VIEWS: 2 PAGES: 28 POSTED ON: 10/8/2011
Newton’s laws of motion A body remains at rest or moves in a straight line at a constant speed unless acted on by a net external force. Force = mass acceleration For any force there is always an equal and opposite reaction force. Newton’s Universal Law of Gravity • Every mass attracts every other mass through a force called gravity • The force is directly proportional to the product of their masses • The force is inversely proportional to the square of the distance between them Newton’s law of gravity M1M 2 F G 2 d Discussion You dig a very deep mine shaft. As you get closer to the center of the Earth, does your weight increase, decrease or remain the same? Why? (Hint: consider what the force of gravity will be at the very center of the Earth.) Where does it come from? For a planet to orbit the Sun, it must constantly accelerate toward the Sun, otherwise it would fly off in a straight line at a constant velocity. Discussion If I drop two balls at exactly the same time and from exactly the same height, with each ball exactly same shape and size but very different masses, which ball hits the ground first? Discussion If I drop two balls at exactly the same time and from exactly the same height, with each ball exactly same shape and size but very different masses, which ball has the greater force acting on it? Why proportional to the mass? All objects, regardless of their mass, fall with the same acceleration. Because F = ma, Fgrav To keep the acceleration a constant, the force must vary m proportional to the mass. Discussion If I swing a ball in a circle over my head with a short string and a long string with each ball moving at the same speed, which ball has the greater force acting on it? Explain why. Why the square of the distance? An inverse square central force law is required to get stable orbits that are conic sections, i.e. orbits that are elliptical. Discussion A ball held on a string is coasting around in a large horizontal circle. The string is then pulled so the ball coasts in a smaller circle. When coasting the smaller circle its speed is a) Greater b) Less c) Unchanged Newton’s form of Kepler’s 3rd law 4 2 3 P 2 a G (m1 m2 ) Discussion Notice that we can only determine the sum of the masses using Newton’s from of Kepler’s 3rd law. In the case of the solar system this sum is dominated by the Sun. Why can’t we figure out the mass of an object by observing its orbit? Can’t we get the force necessary to keep it in orbit and figure out the mass? All objects fall in a gravitation field with the same acceleration regardless of mass. Because being in orbit is just falling, all objects will orbit the same regardless of their mass as long as the mass of the orbiting object is much less than that of the object it is orbiting. Discussion The Moon’s mass (consider it all at the center of the Moon) attracts every atom on the Earth. If every atom has exactly the same mass, is the gravitational attraction of the Moon the same on each atom on the Earth? Explain. Tidal Forces Different distances from a mass will experience different forces and therefore different accelerations. Discussion Consider yourself sitting on the center ball, number 2 in the previous diagram. How will you perceive the motion of the other two balls relative to you? Tidal Forces Tidal forces act to stretch things out along the direction of a gravitating source and squeeze them in the middle. Discussion Does it matter that all the atoms on the earth have the same mass? Or that all three billiard balls have the same mass? Why or why not?
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