Dr. Jie Zou PHY 1151G Department of Physics1 Chapter 12 Gravity

Dr. Jie Zou PHY 1151G Department of Physics2 Outline Newton’s law of universal gravitation Gravitational attraction of spherical bodies Force of Gravity on a mass m on the surface of the Earth Force of Gravity on a mass m above the surface of the Earth

Dr. Jie Zou PHY 1151G Department of Physics3 Newton’s Law of universal gravitation Newton’s law of universal gravitation: The force of gravity between any two point objects of mass m 1 and m 2 is attractive and of magnitude r = the distance between the masses. G = the universal gravitation constant = 6.67  N·m 2 /kg 2. Direction of the force of gravity: directed along the line connecting the masses. The force of gravity between two objects forms an action- reaction pair.

Dr. Jie Zou PHY 1151G Department of Physics4 Exercise A man takes his dog for a walk on a deserted beach. Treating people and dogs as point objects for the moment, find the force of gravity between the 105-kg man and his 11.2-kg dog when they are separated by a distance of (a) 1.00 m and (b) 10.0m.

Dr. Jie Zou PHY 1151G Department of Physics5 Example As part of a daring rescue attempt, the Millennium Eagle passes between a pair of twin asteroids, as shown. If the mass of the spaceship is 2.50  10 7 kg and the mass of each asteroid is 3.50  kg, find the net gravitational force exerted on the Millennium Eagle (a) when it is at location A and (b) when it is at location B. Treat the spaceship and the asteroids as if they were point objects.

Dr. Jie Zou PHY 1151G Department of Physics6 Gravitational attraction of spherical bodies (1) (1) Between a uniform sphere and a point mass: The net force exerted by the sphere on the mass m is the same as if all the mass of the sphere were concentrated at its center. The magnitude of the force between the mass m and the sphere of mass M is

Gravitational attraction of spherical bodies (2) (2) Between two uniform spheres: The force of gravity between two spheres of finite size is the same as if both were replaced by point masses. For example, the gravitational force between the Earth and the Moon is r: center-to-center distance Dr. Jie Zou PHY 1151G Department of Physics7

8 Force of gravity for a mass m on the surface of the Earth Force of gravity for a mass m on the surface of the Earth is Also, force of gravity for a mass m on the surface of the Earth is F = mg. So, the acceleration due to gravity, g, is See Appendix C and the back cover of the textbook for Solar System Data. treehugger.com RERE M E = 5.97x10 24 kg R E = 6.37x10 6 m m MEME

Dr. Jie Zou PHY 1151G Department of Physics9 Force of gravity for a mass m above the Earth’s surface If you climb to the top of Mt. Everest, you will be about 5.50 mi above sea level. What is the acceleration due to gravity at this altitude? 1 mi = 1609 m. Answer:

Dr. Jie Zou PHY 1151G Department of Physics10 Homework See online homework on Hand-written homework: Ch. 12, p. 409, Problems: #12. Note: For astronomical data, see the inside of the back cover of your textbook and Appendix C.