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Motion, Energy, and Gravity

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Motion, Energy, and Gravity Motion, Energy, and Gravity Reminder to take out your clicker and turn it on! Attendance Quiz Are you here today? Here! (a) yes (b) no (c) Opening Day is here! x Clickers • I have not been able to download the online clicker registrations, so can everyone who did not manage to register last time in class please stay during the break to register their clicker—if you aren’t sure, please stay to see if your name appears Today’s Topics • Describing Motion • Mass v. Weight • Newton’s Laws of Motion • Energy • Newton’s Law of Gravitation Describing Motion • All objects in the Universe are moving • Earth is spinning about its axis • Earth orbits Sun • Solar System orbits center of Milky Way • Milky Way and Andromeda galaxy are rushing towards each other • All galaxies, on the largest scale are moving apart (the Universe is expanding) • The two galaxies below are in the process of colliding Describing Motion • Three of the fundamental quantities used to describe motion are position, velocity, and acceleration • Position is how far an object is (in all dimensions) from a reference point • Velocity is the rate of change of position (speed is the magnitude of velocity) • Acceleration is the rate of change of velocity • Because velocity has both a size and direction, an object can accelerate, even when its speed doesn’t change! Mass v. Weight • Mass is an intrinsic property of an object - how much of it is there? (measured in kg) • Weight is the force experienced by an object due to gravity (measured in lbs or Newtons) • Weight, unlike mass, depends on the situation • In the stationary elevator at right, the weight on the scale is the same as it would be standing on the ground • If the elevator moves up or down at a constant velocity the weight on the scale is unchanged • If the elevator accelerates up, the weight on the scale is higher (you feel heavier) • If the elevator accelerates down, the weight on the scale is lower (you feel lighter) • If the cable is cut, and the elevator falls freely, you feel no weight at all (weightlessness) • Pink Panther v. Astronomer Video - 3:30 Pink Panther Quiz How many “cartoon physics” errors did you detect in the video? a) 0 b) 1 c) 2 d) 3 e) More than 3 Mass Quiz Compared to your mass here on Earth, your mass out in the space between the stars would be a) zero b) negligibly small c) much much greater d) the same e) the question cannot be answered from the information given Weightlessness Quiz Astronauts on the space shuttle feel weightless because a) they have no mass in space b) they are in a constant state of free-fall c) they are outside the effect of the Earth’s gravity d) without air there can be no weight e) all of the above Newton’s Laws of Motion • Newton, building on the work of Galileo, formulated three laws of motion • 1st Law - an object moves at a constant velocity (both speed and direction) unless acted on by a force • 2nd Law - The acceleration of an object acted on by a force is proportional to the force and inversely proportional to the mass of the object (a = F/m) • 3rd Law - For any force, there is an equal and opposite reaction force • These laws govern the motion of all objects in the Universe, except the very fast (relativity) and the very small (QM) Example - the Bus and the Bug • Imagine a bug flying into the windshield of an oncoming bus • What is the relative size of the forces the bus and bug feel (Newton’s 3rd Law) Bus-Bug Quiz I In a head-on collision between a bus and a bug, which feels the greater force? a) The bus b) The bug c) They feel the same force d) The question cannot be answered from the information given Example - the Bus and the Bug • Imagine a bug flying into the windshield of an oncoming bus • What is the relative size of the forces the bus and bug feel (Newton’s 3rd Law) • What is the relative size of the accelerations the bus and the bug feel (Newton’s 2nd Law) Bus-Bug Quiz II In a head-on collision between a bus and a bug, which feels the greater acceleration? a) The bus b) The bug c) They feel the same acceleration d) The question cannot be answered from the information given Example - the Bus and the Bug • Imagine a bug flying into the windshield of an oncoming bus • What is the relative size of the forces the bus and bug feel (Newton’s 3rd Law) • What is the relative sizes of the accelerations the bus and the bug feel (Newton’s 2nd Law) abus = Fbug-bus/Mbus abug = Fbus-bug/mbug Circular Motion • An object in circular motion may have a constant speed but its velocity is constantly changing, as its direction of motion changes • Newton’s 2nd Law tells us that there must be a force causing this acceleration • In the case of a ball (or donut) on a string, it is the inward force of the string that keeps the ball (or donut) from flying away • If the string (or donut) breaks, the ball (or donut) will fly away in a straight line (Donut demo) Forces and Orbits • An object in orbit feels the force of gravity from the central object • Imagine running off a platform on a Velocity very tall tower (above the atmosphere) Path • You would fall to the Earth, but the faster you started, the further from the base of the tower you would land Force • If, instead of running, you strapped a rocket to your back, and gave yourself enough initial velocity (about 8 km/s near Earth’s surface), you could fall around the Earth, i.e., you could orbit • All objects in orbit stay in their orbital path due to the force of gravity Weightlessness Quiz Astronauts on the orbiting space shuttle feel weightless because a) they have no mass in space b) they are in a constant state of free-fall c) they are outside the effect of the Earth’s gravity d) without air there can be no weight e) all of the above Moon Quiz The Moon remains in its orbit around the Earth rather than falling to the Earth because a) it is outside of the gravitational influence of the Earth b) it is in balance with the gravitational forces from the Sun and other planets c) the net force on the Moon is zero d) none of these e) all of these Energy • Energy is the central unifying theme of all science • Energy comes in many forms • Kinetic energy (energy of motion) including motion of atoms (temperature) - Note: higher speed means more kinetic energy • Radiative energy (energy of light) • Potential (stored) energy, including mass which is a form of stored energy (E = mc2) • Although energy can change from one form to another, it is always conserved in total Gravitational Potential Energy • When a ball is thrown into the air, it starts with kinetic energy • When it reaches the top of its motion, it momentarily stops • Q: Where did the energy go? A: Into gravitational potential energy • The energy is “stored” in the interaction between the ball and Earth • The evidence for this is that the energy is (almost) completely recovered as kinetic energy when the ball falls back to the ground • High = large GPE Low = small GPE Gravitational Potential Energy in Orbits • Recall Kepler’s 2nd Law - In a given time, a line connecting the Sun to the planet will sweep out an area that is the same in all parts of the orbit • Thus, the planet moves faster when it is closer to the Sun • We can now understand this in terms of energy (KE and GPE) • Since the total energy of the planet is conserved 1. When the planet is closer to the Sun, its GPE is lower, and its KE (and speed) will be higher 2. When the planet is further from the Sun, its GPE is higher, and its KE (and speed) will be lower Interactive Figure – Kepler’s 2nd Law Newton’s Law of Gravitation • Newton knew that gravity caused objects to fall to the Earth • However, his great achievement was to understand that the same force also held the Moon in its orbit around Earth • The force acts on both objects in an equal and opposite manner (Newton’s 3rd Law) • The force is always attractive and has direction (Example: person on Earth) • The correct mathematical relationship is that: 1. The force is proportional to both masses (Newton’s 3rd Law) 2. The force is inversely proportional to the square of the distance between the objects • The quantity G is a universal constant relating masses, distances, and forces, for a given system of units Newton and Kepler’s Laws • KI – Newton’s force law correctly predicts that planets will move in elliptical orbits with the Sun at one focus • KII - We have already seen how gravitational potential energy can help explain that planets move faster when close to the Sun and slower when further from the Sun • KIII - It is possible to derive this law (p2 ∝ a3) from Newton’s law of gravitation Newton and Kepler’s Laws There are some differences between Newton’s and Kepler’s version of planetary (and other) orbits 1. The planets do not technically orbit the Sun; they orbit the center of mass of the system The center of mass of the Solar System is near the edge of the Sun, so the Sun moves very little, but it does wobble a bit about the center of mass 2.
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