Law of Universal Gravitation

Newton’s Law of Universal Gravitation

Equal, opposite forces pull the objects together

Source: Griffith, The Physics of Everyday Phenomena, 4th ed.

d

Newton’s Law of Universal Gravitation

Force between two objects:

F = Gm1m2

d2

m1, m2: masses of the objects

d: distance between objects’ centers of mass

G: universal gravitational constant, 6.672  10–11 Nm2/kg2

Practice Problem 1

• Tom has a mass of 70.0-kg and Sally has a mass of 50.0-kg. Tom and Sally are standing 20.0m apart on the dance floor. Sally looks up and sees Tom. She feels an attraction. If the attraction is gravitational, find its size. Assume that both Tom and Sally can be replaced by spherical masses.

• 5.838 x 10-10 N

Practice Problem 2

• What is the gravitational attraction between two spheres (msphere = 1.67 X 10-

27 kg) at a distance of 5.0 X 10-15 m?

• 7.44 x10-36 N

Practice Problem 3

• A 1.0-kg mass weighs 9.8 N on earth’s surface, and the radius of Earth is roughly 6.4 x 106 meters. Calculate the mass of Earth.

• 9.8 N = (6.67210-11 Nm2/kg2)(1.0kg)(m2)

(6.4x106 m)2

• 6.02 x 1024 kg

Conservation of momentum

• A 0.005-kg bullet is fired with a velocity of 100 m/s toward a 10.00-kg stationary solid block resting on a frictionless surface. What is the a) final velocity of the bullet and block together then, b) the change in momentum of the bullet if it is embedded in the block?

• A: 0.05 m/s

• B: -0.5 kgm/s