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Learning™ Tower of Pisa ©2003 - v 9/05 611-0385 (30-205) Learning™ Tower of Pisa Warranty and Parts: Stability: How To Use: We replace all defective or miss- If a solid body resting on a base 1. Weigh each slug and measure their ing parts free of charge. All products returns to its original position after it diameter and height. warranted to be free from defect for has been tipped a little, it is said to be 2. Stack the 4 enclosed slugs of dif- 90 days. Does not apply to accident, in "Stable equilibrium." Bodies that are ferent materials in any combination misuse, or normal wear and tear. in stable equilibrium cannot be tipped onto the enclosed 6.4 mm dia steel over unless their center of gravity is pin. first raised. 3. Calculate the center of gravity us- Introduction: There is a simple way of knowing ing the following formula: in advance whether a body, resting on C = M h + M h + M h + M h The world famous Leaning Tower g A 4 B 3 C 2 D 1 a given base, will be stable or topple M + M + M + M of Pisa in Italy presents an interesting A B C D over when released. It the plumb line case study in stability. This tower is 4. To check your calculations, place through its center of gravity falls within 56 meters tall with walls that are 2.6 the assembled tower onto our 40- the boundary of the base on which it meters thick at the base. It is built en- 250 Inclined Plane or a suitable rests, the body will not topple over. If tirely of marble. Its construction began textbook. Gradually tilt the tower however this plumb line falls outside in 1173 and was not finished until 200 until the assembly topples. Keep the boundary of the base, the body will years later. It was built as a vertical track of the angle (α) at which the overturn automatically when released. bell tower for the cathedral next door topple occurs. A body is more stable if it requires and apparently began to lean while still C = l a greater force to overturn it. Of the 24 g under construction. The original footer combinations of the 4 enclosed cylin- 2 tan α was inadequate and many attempts to ders, you will quickly see that some 5. Calculate the angle of incline of the reinforce it with concrete have been combinations will topple with a much Leaning Tower of Pisa at each of the attempted. The following table shows smaller angle of tilting (α). years on the above table. Use the how much the tower varied from formula: plumb over the years. α = arctan height of tower ( distance from plumb) 6. The diameter of the base of the Tow- Year Distance out of Plumb er of Pisa is 15.5 m. Assuming that 1298 1.43 meters the tower is uniform in construction, 1360 1.63 meters how much more can the tower lean 1550 3.77 meters before it topples. 1817 3.84 meters 7. How could you save the tower from 1911 4.04 meters toppling? Explain 1935 4.80 meters 1997 5.20 meters Why the Tower Doesn't Fall: The Leaning Tower of Pisa is a symbol of things that seem in danger It was from the top of this tower of falling. Other examples in the real that Galileo dropped two weights in the A world can include: two-decker bus- famous experiment to find out about ses in England, a high load of hay in falling bodies. B a wagon, a skyscraper in a high wind, a car skidding on two wheels around P/N 24-0205 C a curve. Just how far can such objects lean before they actually do overturn? ©Science First® All rights An object can lean without falling reserved. Science First® is a D as long as a straight line leading from registered trademark of Morris & n l m its center of gravity to the center of the Lee Inc. earth passes through the object's base. This center of gravity is an imagi- SCIENCE FIRST® | 86475 Gene Lasserre Blvd., Yulee, FL 32097 | 800-875-3214 | www.sciencefirst.com | [email protected] SCIENCE FIRST® | 86475 Gene Lasserre Blvd., Yulee, FL 32097 | 800-875-3214 | www.sciencefirst.com | [email protected] ©2003 - v 9/05 nary point at which you can consider farther over an object can lean. Thus, 611-0350 Roman Arch - 23 hard- the entire weight of an object to be by concentrating the weight of build- wood blocks in 6 unique shapes. Build concentrated. ings, cards and boasts as low as pos- a working model of the famous arch The drawings below can show you sible, designers make them more stable. strong enough to stand on. how to locate the center of gravity. 611-1050 Build-A-Pulley - Modular Suspend the object (a cut-out represen- block and tackle set large enough to do tation of the Leaning Tower, in these real work. 2" sheaves, brackets. drawings) successively from two or 611-1215 Ring and Disc - 3" di- more points (for example, A, B and C). ameter PVC ring and wood disc. Roll Hang a weighted thread from the point them together down an incline, which of suspension and draw a line behind is faster? the thread as the object hangs from 611-0035 Inclined Plane - Solid each point. The point where the lines aluminum inclined plane and full range intersect marks the center of gravity. of accessories. Investigate acceleration, If you suspend your weight on friction and gravity. Folds for storage, the thread so that it hangs freely from clamps up to 45°, removable protractor the center of gravity point and lean and low-friction pulley. your tower against a wall while its Related Products: 611-0040 Halls Car - Use with ® base stands on the edge of a book, for Science First manufactures low-cost inclined plane, pulley and weights to example, you can find out for yourself. science labs that are available from analyze link between work and energy. As long as the line remains within the most science education distributors. Nearly frictionless due to oil-free base line of the tower, the tower keeps 611-0110 Second Law of Motion Ap- sleeve bearings. ABS plastic car has its footing. The instant the line remains paratus - Is the horizontal component of deep well for weights, wheels snap into within the base line of the tower, the force independent of the vertical ? Shoot place even if dropped. tower keeps its footing. The instant the one ball outward, drop second ball, time 611-1220 Variable Inertia - In- line passes outside, the tower tumbles! both impacts. Plastic molded base, spring stantly change distribution of mass with The lower the center of gravity, the plunger, 2 balls, instructions. 8 balls inserted into your choice of compartments. Load each of two discs unevenly, roll together down an incline. Which is faster? Why? Includes: 8 You can find out how far balls, two discs with hardware, instruc- tions. any object can lean without falling by first finding (left) its center of gravity, or the Leaning point at which it balances Tower of perfectly (below). The object Pisa, the site of Galileo's will not fall as long as a experiment plumb line dropped from this center passes inside the base. Tower outline with lines Outline with pencil SCIENCE FIRST® | 86475 Gene Lasserre Blvd., Yulee, FL 32097 | 800-875-3214 | www.sciencefirst.com | [email protected].
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