave (hollow) lens (Fig. B) spreads them out, or diverges them. That’s why they are called converging lenses and diverging lenses.
A B the Universe. Universe. the world view of the Earth and Man as the center of the Moon –all discoveries that shook the previous orbit Jupiter, and that Venus had phases similar to mountains like those on Earth, that four moons a multitude of stars, that on the Moon there were Galileo discovered that the Milky Way consisted of instruments. new these discoveries with mical From 1609, Galileo made ground-breaking astrono lenses. several copes were also developed, using combinations of Around 1600, in the Netherlands, the first teles circulation. blood of mechanics the explaining thereby capillaries, through used amicroscope to observe the flow of blood tists and physicians. Leeuwenhoek, for example, an important research instrument for natural scien In the early 17th century, the microscope became aids. vision as Middle Ages spectacles have been commonly used used as magnifying glasses, and since the Late transparent were ancient times, In stones precious become visible, and distant appear objects closer. Lenses can be used to enlarge things: small details Why, what,wherefore? 4 - - - Keplerian telescope Play of colors Concentrating reflectors Find out more: science, technology and our daily lives. Today, optical instruments are an integral part of lenses made of different of types refracting glass. combining by chromatic corrected aberration, was In the 18th century, this lens error, known as to avoid the problem of color splitting by lenses. Newton invented the reflecting telescope in 1671
01.06.2013 TECHNOSEUM Prisms and Lenses 1 3 What do mirrors do to A closer look rays of light? Curved reflectors work in a similar way to lenses: Position the chain of mirrors at an angle to the ray they concentrate or disperse light. This is why they path. Create different shapes, either on your own are ideal for optical instruments. or using the templates. You can also use the flexible strips of mirrors. A reflector with a circular cross-section has no exact focal point, but only a focal region.
To focus light rays at exactly one point, the cross-section of the concave mirror must be shaped like a parabola. These mirrors are called parabolic reflectors. Curved reflectors 2 What's happening here?
The parallel rays are completely reflected by the mirrors. They are deflected in different directions depending upon how the mirror surfaces are positioned.
Concave (hollow) mirrors bring the rays together, convex (crowned) mirrors spread them out. Mixing colors Keplerian telescope Prisms and Lenses more: out Find a point source of light (reflectors in car headlamps). nae, and radio telescopes), or to focus the rays from have to be focused (in satellite dishes, radar anten Parabolic “mirrors“ are used whenever incident rays 42 min diameter will begin operation. 2018, an extremely large telescope with amirror 8 m, are used in modern large-scale telescopes. In That‘s why concave mirrors, with diameters up to much more difficult to make than large mirrors. Large lenses with good light-gathering power are solution. attractive an still is mirrors not suffer from chromatic aberration, the use of to build refracting telescopes (using lenses) that did Although it was possible by the mid 18th century to avoid the problem of color splitting by lenses. Newton invented the reflecting telescope in 1671 Why, what,wherefore? 4 -
01.06.2013 TECHNOSEUM Curved reflectors 1 3
What does the distorted image A closer look depict? At the next table you can try to draw your own Each of these distorted images ”circles“ around a anamorphic image. The directions are for a cylinder center point. Place the mirror cylinder into the middle with a diameter of 4.7 cm like the one here. of the distorted image. If you look at the cylinder, the picture is revealed. Anamorphic images are usually drawn using a grid like this one. Simply sketching the outlines while looking at the mirror cylinder is much harder.
Accurate anamorphic images are easy to create today on computers. Anamorphoses
2 What's happening here?
Anamorphoses (from the Greek: ana – back, morphe – shape) are distorted images that look normal when they are seen from a certain angle or transformed by curved mirrors or special lenses. 4 Why, what, wherefore?
In the 17th and 18th century, painters created very sophisticated and detailed anamorphic images on painted ceilings in churches and palaces.
Some of the first known anamorphic images were done by Leonardo da Vinci. He drew the distorted head of a child and an eye in a sketch dated 1485. The pictures only appear normal when viewed from a very oblique angle.
Anamorphic images are frequently used today for marking roads. Keep your eyes open the next time you walk through town and no longer see the images from the driver‘s (or passenger's) perspec- Anamorphoses tive. You should be able to see the distortion of arrows, words or cycle-lane symbols clearly.
Giovanni Battista Tiepolo: Santa Maria della Visitazione, ceiling fresco, Venice 1754
Anamorphic images around us. Look at the figures on the left at an angle from the bottom: the perspective of a road user. The distorted markings are shortened and their meaning becomes clear. 01.06.2013 TECHNOSEUM 01.06.2013 1 3 How a “peep hole” can help in A closer look perspective drawing! To draw a three-dimensional object in perspective, Position the object that you want to draw and take the artist imagines the drawing surface to be a seat. Choose a pen and look through one of the between them and the object. They find the places two holes. Draw the outline of the object directly on the drawing surface where the lines of sight onto the glass pane. between their eye and the various parts of the object pass through the drawing surface.
Depending on the shape of the object, constructing these points can be easy or difficult. In contrast, the glass pane drawing method allows the job to be done quite simply.
Dürer's Perspective 2 What's happening here?
You will see that the drawing on the glass pane is an accurate drawing of the object.
Without this device it would be much more difficult to produce a correct drawing in perspective – try it out yourself. enough for practical purposes. accurately “mechanice” solved (mechanically) be could problems geometric mathematical and which methods and instruments were developed with world during this period, anumber of different In keeping with the mechanized conception of the paper. then be printed by transferring them onto wet glass pane. The drawings on the glass panes could In one of his images aseated man is portrayed on a geometrically. scene the reconstruct exactly having to without perspective, in different motifs could be used to help produce drawings of Dürer described various devices and methods that Measurement with Compass and Ruler, Albrecht earlyAs as 1525, in his Course in of the Art such as the ones here were widely used. invention photography, of constructions auxiliary represent landscapes, objects, and people. Until the se and aknowledge of perspective so that they can spatial sen need draftsmen and Commercial artists Why, what,wherefore? 4 - Compass and Ruler, 1525 Albrecht Dürer: of ACourse Measurement in with the Art Drawing the glass with pane method. aportrait
01.06.2013 TECHNOSEUM Dürer's Perspective 1 2 How many mirror images do What's happening here? you see? You see an endless sequence of mirrors and spaces, Look through one of the pairs of holes in the first like a corridor that appears to grow darker in the mirror and count the reflections! distance. What happens when you turn or tilt the hanging mirror slightly? By turning or tilting the mirror, you see a corridor that curves to the side, or upward or downward.
mirror first, some are reflected in both mirrors one, twice, three times or more before they reach your Endless Mirrors 3 eye. It gives the appearance of one room after ano- ther without end.
A closer look Because the light rays are absorbed by the mirror‘s glass layer, the image appears darker and darker the The rays of light from the objects you see can reach more often the light has been reflected. your eye by many different routes. Some travel to your eye directly. Some are reflected in the opposite
Line of sight 1. Image Line of sight 2. Image 3. Image 2. Image 3. Image
etc.
etc. Würzburg Residence.Würzburg use of this effect. Anearby example is in the Baroque palaces was the Hall of Mirrors that made One of the more lavish architectural features in Why, what,wherefore? 4
01.06.2013 TECHNOSEUM Endless Mirrors 1 3 What colors are made when the A closer look disks overlap? What we perceive as white light is a mixture of Overlap two or three of the transparent disks and different colored rays of light. look through them! What color do you see? The disks act as filters: they only allow certain colors to pass through them. They also reduce brightness. Because the disks remove light, this type of color mixing is known as “subtractive” colour mixing.
Other colors are produced by “additive“ mixing: if three spotlights in the primary colors “red“-“green“- “blue“ or ”cyan“-“magenta“-“yellow“ are aligned so that their beams overlap, white light is produced. Mixing Colors
2 What‘s happening here?
Each disk is a filter that only allows some of the white sunlight through: the primary colors ”yellow“, ”magenta“ (pink) or “cyan“ (turquoise).
If two disks overlap, the effect is that you see the primary colors „blue“ (blue-violet), ”green“ (yellow-green) or ”red“ (yellow-red).
If you overlap all three disks, they filter virtually all of the light so that almost nothing remains, and they appear black. Prisms and Lenses and Prisms more: out Find television. and film and 20th centuries for color printing, photography, These discoveries became significant in the 19th of colors. theory modern scientific foundationthe for first the with the wave-like nature of light in 1670 and laid the separation of light into aspectrum by aprism during the Middle Ages. Isaac Newton explained This phenomenon was studied by Arab scientists often seen in nature in rainbows. White light split into acolorful spectrum is most Why, what,wherefore? 4
01.06.2013 TECHNOSEUM Mixing Colors
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Preindustrial trades Breeding ground of industrialization
As cities and trade flourished, specialized trades evolved from the 12th century onward for making more complex and elaborate items than those made by blacksmiths or carpenters.
Watchmakers and mechanics developed the woodturning lathe into a lathe for making round components out of solid metal.
Coin makers minted coins from sheet metal. The coins needed to be uniform and forgery-proof. The makers developed rolling mills for the sheet metal as well as presses to punch out and stamp the coins.
The instruments of the metalworking industry originated from these small, early machine tools: heavy rolling mills, large presses, and above all metal-removing machines for turning, drilling, planing, milling and polishing.
1 3 How do you make wooden A closer look components with a circular cross-section? Both devices are manual lathes driven by a treadle. The workpiece pivots on two iron points, so that it can Ask a TECHNOscout for help! only turn about its longitudinal axis. First put on your safety glasses! Hold the tool with both hands and place it on the It turns towards the tool when the treadle is pressed tool rest. Press down on the treadle and guide the down, and backwards when the spring pulls the drive cord and the treadle back up again. lathe tool against the turning wood as you press down with your foot. When the cutting edge touches the workpiece at the Pole Lathe correct angle, it cuts off shavings as the workpiece turns forward, producing a circular cross section.
When the workpiece is turning backwards, the tool has to be pulled back a little so as not to damage the blade edge.
The turner holds and guides the tool; the tool rest Ask a TECHNOscout! supports the tool without limiting its mobility.
With practice, the turner can make a variety of handcraf- ted shapes with flowing contours, as long as they do not 2 need to be particularly accurate. Turning technical parts with straight contours is difficult, especially if they are made of hard, tough materials such as What's happening here? iron, and if accuracy is a high priority.
The workpiece is turned manually. The tool cuts off shavings and produces a circular cross-section because the workpiece is turning
The woodturner can make pieces with all sorts of profiles, because they are free to move the tool so easily.
However, the end product completely depends on the strength and skill of the woodturner. with enough precision. precision. enough with manufacture almost all of types machine parts in industrialization, by making it possible to The lathe played afundamentally important role shapes. handcrafted curved produce straight technical contours, but it was unable to This kind of lathe made it very easy to make guiding the cutting tool in astraight line. a positive-action mechanism for holding and The hand was replaced by the cross slide, and hand turning could not meet the demand. more and more iron machine were parts needed, At the of start the industrial age, around 1800, shapes, even for technical parts. usual method for making rotationally symmetrical Up until the 18th century, turning by hand was the Why, what,wherefore? 4
01.06.2013 TECHNOSEUM Pole Lathe 1 3 How obedient are your hands? A closer look
To attach a paper template to the metal plate, It’s intrinsically difficult to create a curved contour flip the pen up, press the metal plate down and slide by controlling two straight movements using two the template into the holder. hand cranks. Using both cranks simultaneously, copy the pattern onto the template. Early in the 19th century, the two-hand tester was Try to guide the pen within the 8-shaped groove. used to test not only the ability to use both hands independently and in a smooth and coordinated way, but also to test the steady hand of the test subject.
Two-hand Tester 2 What's happening here?
You are moving the pen along x- and y-axes.
It is difficult to stay in the groove because both hands are making different movements, and this requires coordination.
How would you get on if you were short of time? contours. the precision work required for pieces with curved turner’s technical skill was also indispensable for machine with parts straight contours. However, the The cross slide was useful for manufacturing lathes. manuallyon: operated lathes evolved into machine This was adecisive step on the path to mechanizati straight movements, is demonstrated by this exhibit. The principle of the cross slide, which only allowed Why, what,wherefore? 4 -
01.06.2013 TECHNOSEUM Two-hand Tester
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Power and Motion Mechanical principles for the world of technology
Scientists, mathematicians, and engineers studied the laws and principles of mechanics and applied them to technical questions: problems of structural design and machine dynamics.
They examined theoretical and experimental relationships between force and motion with rigid bodies and flowing liquids, inertia and acceleration of rotating masses, elasticity, bending and strength of beams, and the shape and load-bearing capacity of arches.
They discovered the mechanical principles of conservation of momentum and energy, and used them to explain the processes of pressure and impact.
The newly developed differential calculus was an effective mathematical tool. The fact that one could now model even complex mechanical systems and predict their behavior was a great contribution towards the mechanization of the world view and the leading role of mathematics.
1 3 Flying with hot air? A closer look
If the balloon is at the base station, press the red The surrounding air applies a lifting force to the button to turn on the heater. balloon. This buoyancy force is as great as the Hold the red button down: the air in the balloon is weight of the surrounding air that the balloon, now being heated. You can read the temperature because of its volume, has displaced. on the upper display panel. The right-hand panel shows the temperature to The air in the balloon expands as it heats up. The which the air should be heated. balloon isn't airtight, so the excess air no longer Once this temperature has been reached, press the fits in the balloon and escapes. This continuously green button to release the balloon. reduces the weight of the air in the balloon, and therefore also the overall weight of the balloon and the air inside it.
Once the total weight is less than the constant
Hot Air Balloon buoyancy force provided by the surrounding air, the balloon starts to rise. This is like a light piece of cork rising to the top in heavier water. 2 What's happening here?
The balloon rises when you press the green button.
The greater the difference in temperature between the air inside the balloon and the surrounding air (see lower display panel), the faster and higher the balloon rises.
As the air in the balloon gradually cools down to the ambient air temperature, the balloon descends back to the base station. helium or hydrogen. or helium temperature air ambient lighter already is than air: filled with hot air, but with a gas that even at the engines and could be steered. They were no longer The airships were propelled by internal combustion Mannheim-Rheinau. in airships Schütte-Lanz called te together with Karl Lanz started building the so- airship LZ1 at Lake Constance. In 1909, Johann Schüt years later. In 1900, Count Zeppelin launched the first The great age of airships started agood hundred Traitteur.from duced the lightning rod to the Kurpfalz, and others in 1784: by two Hemmer, who had recently intro They were unmanned. 10 launches were documented of paper, with aburner hanging below the balloon. (Electoral Palatinate) started making hot-air balloons Impressed by these attempts, people in the Kurpfalz to fly in such balloons for the first time. aircraft. In the same year, human pilots actually dared cular fashion that man can actually fly lighter- than-air ched an unmanned hot air balloon, proving in specta in 1783: on June 5th the Montgolfier brothers laun One of humanity’s cherished dreams became reality Why, what,wherefore? 4 - - - - and arange of up to 10,000 km. balloonsport for heavy loads of up to 160 tonnes ted around 2000. The project was to build trans The much hoped-for Cargolifter project was abor equipment, or for advertising and pleasure flights. recording and Earth’sthe atmosphere, sporting as the airplane, balloons continued to be used to study While(USA). the No. 1mode of air travel became when 129 the LZ exploded on landing in Lakehurst The airship industry came to an abrupt end in 1937 book from 1796book Contemporary of various hot depiction air balloons in acalendar - -
01.06.2013 TECHNOSEUM Hot Air Balloon
Giant gear ratio
Why can the first gearwheel turn if the last gearwheel is fixed? Where does the motion “disappear” to? Can motion disappear?
What's happening here? The topmost gearwheel turns approximately once every 5 seconds. Every gear pairing reduces the number of revolutions by 10 and increases the time for each rotation 10-fold. With 18 gearwheels the last gearwheel would take 15 billion years to turn around just once!
A closer look
The overall gear ratio of18 gears, in other words 17 transmission steps, is
17 (0.1 x 0.1 x 0.1 x ... x 0. x 0.1 x 0.1) = (0.1)
So the rotation time of the last gear is
17 9 5 x 10 seconds: a little more than 15 x 10 years, so a good 15 billion years.
This time is larger than any time that we can understand. The Earth is about 5 billion years old. The Universe about 15 billion years old.
The overall gear ratio here is much too large to be of practical use. The force from the motor has been increased so much that the mechanism will destroy itself at some point, because the last gearwheel is fixed.
But this takes a very long time: it won’t happen until the play in the axle bearings and between the gears’ tooth flanks, the so-called “lost motion”, has been all taken up.
Why, what, wherefore? Ridiculously large gear ratios can be found in the machine journals of engineers from the Renaissance period and the 17th century.
However these fantasies were critically tested and rejected at the start of the 18th century: the time and effort needed to move heavy loads was much too expensive, and the complicated gear technology was often much too costly and sluggish. This is when a “rational", use-oriented machine technology began to develop.
When manpower proved too weak as a driving force and low gear ratios took too much time, it made sense to look for more powerful drive systems. Engineers started to recognize the potential of air and steam and the hydraulic power of fluids as innovative drive options.
Key to the image: Salomon de Caus, court engineer and master builder from the Kurpfalz [Electorate Palatinate], comments on this image that the man at the top at the hand crank would have to turn the crank for 298 and a half days, 10,000 times per day, for the wheel at the bottom to make a single rotation! (Salomon de Caus: Von gewaltsamen Bewegungen. Beschreibung etlicher, so wohl nützlichen als lustigen Machiner. [Movements by Force. Description of Numerous Useful Yet Funny Machines.] 1615)
1 3 An arch as inverted chain? A closer look
Naturally, only the shape of the chain is inverted. The individual links of the hanging chain can only absorb You can see this by stacking the marked building or transmit tension forces. The typical catenary shape of a blocks on top of one another so that they form hanging chain arises because of this. an arch that symmetrically mirrors the chain that is hanging down. Catenary Arch 2 If you mirror the catenary curve upwards and use construc- tion elements that can absorb and transmit compression forces, then the force relationships can be inverted. What's happening here? Because the chain links are joined flexibly, only tension forces Arrange the building blocks on the larger part of the (and not bending or lateral forces) can be transmitted along the hanging chain. The same is true for an arch in the form table so they form an arch that lies flat on the table, of a catenary curve, except that the forces involved are as shown in the diagram. compressive, not tensile.
Start with block A1 about a hand’s width from the side of the frame. Keep adding blocks until the arch is complete.
Make sure the arch is lying exactly as it should. The blocks must be touching completely, without any gaps. The bottom edges of A1 and E1 must lie exac- tly on the dividing line between the two parts of the table.
Carefully raise the portion of the table with the arch until it is vertical. If the arch stands, fold the table gently back down to its original position. If you have worked carefully, the arch will be stable! Corbels Leonardo‘s Bridge arch Catenary Find out more: mical dome that saves on materials. axis, you get the ideal form for astable and econo If you rotate the catenary arch on vertical its central of balls in balance, even if it is unstable. balls. The compression forces keep the arch made stones of acatenary arch with completely smooth a “thought experiment”, he replaced the v-shaped cian and engineer Giovanni Poleni (1685 –1761): in mathemati illustrated was Italian the by moments pression forces and no transverse forces or bending The fact that this form of arch involves only com optimal arch is the inverted catenary arch. of forces and load-bearing capacity. The result: the distribution form, their words the other in structures, studying the science of arches and the theory of begin Poleni Giovanni and Stirling James Gregory, cians and engineers such as Philippe de la Hire, David until 17th the Not mathemati physicists, did century design. knowledge gained by experience and the rules of was possible because the master builders used buttress support structures. Building these edifices provide particularly clever examples of arch and building arches and vaults. Gothic cathedrals Ever since ancient times, people have been Why, what,wherefore? 4 - - - - Tempio Vaticano. 1748 istoricheGiovanni della Memorie gran Poleni: cupola del
01.06.2013 TECHNOSEUM Catenary Arch Compression 1 Tensile 3 Flat or on edge: In which position A closer look is a board stiffer? Compression When you stand on it, the top of each board is Tensile Try out both boards. subject to a compression force (squashing) and the Stand on one, then on the other. bottom of each board is subject to a tensile force But please don’t rock back and forth – (stretching). you might fall off! It’s a good idea to hold on to the railing. The greater the distance between the compressive forces and the tensile forces in the board, the stronger the board is because these internal forces work through longer levers against the external load.
This is why the board that’s on edge bends less than the one that lies flat. Bending beam
Compression Tensile 2 Compression What's happening here? Tensile
Both boards have the same shape, but their load-bearing capacities are different.
The flat board clearly bends when you stand in the middle.
With the upright board it’s hard to see that it's bending at all. It is much stiffer and stronger.
The load-bearing capacity of a board depends on the direction in which it is loaded. Compression Tensile 4 Compression Why, what, wherefore? Tensile
From experience master builders had long known that beams placed on edge are stronger. But until early modern times they knew little about the pat- tern of forces inside the beam and how to calculate the load-bearing capacity from that.
As technology evolved in the 17th and 18th Galileo Galilei: Discorsi e dimostrazioni matematiche. 1638 [Discussions and centuries, the laws of beam bending were studied mathematical demonstrations] intensively: by mathematicians and physicists like Galileo Galilei, Edme Mariotte, Robert Hooke, Jakob Bernoulli and Leonhard Euler and by engineers like Jakob Leupod. They investigated how to calculate
the load-bearing capacity and the bending under Bending beam load of beams made of various materials.
Charles Augustin Coulomb (1736 – 1806) and Louis Marie Henri Navier (1785 – 1836), from the French school of scientific technology, ultimately developed the formulas of beam theory in the 18th and early 19th century that are still used today.
The knowledge that upright building components are stronger than those lying flat is often applied in Jakob Leupold: Theatrum Pontificiale, Oder Schau-Platz der Brücken und machines and buildings: look at the many I-beams Brücken-Baues [Or the Stage of Bridges in our museum building, for example. and Bridge Construction]. 1726
Steel beams: I-beam, placed upright, reinforced in the zones of greatest tensile
and compression forces. TECHNOSEUM 01.06.2013 1 3 A stable arch made only of blocks A closer look without glue? All arches are started left and right on fixed abut- Build the arch between the abutments with the ments with the so-called springing stones and end help of the support pieces. When the arch is finis- at the top in the middle with the keystone. Today hed, the support pieces need to be pulled away they are built using a support structure called the simultaneously and quickly. centering. The centering is removed once the arch Now you can step onto the arch – step carefully in becomes stable after the last stone has been put in the middle. place.
The joints between the stones have to point towards the midpoint of the arch for the effective Arch bridge lateral transmission of force to the abutments. You can see this easily in masonry bridge arches and arched roofs.
2 What's happening here?
The pressure on the stones in the middle of the arch is transmitted through the other stones out to the sides and into the fixed abutments. In this way the arch stabilizes itself. Corbels Leonardo Bridge arch Catenary Find out more: form replaced traditional rules of thumb. capacity. The scientific basis of this architectural form, the distribution of forces, and load-bearing its studied this classic brick construction: arched its From the 17th century, physicists and engineers buildings. dern aqueducts from the Roman Age as well as in mo in or bridges tunnels, and archways,ancient vaults, ennium. This construction principle can be found in have been known since the first pre-Christian mill Brick arches with the keystone and side abutments Why, what,wherefore? 4 - - Bernard Forest de Bélidor: La Science des Ingenieurs. 1813 Science Ingenieurs. des Bélidor:Bernard La de Forest Marie Riche de Prony: Neue Architektura Prony: RicheMarie Neue de Hydraulika. 1795
01.06.2013 TECHNOSEUM Arch bridge 1 2 A long bridge made only of What's happening here? wooden sticks? Start at one end and build the bridge piece by The pictures show you how to do it. piece. Make sure that the sticks already in place do You will see: two hands are enough. not slip. The span of the bridge increases and you can eventually bridge the entire gap.
3 Leonardo's Bridge Leonardo's A closer look
The sticks are held together by their own weight and by friction, which is why the surface of the sticks mustn't be too smooth.
The bridge stays up even under a load, until a stick breaks – but don’t chance it! Corbels Vaulted arches arches Catenary Find out more: boxes. removal examples are collapsible boxes and cardboard in architecture and technology. Some everyday This construction principle still plays amajor role which can be assembled quickly. are short compared to the span of the bridge and This is why Leonardo‘s Bridge is made of pieces that can be pursued and beaten into retreat.” enemy the which with bridges transportable and “I have the instructions on how to construct light thinking was to use it for military purposes: that was easy to transport. The goal of his construction of an ultra-light arch-shaped bridge Around 1480 Leonardo da Vinci planned the Why, what,wherefore? 4 Leonardo da Vinci: CodexLeonardo da Atlantico Vinci:
01.06.2013 TECHNOSEUM Leonardo's Bridge 1 3 Can the gap be bridged with the A closer look building blocks? In order to keep the stones from falling, the weighted porti- on over the gap must have a big enough counterweight over Stack the building blocks on top of each other to the land. Let’s look at the method described above where build a bridge that is supported on both sides but the stones are slid gradually over the gap. has no other supports. Tip: Think about using some of the building blocks The top stone can be slid forward by half its length, the as counterweights. second topmost stone by 1/4. 4/4 of the effective weight of the top two stones is located over the gap and 4/4 over the land—the system is balanced.
The third stone can only be shifted by 1/6 of its length. 9/6 of the weight of the top three stones is located over the void and 9/6 over the land. Corbel stones The fourth stone is shifted forward by 1/8 and thus has an overhang of 1/2 + 1/4 + 1/6 + 1/8 = 1/2 · (1 + 1/2 + 1/3 + 1/4)= 1/2 · (12 + 6 + 4 + 3)/12 = 25/24 in other words a little more than one stone.
As a general rule, the nth stone is shifted by 1/2. The entire 2 overhang is thus half the sum of the so-called harmonic series: 1/2 · (1 + 1/2 + 1/3 + 1/4 + ...)
What‘s happening here? Since the sum of this series has no final limiting value, the stones can be built as far over the gap as you want, as long The general idea is that the weight of the stones as you’ve got enough bricks to build the stack as high as you want. that overhang the gap must be balanced by a coun- terweight on the banks. Apart from the solution using the harmonic series, as A limited overhang can be achieved like this: stack indicated above, there are many other arrangements that the stones on both sides of the gap one on top of can be used to get an even bigger overhang on both the other and then slide the uppermost stone on sides – it's even possible to completely bridge the gap. both sides as far as possible over the gap, then the second uppermost stone (together with the top stone) and so on. With this number of stones, you can’t completely bridge the gap with this method. Now you need to use your imagination: find other ways to stack the stones that make sure that the stones over the gap are counterbalanced with enough weight on the banks. Leonardo's Bridge Vaulted arch Catenary Arch Find out more: load. hanging counterbalance to the long crane arm and its tion cranes. concrete Heavy blocks provide the This principle is applied today in large construc principle for achieving large overhangs. which is an application of the counterbalance girder named after him in the 19th century, Gerber (1832 –1912) developed the Gerber For building long-span iron bridges, Heinrich technique used in ancient buildings. technique. You can find this corbelled arch with layered offset stones is an ancient Building bridges, arched doorways or vaults Why, what,wherefore? 4 - Scotland, built 1882-1890 of Inventions. Book 1901) (The the on girders railroad in Gerber of over bridge Forth the Firth girder (The Book of Inventions. Book girder 1901) (The Demonstration of the counterbalnce technique using the Gerber beams to arches] 1983) From zum [Bridges. Bogen. Brücken.Heinrich: Vom Balken corbel arch(Bert in profile technique: old Thousand-year
01.06.2013 TECHNOSEUM Corbel stones 1 3 Let the planets roll! A closer look
Roll one ball along the rim of the funnel, the other The funnel illustrates the effect of gravity between diagonally away from the rim! a central body and the bodies that orbit around it Watch their trajectories and speeds. Trying letting (for example Earth/Moon or Sun/planets). several balls roll at the same time, clockwise and counter-clockwise! Its sloping sides become steeper and steeper towards the middle, so that the force of gravity resulting from the weight of the ball, which is directed towards the hole, becomes stronger the closer the ball is to the middle. The same applies to gravity: it gets stronger the closer the orbiting objects are to the central object.
Potential well The balls that initially started off with a circular trajectory, slow gradually due to rolling friction, and run along slightly elliptical paths, like the 2 planets do. Balls started at an angle, however, move rather like What's happening here? comets, with large changes in their distance from the center. Balls that start along the rim roll in a circular/spiral orbit that gets smaller and smaller until the balls disappear into the hole.
Balls started diagonally roll in an extremely elliptical orbit. They roll close to the center and are strongly deflected, swing far out again, and repeat this trajectory until they disappear into the hole. central body, greater gravitational force. the the through shape: its the shorter the distance from the planets and comets but also the gravitational pull It illustrates not only the speeds and orbits of realities. cosmic reproducing the exactly without system geometrical and physical properties of our solar mechanical analogy that represents certain The potential well, also called agravity well, is a Why, what,wherefore? 4
01.06.2013 TECHNOSEUM Potential well 1 3 Can water lean into the curve? A closer look
Turn the small hand crank and watch the surface of When the tank spins, it creates centrifugal force. the water between the two panes of glass. This force pushes the water towards the outside until an equal counter pressure has built up through the ever-higher columns of water in the outer zones.
The centrifugal force increases proportionally to the distance from the axis of rotation. When equilibri- um is reached, the surface is a rotated parabola (paraboloid). For every water particle there is a balance between the outwardly directed centrifugal force and the inwardly directed force resulting from the pressure gradient of the inwardly decreasing Water Parabola Water 2 water columns. What‘s happening here?
The water surface begins to curve inward. The faster you turn the crank, the higher the water rises at the sides.
If you turn the crank fast enough, there may be no water at all left in the middle. moving body. a “relative” motion with respect to the other executing only was which and space absolute, static executed a“true” circular motion with respect to ding on the effect of centrifugal forces, which body So for Newton it was possible to decide, depen between the water and the bucket is the same. loidal. In both cases, however, the relative motion keeps spinning and the surface remains parabo water the formed, then has paraboloid the after the water surface stays level. If you stop the bucket moving, started has water the before spinning, In the first moments after the bucket has been set rotated with respect to an absolute, static space. the bucket was an indication that the water actually For him, the fact that the water rose to the edge of role in the thinking of Isaac Newton (1643 –1727). This “Bucket Experiment” played avery important manufacturing. liquids of differing density in laboratories or or in ultra-fast rotating centrifuges for separating deliberately, for instance in spin dryers at home round acurve. We also use centrifugal force for instance in acar or on abicycle when travelling We often see or feel the effect of centrifugal force, Why, what,wherefore? 4 - - his theory of relativity. of theory his was not questioned until Albert Einstein introduced influenced the physical world view and their validity mechanics. For more than hundred two years they this postulate was the foundation for his laws of time,Together absolute of postulate the with space remains consistently level and motionless. absolute object, external relation to an without and Natural Philosophy” of 1687 that, due nature its had postulated in his “Mathematical Principles of This was very important for Newton because he
01.06.2013 TECHNOSEUM Water Parabola 1 2 Why do the rollers travel at What's happening here? different speeds even though Both rollers weigh the same because they are made of the they weigh the same? same components.
Place both rollers in the starting position. But these components are arranged differently: on one roller It doesn’t matter which side they are on. a lot of the mass is close to the axis, and on the other roller, Rollers Let them go at the same time. a lot of the mass is near the outer edge.
The roller with the mass located further out is more sluggish: it takes longer to start rolling and also has a lower speed at the lowest point in the track.
Nevertheless, both rollers reach the same height at the other side, though not at the same time. 3 A closer look
Both rollers start at the same point. Since they both weigh the same, they have the same potential energy. As they start rolling and speed up, this energy is converted into kinetic energy of straight-line motion and rotational motion.
The more sluggish roller with the mass located towards the outer edge has to use more energy than the other roller to get it turning, which is why there is less energy left over for the straight-line motion. The more sluggish roller rolls more slowly.
Since both bodies start at the same point, they reach the same point on the other, upward-sloping, side of the track despite different running times, because the energy of their motion is converted completely back into potential energy at the highest point.
energy and keep the saw blade moving by force. getting stuck, the heavy flywheel would release its this low motor power. If the saw were in danger of through thicker significantly couldwith saw beams weak circular 500-watt saw with aflywheel, he For example, if a do-it-yourselfer were to equip his fluctuations in load and the machine runs smoothly. is needed. In this way, flywheels even out sudden the engine’s kinetic energy and release it when it level F, have large and heavy flywheels.They store Many historic machines, like our steam engine on Why, what,wherefore? 4 Cylinder piston steam engine, Maschinenfabrik Esslingen, Level F) 1908 (TECHNOSEUM, masses as small as possible. rotation. In these cases, to we try keep the flywheel and precisely, or to rapidly change their direction of machines it can be important to stop them quickly don’t have large flywheel masses. Even with other must be able to stop quickly, which is why they But be careful! For safety reasons acircular saw
01.06.2013 TECHNOSEUM Rollers 1 3 Which ball wins? A closer look
The one with the shortest track? Or one of the others? All the balls have to overcome the same difference in height, which is why at the end they all move at the same speed, regardless of which track they are rolling on. Try it yourself. Put the balls into the starting position But it’s not the final speed that decides the running time, it's and press the lever. the average speed over the entire track.
The flatter the beginning of the tracks in our experiment, the worse the balls do in the race. For example, the ball on the straight track does in fact have the shortest path, but its
Racing Balls Racing startup acceleration and average speed are too slow.
The track with the fastest ball is the steepest at the top: the ball can accelerate the best out of the gate and pick up speed. It has the greatest average speed. Even though this track is the longest and actually slopes up towards the end, the ball on this track finishes first.
If we had made the track steeper at the top, the ball would not have finished any sooner. In fact it would have finished later: the greater distance now outweighs the advantage of its high speed.
The shape of track that gives the shortest journey time is cal- led the brachistochrone curve (Greek: fastest). In mathemati- cal terms this is a cycloid, in other words the curve traced out by a point on a rolling wheel (diagram see No. 4 “Why, 2 what, wherefore?”) What's happening here?
The fastest ball is the one nearest to you, on the track that droops down.
Would you have guessed that? It's not the shortest track that is fastest, but the longest! gineering. lie the historical roots of mechanical and civil en physics and to the vital role of mathematics. Therein great contribution to the mechanistic world view of and predict the behavior of complex systems was a thematics and simple laws of mechanics to calculate stics, dynamics or hydraulics. The ability to use ma mathematically, be it in celestial mechanics, stati during which mechanical problems were modelled The 17th and 18th centuries were the great age mal problems like the one above. developed from differential calculus to solve extre a few decades old. The calculus of variations was The differential calculus needed to do this was only Huygens –found the correct solution: the cycloid. Bernoulli as well as Leibniz, L’Hospital, Newton and period –Johann Bernoulli himself, his brother Jakob this of mathematicians distinguished most The one point to the other in the shortest time.” has been put inside and let go covers the path from a correspondingly curved thin tube, alittle ball that should be selected along which, if it is replaced by ber of curves that connect both points, that curve Bernoulli, “is as follows: among the endless num “The point of the exercise”, according to Johann lower point in the shortest time. weight, would move from the higher point to the find the curve along which a point mass, due to its not one directly above the other. The goal was to blem”. Imagine points two at different heights, but Basel, published an “invitation to solve anew pro In 1696, Johann Bernoulli, amathematician from Why, what,wherefore? 4 ------l’Usage des Instruments. 1784) Instruments. des l’Usage aux Amateurs la de Physique, sur Choix, le la Construction et L’Art shape is generatedcycloid (Nollet: ou Avis Expériences, des 18thAn ball-race centrury experiment. This how also the shows
01.06.2013 TECHNOSEUM Racing Balls 1 3 Why don't all the balls swing A closer look together? The product of the mass of a body and its velocity Pull one or more of the balls to the side and let is called momentum. When several bodies collide, them swing back against the other stationary balls. the sum of their linear momentums remains the same. However, this law allows several outcomes from the collision: for example, a fast sphere could set many smaller spheres into slower motion.
Because these spheres are very elastic, almost no
Click-Clack kinetic energy is lost when they collide. So here the law of conservation of energy also applies. That means that the sum of the products of the masses and the squares of their speeds must remain the same. However, this law also allows several out- comes from the collision.
However, since both laws always apply, the principle of linear momentum and the law of conservation of energy, there is only one solution that satifies both laws: after every collision, the moving masses and their speeds have to remain the same. This is why the same number of spheres always stay in motion at the same speed. 2 What's happening here?
However many balls hit one end of the row, the same number move away from the other end. The other balls do not move.
There are two important factors at work here to create this effect. First, all the balls weigh the same and second, almost no energy is lost during the impacts. effect on components. on effect calculate the size of the exchanges and the resulting tantly being exchanged. It is the engineer’s job to rear-end collision. Momentum and energy are cons when atram rumbles over the rails or if there is a hammer anail into the wall, when adoor slams, the blacksmith’s workshop, in snooker, when we world is full of desired and undesired impacts: in they also play an important role in technology. The Not only are the laws interesting scientifically, but calculation. and through thought, experiments discovered laws the kinetic energy as well as the law of impact. They studied the laws of conservation of momentum and Johann Bernoulli and Jean le Rond d’Alemberts and Daniel Leibniz, Wilhelm Gottfried Huygens, cians and physicists like René Descartes, Christiaan 17th the In 18th and century, eminent mathemati Why, what,wherefore? 4 - - l’Usage des Instruments. 1784) Instruments. des l’Usage Amateurs la de Physique, sur Choix, le la Construction et L’Art18th century (Nollet: ou Avis aux Expériences, des A click-clack Cradle) from (Newton‘s experiment the
01.06.2013 TECHNOSEUM Click-Clack 1 2 And round it goes… What's happening here?
Set the balls, rings and discs rolling on the The objects roll for a surprisingly long time. Once turntable. they have reached their full speed of rotation Watch how they move on the turntable. after being placed on the turntable, they are stable. Their positions change only very slowly: the rolling objects wander back and forth, move towards the center and back out again, they overtake and go around one another. Once their own rotational
Turntable energy is dissipated, they slide off the turntable.
3 A closer look
Here you see the highly complex interaction of inertial forces in rotating systems. The movements of the rolling objects illustrate the play of centrifugal forces, gyroscopic forces, and Coriolis forces.
Centrifugal force is a radial force directed outward. Gyros- copic forces, through the object’s own rotation, stabilize its position on the turntable. When the object’s own rotational speed decreases, the stabilizing gyroscopic effect becomes weaker.
Coriolis forces act tangentially. If the rolling object wanders towards the outer edge or towards the center, in other words into zones where the turntable surface is moving fas- ter or slower, then the Coriolis force acts tangentially in the direction of movement of the turntable surface, or against it.
Any change in inertial forces affects the position and speed of the rolling object. But the reverse is also true. Any change in the position and speed of the object influences the forces of inertia. And so on and so forth. 01.06.2013 TECHNOSEUM Turntable 1 3 Everything under control? A closer look
Turn the knob to set the pendulum spinning. Even systems in which only the simple laws of me- Watch how the bent arm and the pendulum rod chanics operate, such as this one, can behave cha- continue to swing by themselves and turn back otically. Such systems are highly sensitive to outside and forth. influences. Can you predict the movements? Do you recognize any rules? The slightest change in starting conditions or the smallest disturbance in the process can trigger sur- prising, unpredictable effects.
The chaotic behaviour of purely mechanical systems is sometimes desirable, for example when we play with dice, play roulette or play the lottery. Chaotic Pendulum
2 What‘s happening here?
The swinging movements are chaotic and unpredictable even though only the simple laws of mechanics are in operation here. order to increase their success rate. the casino tries to recognize probability patterns in period possible. Asystem player in the lottery or in models that provide forecasts over the longest A good example is the attempt to create weather chaos. the within structure and order often using computer simulations, to see if there is Modern physics focuses on these chaotic systems, events. of course the ting of abutterfly’s wings, can completely change the slightest influence, such as the proverbial bea scale that are so complex and sensitive that even On the other hand, there are systems on alarge position and movement of an object. scale, it is impossible to determine exactly both the king. On the one hand, at the microscopic quantum 20th century physics put an end to this way of thin happened. that had ything ever and to happen going that was everything particles, in principle you would be able to calculate just one moment the location and movement of all Earth. People believed that if you knew exactly for ding to fixed mathematical laws: in heaven and on accor happened chance.such thing as Everything In the mechanistic world of physics, there was no Why, what,wherefore? 4 - - - -
01.06.2013 TECHNOSEUM Chaotic Pendulum
Station text
Mechanization of brainwork Calculation with machines
The combination of mathematics and mechanics in the thinking of the 17th and 18th centuries fostered the development of calculating machines that could be used to do complex but routine mental jobs more simply and more accurately than people could: addition, subtraction, multiplication and division.
Until then people only had basic calculating tools available, such as the abacus, calculating tables or Napier’s bones.
Astronomers, scientists, clockmakers, surveyors, map and globe manufacturers, bankers, tradesmen, tax clerks and statisticians: they all had an ever-increasing influx of data to process according to fixed rules of calculation, and were therefore extremely interested in easy-to-operate, reliable calculators.
Schickard’s calculating machine in 1623, the pinwheel calculator by Leibniz and the first fully functional calculator by Philipp Matthäus Hahn in the 1770’s led the way to the first large-scale production in 1820.
Leibniz’s early idea of a binary calculating machine, put down on paper in 1679 but never made, coupled the mechanical thought processes of that time with the binary logic of modern data processing.
Thousand 500 Five hundred Thousand 100 Hundred 500 500 Five hundred Fifty 100 100 Hundred 500 20 Ten 10 Fifty 100 According to Adam Ries … Five 10 20 Ten 10 3 One 3 Choose a three-digit number and put it in the Five 10 623 468 623 - 468 first column: 3 One 3 for each one, ten and hundred, place a stone 623 468 1000 623 - 468
on the corresponding line. If you have five ad- 1000
jacent stones on a line, replace them with one 50 100 in the space above. Put another number in the 40 50 second column. 50 100
40 50 1 5
To add, shift both numbers’ stones into one 623+468 = 1091 1 5 column. Replace five ones with a five, two fives = 155 with a ten, five tens with a fifty etc. 623+468 = 1091 = 155 Read the result and check it by adding it up on 500 paper. 100 500
To subtract, place the minuend (the starting 100 20
number) in the first column and the subtra- Calculating Board 20 hend (the one you’re taking away) in the last, 3
so that you don’t forget it. So that there are 623 - 468 enough stones to subtract in each line of the 3 minuend, hundreds have to be reduced to 623 - 468 fifties, fifties to tens, tens to fives and fives to
ones. Only then can you subtractThousand as many sto- 500 nes in each line as the subtrahendFive hundred has there. 100 Hundred 500 Clear the subtrahend, readFifty the result and 100 20 check it. Ten 10 Five 10 3 One 3 623 468 623 - 468
1000
50 100 40 50
1 5 623+468 = 1091 = 155
500 100
20
3 623 - 468 results of calculation. of results “According to Adam Ries” when they give the pen and paper. In Germany, people often say sheet. Then people started doing calculations using calculate using acalculating board or a calculating Well into the 18th century it was customary to superior to Roman numerals. the new number system in Germany, since it was used Indian-Arabic numerals. This helped to spread With written calculation “with the quill pen” he cleverly shifting the counters to the correct lines. being laid out and the result was achieved by wards the top. Calculation started with the counters columns, the lines of which increased in value to- by shifting counters on alined board with two board or calculating table, called “on the lines”, Here Ries described calculating on the calculating measures. and masters as well as anyone that dealt with weights It was written for businessmen, craftsmen, mint the 17th century it had been published 60times. was first published in 1522, and by the middle of hen und Federn” [“Calculating on lines and quills”] His most renowned work “Rechnung auff der Lini “Electoral Saxon Court arithmeticus“ in Annaberg. mathematician master was and Mountains), (Ore *1492 Staffelstein (Franconia), †1559 Annaberg Adam Ries (often also called Adam Riese), Why, wherefore? what, - (Adam Ries: Rechnung Linien der 1525) vnnd Federn. (Adam Ries: auff are to used compute “on numbers the lines”. the rightOn side of the calculating board, calculating stones
01.06.2013 TECHNOSEUM Calculating Board
...
... 20 ...
Thousands/Five thousands
ender 400 Hundreds/Five hundrends
erter 468 + 623 Add tens 10 50 Tens/Fifties Ancient calculation tools – 3 5 Ones/Fives still in use today! 100 500 468 Choose a three-digit number
and assemble it on the middle bar: for every one, ten or hundred, a bead is mo- 468 + 623 Add hundreds ved from the left to make a row touching the bar. If there are five beads against the bar, -2 5
Abacus I move them back and move a bead from the 468 + 623 Add ones right against the bar to replace them.
In the row above, two beads from the right correspond to one from the left (that is the = 1091 Carry five hundreds
tens carry).
Write down a second number and add it! 468 + 623 Carry tens Start with the ones. If there aren’t any beads
on the left, take a five from the right and
... move the extra ones back to the left. = 1091 Carry thousands ... 20 ... If necessary carry 10: move two fives back to Thousands/Five thousands
ender the right400 and instead move a ten Hundreds/Five to the hundrends bar.
erter 468 + 623 Add tens 10 50 Tens/Fifties
3 5 Ones/Fives Keep going like this, adding tens, hundreds, etc. and making all the necessary carries, befo- 100 500 468 re you move to the next highest level. Finally, read off the result and check it by hand.
468 + 623 Add hundreds
-2 5
468 + 623 Add ones
= 1091 Carry five hundreds
468 + 623 Carry tens
= 1091 Carry thousands (fives and fifties) can be moved back and forth. column (ones and tens etc.) and asmall column horizontal rods, on which drilled beads in alarge A typical abacus consists of awooden frame with These abacuses are usually still made of wood. millennia. over East. The design and materials have hardly changed used today in large numbers in countries of the Far ofThe type abacus shown here is still made and started to do calculations on paper. Europe well into the 18th century. Then people Doing maths with the abacus was customary in “calculi” pebbles). (calculating culating board, which is comparable, used coins or usually made of wood or glass; sometimes the cal that is more than years 3000 old. It holds beads, The abacus is asimple mechanical calculation tool Why, wherefore? what, -
01.06.2013 TECHNOSEUM Abacus I 1000 1000000 100 100000 10 10000 1 1000
100 3 Tens: 2 468 + 623 A decimal system you can 10
1 touch 1000000
1000003 468 Set a number: for each one, ten and hundred, 10000 slide a bead to the right. 1000 1000 100 100 Write down a second number and add it! 10 10 Start with the ones. If there aren’t enough on 1 1 1000000 1000000 the left, move as many as you can to make a 100000 Abacus I 3 Ones: 2 von 3 468 + 623 100000 Hundreds: 6 468 + 623 row of ten on the right. 10000 10000 Exchange these for a bead of ten in the next 1000 1000 100 row (10 carry), move them all back to the left, 100 10 and then move the missing ones back to the 10 1 right. 1000000 1
100000 3 Ones: 10 Carry 468 + 623 Keep going, adding tens, hundreds, etc. and 10000 H3u ndreds: 1000 Carry = 1091 making all the necessary carries before you 1000 100 move to the next highest level. 10 1000 Read1000 0off00 the result and check it by hand. 1 100 100000 10 10000 3 Ones: 1 rest of 3 468 + 623 1 1000 1000
1000100000 1030 Tens: 2 468 + 623 1000100 10 100010 1
10001000
10001003 468 3 Tens: 2 468 + 623 100010
10001 1000
1000100000 100
10001003 468 10 100010 1 1000000 1000 1000 1000000 100000 1030 Ones: 2 von 3 468 + 623 1000100 Hundreds: 6 468 + 623 10000 10 100100 1000 1 10001 1000100000 100 1000000 1000100 3 Ones: 2 von 3 468 + 623 1000100 Hundreds: 6 468 + 623 100010 1000000 100010 1000
100000 1000 1030 Ones: 10 Carry 468 + 623 10000 1H030u ndreds: 1000 Carry = 1091 10 1000 10 1 1000100000 1
10001000 3 Ones: 10 Carry 468 + 623 100010 H3u ndreds: 1000 Carry = 1091
1000
1030 Ones: 1 rest of 3 468 + 623 10 1
3 Ones: 1 rest of 3 468 + 623 easy to understand. to easy for illustrating the decimal system and making it beads for ones, tens and hundreds, etc., is still good The simple abacus like the one shown here with started to do calculations on paper. Europe well into the 18th century. Then people Doing maths with the abacus was customary in “calculi” pebbles). (calculating culating board, which is comparable, used coins or usually made of wood or glass; sometimes the cal that is more than years 3000 old. It holds beads, The abacus is asimple mechanical calculation tool Why, wherefore? what, -
01.06.2013 TECHNOSEUM Abacus I I You can calculate with these 8 7 1 2 0 bones! 7 2 1 8 2 7 8 1 1 2 8 7
Multiply a multi-digit number by a 1 0 0 0 0 single-digit factor. 1 2 8 7
Set up a four-digit number by placing four bones 2 0 0 1 1 (or rods) next to each other, so that your chosen 2 4 6 4 number appears in the lower triangles of the top row of rectangles. 3 0 0 2 2 3 6 4 1 Place the rod with the digits 0 to 9 to the left of your rods. Then choose a one-digit factor on 0 0 3 2 this rod and place a sheet of paper below it as a 4 4 8 2 8 Napier's Bones ruler. 0 1 4 3 The line shows the multiplication result in an 5 4+1 3+8 2+2 5 0 0 5 unusual way: ones, tens, hundreds, etc. are found by adding the numbers in each diagonal 0 5 11 1 4 4 4 8 column. It is best to add them up by hand, 6 6 2 8 2 for the final result. If the sum is higher than 10, carry a 1 into the next diagonal column. 1 7 0 5 4 To multiply by multi-digit factors, repeat the 7 4 6 9 process accordingly and then add the results. 8 0 1 6 5 8 6 4 6
1 9 0 7 6 9 8 2 3 Wilhelm Schickard. Wilhelm calculating box) and the calculating machine made by This method was the forerunner to the promptuary (a the rods to next each other. of and one- multi-digit numbers possible by placing digits from 1to 9, made multiplication and division number on each of four its sides and multiples of the four-sided wooden rods, marked with aone-digit calculating rods that were named after him. These logarithms. For this John Napier developed the without even easier such calculationsBut made were easy.extraordinarily logarithms, which made multiplication and division Jost Bürgi in Switzerland conceived of calculating with Independently of each another, John Napier and an and self-taught scientist. †1617 mathematici Merchiston Scottish Castle, a was *1550 Merchiston Castle near Edinburgh, John Napier (also Neper in Latin), Lord of Merchiston, Why, what,wherefore? -
01.06.2013 TECHNOSEUM Napier's Bones
0 0 0 0 1 1 2 8 7
0 0 1 1 2 2 4 6 4
0 0 2 2 3 3 6 4 1
0 0 3 2 4 4 8 2 8
0 1 4 3 b 4+1 3+8 2+2 5 5 0 0 5
0 1 4 4 5 11 4 8 6 6 2 8 2
0 1 5 4 7 7 4 6 9
0 1 6 5 8 8 6 4 6
0 1 7 6 9 9 8 2 3 X Schott's calculating box Multiplication made easy Ones, tens, hundreds, etc. are in the diagonal columns and are added up by hand to get the final Multiply a multi-digit number by a one-digit factor. result. If the individual number is higher than 10, the 1 is carried over to the next diagonal column on Using the four rollers, set up a four-digit number so the left. that the digits appear in the lower triangles of the top row of squares. On the sidebar with the single For multiplication with multi-digit factors, the pro- digits, select the one-digit factor and place a sheet cess is repeated accordingly and the results are then below it as a ruler. added together.
The rows show the result of the multiplication in Since the entire multiplication table is marked on the same way as Napier’s rods: each roller, multiplication is faster than with Napier's rods, which have to be selected and exchanged. in academic circles. academic in riosa” of 1664 and thus made them better known in his publications, for instance in his “Tecnica Cu von Guericke’s experiments on vacuums extensively scientists such as Otto von Guericke. presented He Schott exchanged correspondence with leading Philipp Schönborn. von matician and confessor of Electoral Prince Johann death. At the same time he was the Court Mathe where he taught mathematics and physics until his In 1655, he returned to Würzburg as aprofessor, Jesuit School in Palermo. the at theology moral and philosophy mathematics, Years’ War, Schott left for Sicily where he taught University of Würzburg. In the turmoil of the Thirty simultaneously started studying philosophy at the In 1627 Schott joined the Order of the Jesuits and period. Baroque the burg, was ascientific author and a teacher during Gaspar Schott, *1608 Königshofen, †1666 Würz Why, wherefore? what, - - - tens. porating an addition process that carried over the incor by calculator his in results interim of adding Around 1623 Wilhelm Schickard mechanized this multiplication. final the for diately deduce the interim results and add them up these rollers to the desired number, you can imme small multiplication table is marked. By turning wooden rods it has cylindrical rollers on which the principle of Napier‘s rods. But instead of four-sided Schott‘s calculating box works according to the not appear until years two after his death. des adetailed description of his calculating box, did “Organum Mathematicum”,Schott's inclu which - - -
01.06.2013 TECHNOSEUM Schott‘s calculating box Binary system: It doesn't get any You find out what the decimal number is by adding up easier! the red numbers with circles just above them (the num- bers in bold). So for example the binary number 100101101011 means When a number is represented in binary, the digit decimal 2048 + 256 + 64 + 32 + 8 + 2 + 1 = 2411. in each position can only be a 0 or a 1. Each positi- on has the double value of the position to its right. If you wanted to add a 1 to this number, you would Let’s compare: in the decimal system, the digit in have to move the bead in the ones’ position at the each position can be 0, 1, 2…9, and each position far right down to the bottom. But the bead is already has ten times the value of the position to its right. at the bottom, so you have to move it to the top and The number represented in binary code is achieved move the bead in the next highest position to the by adding the values of those positions where there bottom. You’re carrying two, just like carrying ten in is a 1. For example, the numbers 0 to 8 are ob- decimal calculations. But the bead in this position is tained like this: also already at the bottom, so you have to bring this one to the top as well, and now move the bead in the Binary Decimal Decimal third place to the bottom. Now you can read the result 0000 0+0+0+0 0 from this addition: 0001 0+0+0+1 1 100101101100 (binary) or 2412 (decimal). 0010 0+0+2+0 2 Binary Abacus Binary 0 011 0+0+2+1 3 12 11 10 9 8 7 6 5 4 3 2 1 0100 0+4+0+0 4 0101 0+4+0+1 5 0110 0+4+2+0 6 2048 1024 512 256 128 64 32 16 8 4 2 1 = 2411 0111 0+4+2+1 7 12 11 10 9 8 7 6 5 4 3 2 1 1000 8+0+0+0 8 usw.
With the 12-digit binary abacus you can represent 2048 1024 512 256 128 64 32 16 8 4 2 1 = 2412 4096 different numbers: from 000000000000 (all beads at the top, the number 0 in decimal) to 111111111111 (all beads at the bot tom, 4095 in You can, of course, add larger binary numbers using decimal). the same principle. The bead in the relevant position is shifted downwards. If it is already in the lowest positi- Each bead can only take two positions: up on, take it to the top and move the next highest bead (numerical value 0) or down (numerical value 1). down. With 12 positions, 4096 combinations are possible. Each of these combinations of zeros and ones corresponds to a decimal number. data processing. data way for implementing digital circuitry in electronic Boolean algebra. With binary its logic, it paved the matician George Boole developed asystem of logic: 19th through the Midway century, British mathe beginning of the 18th century. described it in detail in his publications at the Gottfried Wilhelm Leibniz studied it intensely and became known in Europe in the 17th century. found in the 3rd century B.C. in India. This system Early forms of the binary numbering system are do. binary to decimal, which Leibniz's machine didn’t due to the need to convert decimal to binary and particularly computing capabilities, high-speed their and electronic components in the 20th century and be realized until the coming of electro-mechanical with amachine using the digits 0and 1could not modern data processing. But the idea of computing the principle of the binary, two-digit logic used in Just like the binary abacus, this machine follows done mechanically. ne, conceived by Leibniz in the 17th century, this is machi calculating binary reconstructed the in but In this exhibit you had to do the by carry hand, Why, wherefore? what, - -
01.06.2013 TECHNOSEUM Binary Abacus A 300-year-old idea: Basis of modern data processing
Press the white “reset” button on the model’s left side in case there are still balls in the lower compartments.
Lift up a ball from the back part of the model to the top and let it roll under the glass pane. Use the movable slider to guide the ball to the compartment on the far right (binary numerical value 1, decimal 1) or to the compart- ment in the middle (binary 10, decimal 2).
Repeat this process several times. Watch the balls’ movements and their positions in the lower three compartments. You will notice that you are adding up balls in the binary system:
If you guide a ball to the right, you are adding the binary numeral 1 (decimal 1). If you guide a ball to the middle then you are adding the binary numeral 10 (decimal 2).
You can read the results directly from the positions of the balls in the lower compartments:
binary 000 001 010 011 100 101 110 111 decimal 0 1 2 3 4 5 6 7 Leibniz's binary calculating machine to column, as is necessary for multiplication. be moved in such away and shifted from column would They nothing and others. throughtions, the balls could fall into channelsposi open through the closed in those that correspond to 0. Small dice or open in the positions that correspond to 1and remain such that they can be opened and closed. It would be fort in the following manner: abox should have holes ef much without and easily machine. very Certainly ”This kind of calculation could also be done with a on in the binary number system: calculati simple of calculator, advantages the using known is that Leibniz was thinking about abinary novative stepped drum technology. Much less well His decimal calculator became famous with in its machine.”a could do the work just as accurately with the aid of to waste their time in calculation when any peasant motto: “It is beneath the dignity of excellent men his to according machine, calculating the veloping Among other things he occupied himself with de problems. physical mathematical and dealing with notation for it that made it particularly suited for veloped it independently of Newton and found a de He calculus. infinitesimal was achievements which he did not study. One of his greatest last great polymaths: there was virtually no subject cist, and diplomat and is considered as one of the Hanover, philosopher, a was mathematician, physi Gottfried Wilhelm Leibniz, *1646 Leipzig, †1716 Why, what,wherefore? ------electronic data processing. data electronic basis of the binary, two-valued logic of modern-day too complex. But Leibniz’s idea did become the system decimal/binary/decimal would have been Leibniz’s time; the used carry in the numerical in constructed were machines calculating binary structed from this information are seen here. No Two functional acrylic models glass) (wood/ recon 1679). manuscript, Latin Dyadica, wise they do not come out.” Progressione (De necessarily always two come out together, other Because the whole thing can be set up so that hole if it alone wants to pass through the exit. reby one is always taken away, which stays in the Then all the balls fall into the channel, next whe ther, after the machine has been set in motion. should be able to move from one channel to ano The channels represent columns, and small balls - - - -
01.06.2013 TECHNOSEUM Leibniz's binary calculating machine 1 3 How can you make the confetti A closer look float and fly? When the plexiglass carries a negative charge, its Take a cloth and rub it briskly and firmly over the surroundings have a positive charge relative to it. surface of the plexiglass plate. Try it on different Positively charged pieces of confetti are attracted places on the surface. by the negatively charged plexiglass and ‘jump’ up to it. Once they have risen, the pieces release their positive charge and then immediately take up the negative charge of the plexiglass. The pieces are then attracted by the positively charged table. The same process is repeated but now in the opposite direction.
Shock the confetti 2 What's happening here?
Rubbing with the cloth electrically charges the plexiglass. Now, compared to the plate, the sur- roundings have an opposite charge. The plexiglass and the table are like the two poles of a battery. These two charges attempt to balance each other out. However, since there is no electrical conductor, the pieces of confetti jump back and forth between the table and the plate as if they were fleas. Just like a small ferry, the confetti pieces carry a small charge with them on each jump between the table and the plate. back in the other direction. other the in back ver, the particles stay at the pole and do not move ge to the pole having the opposite charge. Howe Like the confetti, they move to transport their char electrons; in salt solutions, the particles are ions. between the atoms. In metals, the particles are have an electric charge and that can move freely charge carriers. Charge carriers are particles that Every conductive material contains freely movable Why, what,wherefore? 4 - -
01.06.2013 TECHNOSEUM Shock the confetti 1 3 How can you generate static A closer look electricity? You can also transfer the electrical charge from Here is a selection of various rods and different the rod onto the metal sphere of the electroscope, materials to rub on the rods. Try different combina- by sliding the rod against the metal sphere. Just tions. Each time, move the rod slowly towards the touching the sphere isn't enough – if the rod is an small metal sphere on top of the electroscope. insulator charges cannot flow along it. When you then remove the rod, the electroscope remains charged.
When you repeat this process using other material combinations, two possible outcomes can occur: The new rod has the same polarity as the charge on the electroscope and the deflection of the metal leaves is even greater. Or, the rod has the opposi- te polarity and the electroscope is discharged, or its polarity is even reversed. The metal leaves fall, and if the polarity has been reversed, immediately spread apart again. Frictional ElectricityFrictional 2 What's happening here?
With the right combination of materials, you can rub electrical charges onto the rod. The greater the charge on the rod, the sooner the metal leaves of the electroscope starts to spread apart.
The electric field of the charged rod attracts the opposite charges in the electroscope and pulls them upwards, while pushing the identical charges away toward the metal leaves. The two leaves therefore become charged with the same polarity and repel each other, spreading apart. doesn’t build up to create apainful spark. flow away as soon as it is created and therefore when you lift yourself off the cushioned seat can car before you stand up. The charge that you create make sure you are touching the bodywork of the A word to the wise: when you get out of acar, soles. plastic door knobs or other people if you wear shoes with You will be familiar with the painful sparks from static electricity because we encounter it daily. We know all about generating electric charges and Why, what,wherefore? 4
01.06.2013 TECHNOSEUM Frictional Electricity Lightning Cabin Electric Whirl 1 1 How does a lightning rod work? An ion-propulsion drive from the baroque era? Use the right handwheel to position the two spheres on the sliding carriage opposite to the left-hand two spheres on Use the right handwheel to position the two spheres on the the fixed rail. Now turn the crank handle of the electrostatic sliding carriage opposite to the two middle spheres on the generator clockwise. fixed rail. Now turn the crank handle of the electrostatic
Lightning generator clockwise. 2 What's happening here? 2 What's happening here? The cloud builds up a voltage relative to the ground. When the voltage is high enough, it discharges in the form of a The neighboring antenna is grounded and the electric whirl spark, like lightning. The lightning rod and the cabin are part builds up a voltage relative to its surroundings. The electrical of the ground. Because the lightning always seeks the shor- field at the tips increases to such an extent that the air is char- test path, it strikes the lightning rod first. After striking the ged and subsequently pushed away, which in turn pushes the rod, the lightning continues to travel through the lightning rod tip the other way. Every once in a while, a spark is generated: to the ground because the lightning rod has a lower electrical an instantaneous discharge strikes the antenna. The repulsion resistance than the cabin. of bodies charged with the same polarity is used in the elec- troscope (the other experimental station) to detect electrical charges. 3 A closer look 3 An electric shock from the electrostatic generator would be A closer look painful but not deadly – the electric currents are too low for this. All the connectors and the poles in these experiments The strong electric field at the tips of the arms causes ioniz- are spherical. Using pointed poles would, with such high ation of the surrounding air. Thus, the electric charge of the voltages (up to 120,000 volts), result in point discharges. The electric whirl is dissipated in the form of ions in the air. Putting electrical field would be so strong at the points that the cur- it another way, under high voltage, the otherwise insulating rent would flow directly into the ionized air before a spark is air becomes conductive. Charges are flowing steadily, in cont- produced. You can observe this effect at the middle demons- rast to lightning. This effect is called point discharge. tration. In a point discharge, the charges flow at a constant rate. Lightning, on the other hand, is an avalanche of ions that instantly makes its way through the air. birds would not fly. not build up avoltage relative to surroundings its and the the shotgun was not grounded, the sphere in the tree could the birds as the opposite pole relative to the surroundings. If grounded.be Only then can the sphere hold acharge with For the birds to repel each other, the hunter‘s shotgun must closerA look 3 other any longer. Therefore, the birds fall down. sphere are discharged instantaneously and not do repel each in the form of aspark onto the shotgun. birds The and the other. When the voltage is high enough the sphere discharges birdsThe are charged with the same polarity and repel each sphereThe with the paper birds becomes electrically charged. here? happening What's 2 clockwise generator the fixed rail.Now turn the crank handle of the electrostatic sliding carriage opposite to the right-hand spheres two on Use the right handwheel to position spheres the two on the by lightning? How can abird shot be down 1 Hunter Electric of electrical charges. of electrical electroscope (the other experimental station) for the detection bodies chargedbetween with the same polarity is used in the theges. In dark, you may even small see sparks. repulsion The stands up and you can hear the crackling noise of the dischar When you then take your off sweater, for example, your hair fiber over each other, the pieces of clothingbecome charged. For example, if you wear layers of clothing made of synthetic You’re Hunter: Electric probably familiar with this effect. high-voltage technical equipment, pointed are poles avoided. spark can occur. all In high-voltage experiments and for all would dissipate the charge electric through the air before a Pointedhere). poles would lead to point discharges, which to needed ges make large sparks (120,000V on our machine used on machines designed to generate high the very volta Point discharge Whirl: is the reasonElectric why spheres are so, he followed adesign of Benjamin Franklin. the Electoral Palatinate in 1776 with lightning rods. doing In demy of Sciences) equipped all castles and powder towers of Mannheimer Akademie der Wissenschaften (Mannheim Aca the 18th century. Physicist Johann Jakob Hemmer from the ofaction lightning rods began to studied be in the middle of The insurers. building by required are they cases, many In cabin: Lightning Why, wherefore? what, 4 The benefits benefits The of lightning rods areobvious. - - -
01.06.2013 TECHNOSEUM Lightning 1 2 How can this be used to produce What's happening here? sparks? Rubbing the plexiglass disk gives it an electric charge. When you put the metal plate on the disk, the charge on the disk induces
1 Lift the metal plate off the a difference in charge between the top and bottom of the plexiglass disk using the plastic metal plate. Touching the upper side of the metal plate with the handle. discharger (or for the less fearful, with a finger) allows charge to flow away from the top side of the plate. The plate is now only charged by the charges on the lower side. When the metal plate is lifted up and off the plexiglass disk, the 2 Rub the plexiglass disk with charges are spatially separated. As soon as the sphere of the the cloth discharger comes close to the metal plate, charge equalization takes place in the form of a spark.
3 and put the metal plate back Electrophorus down onto the plexiglass disk. 3 A closer look 4 Now, touch the metal plate Rubbing the surface of the disk with the cloth creates a briefly with the brass sphere negative charge on the plexiglass disk. If you hold the back on the tip of the discharger. of your hand close to the disk, you should be able to feel and see that the fine hairs are attracted to the disk. If the metal plate (conductor) is placed on the charged plexiglass disk (insulator), the electrons on the metal plate 5 Then, lift the metal plate off are shifted, because charges of the same polarity repel each the plexiglass disk again other. The negative and positive charges are now on opposi- te faces of the plate. This phenomenon is called electrostatic induction. Overall, the metal plate is still electrically neutral because it carries the same number of positive and negative charges. 6 and move the discharger If the charge on one side of the metal plate is dissipated by towards the metal plate. You connecting it to ground (for example, by touching it with a will hear a crackling noise as hand) the plate is no longer neutral. In our experiment, the a spark jumps across to the plate is charged positively because the negative charges have discharger. been dissipated. Because the metal plate and the plexiglass disk now carry charges of the opposite polarity, they attract each other. When the disk and the plate are separated further, the voltage increases even more. The voltage increases so much that a spark flies through the air as soon as a grounded ob- ject comes close to the metal plate. cabin, the electric whirl, hunter. the and electric cabin, the lightning the with experiments for the voltage the generators. Amachine of this is used type to create nized and advanced to make so-called electrostatic Later, the principle of the electrophorus was mecha figures). (Lichtenberg patterns tree-like attracted to certain of parts the surface to produce struck, he discovered that dust particles were sparks up to 70 cm in length. Where the sparks with adiameter of 2.5 m. It allowed him to create electrophorus built an Göttingen, from scientist Georg Christoph Lichtenberg (1742 –1799), a Perpetuo.” “Elettroforo instrument this improved by Alessandro Volta in 1775. called He ciple has been known since about 1750 and was the early days of the study of electricity. The prin The electrophorus was avery important device in Why, what,wherefore? 4 - -
01.06.2013 TECHNOSEUM Electrophorus 1 2 Can electrical charges be put in What's happening here? a jar? The glass container is called a Leyden jar and is a predecessor of today’s capacitors. Capacitors are electronic components This demonstration starts out like the electrophorus that store and later release electrical charges. As you can demonstration. see, a charge from the electrophorus can be put into the Leyden jar and transported to the electroscope. The electros- cope lets you see the electrical charge: the pieces of foil have 1 Lift the metal plate off the the same electrical polarity and repel each other. plexiglass disk using the plastic handle. Leyden Jar 2 Rub the plexiglass disk with 3 the cloth A closer look
Compared to batteries, capacitors can store and release only 3 and put the metal plate back small amounts of electrical charge. However, while batteries down onto the plexiglass disk. depend upon fairly slow chemical reactions, the storage pro- cess in the capacitor is purely physical. Therefore, capacitors can store and release charges almost instantaneously.
The higher the voltage applied to a capacitor, the greater 4 Now, touch the metal plate the amount of charge stored on the capacitor. The amount briefly with the steel sphere on of charge stored on a capacitor increases in proportion to the top of the glass container. the applied voltage. The proportionality factor depends on the size and construction of the capacitor and is called capacitance:
Amount of charge (Q) = Capacitance (C) · Voltage (U) 5 Hold the sphere of the in short: Q = C · U glass container against the electroscope. The metal leaves The Leyden jar is a glass container that is coated on the inside spread apart. A charge has and on the outside with a metal foil. When you touch the Ley- been transferred. den jar, the foil on the outside is grounded by your hand. The foil on the inside is electrically connected to the sphere, but is insulated from the outer foil by the glass. That is why the inner foil can be charged relative to the outer, grounded foil.
The capacitance of the Leyden jar increases with the surface area of the foils and with decreasing thickness of the glass. The capacitance also depends on the kind of glass. electronics. among the most important components in in radios, television sets, and computers and are high voltages. Capacitors are used by the hundreds pinhead because they do not have to withstand Today's capacitors are often only as large as a voltages. high sometimes used for electrical experiments with with high voltages. That is why the Leyden jar is jar has asmall capacitance, but can be charged to modern capacitors of the same size, the Leyden electrical charges in water-filled bottles. Compared in Leyden (Holland), when people tried to store The Leyden jar was developed in the 18th century Why, what,wherefore? 4
01.06.2013 TECHNOSEUM Leyden Jar 1 2
How far is it to the blue pillar What's happening here? near the hot air balloon? On the sheet a “map” at a scale of 1:50 of the Put a piece of paper on the left-hand table. Attach baseline and the blue pillar has been created. The a sighting ruler to peg 2 and turn it until you have distance to the pillar can be measured from this the middle of the blue pillar in the sight. Now, draw sheet rather than by measuring the actual distance a bearing line along the beveled edge of the ruler to the pillar. onto the sheet. Repeat the process at the right- hand table with the other sighting ruler attached to peg 3. 3 A closer look Position finding Position
The tables are placed with the pegs for the sighting rulers over the endpoints of the 4 m long, red baseline.
The intersection of the two bearing lines on the The distance between holes 2 and 3 on the test sheet is a de- test sheet marks the position of the pillar. piction of the base line on a 1:50 scale. A triangle having this scale and including the baseline and the sighted point is drawn during the bearing process.
1 1 This measuring method is called triangulation because it invol- ves constructing a triangle. The method is fairly inaccurate if 15 m 15 m the sighting angle and the distance are drawn on paper, as in our example. However, if the baseline and the sighting angles are measured accurately, and if the distance is then calculated 10 m 10 m using trigonometry, you can get very precise results.
5 m This precisely derived distance can be used as a new baseline 5 m for determining even greater distances. These distances, in turn, can be used as the basis for even greater distances and 0 m 2 3 so on. 0 m 2 3 Triangulation can thus be used to measure the largest dimensi- ons: the size of countries, continents, or of the globe, or even for astronomical distances, such as the distance between the Check the distance between the red baseline and Earth and the Moon or between the solar system and nearby the blue pillar with the measuring wheel! stars. countries, continents and, finally, entire the globe. In the 18th century, people began measuring vast half-tunnels. hardly any offset at the meeting point of the two Samos that was built from both ends and that had We do know, however, that atunnel was dug on It is not known when triangulation was first used. Why, what,wherefore? 4 part 1.part 1763) of all mathematical sciences], [Elements Wissenschaften (Christian Wolff: Anfangsgründe aller mathematischen Trigonometrical measurement distance
01.06.2013 TECHNOSEUM Position finding