1. Gravitation Examples Answers 1. Two balls have their centers 3.0 m apart. One ball has a mass of 10.0 kg, while the other ball has a mass of 15.0 kg. Calculate the force of gravity between them. F g = m 1 = 10.0 kg m 2 = 15.0 kg r = 3.0 m G = 6.67 x 10 -11 N m 2 /kg 2 F g = ? G m 1 m 2 r2r2 = ( 6.67 x 10 -11 N m 2 /kg 2 )( 10.0 kg )( 15.0 kg ) ( 3.0 m ) 2 F g = 1.1 x 10 -9 N

2. 2. What is the gravitational force between two spheres of mass 10.0 kg each when they are 4.0 m apart? F g = m 1 = 10.0 kg m 2 = 10.0 kg r = 4.0 m G = 6.67 x 10 -11 N m 2 /kg 2 F g = ? G m 1 m 2 r2r2 = ( 6.67 x 10 -11 N m 2 /kg 2 )( 10.0 kg )( 10.0 kg ) ( 4.0 m ) 2 F g = 4.2 x 10 -10 N

3. 3. The gravitational force between two spheres is 3.50 x 10 -7 N when they are 8.00 m apart. One sphere has a mass of 5.00 x 10 2 kg. Calculate the mass of the other sphere. F g = 3.50 x 10 -7 N r = 8.00 m m 1 = 5.00 x 10 2 kg G = 6.67 x 10 -11 N m 2 /kg 2 m 2 = ? F g = G m 1 m 2 r2r2 r2r2 r2r2 r 2 F g = G m 1 m 2 G m 1 m 2 = G m 1 r 2 F g Solve for m 2

4. F g = 3.50 x 10 -7 N r = 8.00 m m 1 = 5.00 x 10 2 kg G = 6.67 x 10 -11 N m 2 /kg 2 m 2 = ? 3. m 2 = G m 1 r 2 F g = ( 6.67 x 10 -11 N m 2 /kg 2 )( 5.00 x 10 2 kg ) ( 8.00 m ) 2 ( 3.50 x 10 -7 N ) m 2 = 672 kg

5. 4. The gravitational force between two objects is 8.00 x 10 -8 N. If one object has a mass of 3.00 x 10 2 kg and they are 2.5 m apart, what is the mass of the other object? F g = 8.00 x 10 -8 N r = 2.50 m m 1 = 3.00 x 10 2 kg G = 6.67 x 10 -11 N m 2 /kg 2 m 2 = ? F g = G m 1 m 2 r2r2 r2r2 r2r2 r 2 F g = G m 1 m 2 G m 1 m 2 = G m 1 r 2 F g

6. 4. F g = 8.00 x 10 -8 N r = 2.50 m m 1 = 3.00 x 10 2 kg G = 6.67 x 10 -11 N m 2 /kg 2 m 2 = ? m 2 = G m 1 r 2 F g = ( 6.67 x 10 -11 N m 2 /kg 2 )( 3.00 x 10 2 kg ) ( 2.50 m ) 2 ( 8.00 x 10 -8 N ) m 2 = 25.0 kg Solve for m 2

7. 5. The mass of the earth is 6.0 x 10 24 kg. If the distance between the centers of Earth and the Moon is 3.9 x 10 8 m, the gravitational force between them is about 1.9 x 10 20 N. What is the approximate mass of the Moon? F g = 1.9 x 10 20 N r = 3.9 x 10 8 m M m = ? M E = 6.0 x 10 24 kg G = 6.67 x 10 -11 N m 2 /kg 2 m 2 = G m 1 r 2 F g M M = ( 6.67 x 10 -11 N m 2 /kg 2 )( 6.0 x 10 24 kg ) ( 3.9 x 10 8 m ) 2 ( 1.9 x 10 20 N ) m 2 = 7.2 x 10 22 kg M M = G M E r 2 F g

8. 6. The gravitational force of attraction between two identical spheres is 4.00 x 10 -7 N when their centers of mass are 3.00 m apart. Calculate the mass of each sphere. F g = 4.00 x 10 -7 N r = 3.00 m G = 6.67 x 10 -11 N m 2 /kg 2 m 1 = m 2 = ? F g = G m 1 m 2 r2r2 F g = G m 2 r2r2 Since spheres are identical, they have equal masses: m 1 = m 2 Let m 1 = m 2 = m

9. F g = 4.00 x 10 -7 N r = 3.00 m G = 6.67 x 10 -11 N m 2 /kg 2 m 1 = m 2 = m 6. Solve for mF g = G m 2 r2r2 r2r2 r2r2 r 2 F g = G m 2 GG m 2 = G r 2 F g m = G r 2 F g

10. F g = 4.00 x 10 -7 N r = 3.00 m G = 6.67 x 10 -11 N m 2 /kg 2 m 1 = m 2 = m 6. m = G r 2 F g = 6.67 x 10 -11 N m 2 /kg 2 ( 3.00 m ) 2 ( 4.00 x 10 -7 N ) m = 232 kg

11. 7. The gravitational force of attraction between two bowling balls, each of mass 6.0 kg, is 5.0 x 10 -9 N. Calculate the distance between the bowling balls. F g = 5.0 x 10 -9 N m 1 = m 2 = 6.0 kg G = 6.67 x 10 -11 N m 2 /kg 2 r = ? Solve for rF g = G m 2 r2r2 r2r2 r2r2 r 2 F g = G m 2 FgFg FgFg r 2 = FgFg G m 2 r = FgFg G m 2

12. F g = 5.0 x 10 -9 N m 1 = m 2 = 6.0 kg G = 6.67 x 10 -11 N m 2 /kg 2 r = ? 7. = 5.0 x 10 -9 N ( 6.67 x 10 -11 Nm 2 /kg 2 )( 6.0 kg ) 2 r = 0.69 m r = FgFg G m 2

13. 8. The gravitational force of attraction between a rock of mass 10.0 kg and a rock of mass 40.0 kg is 5.5 x 10 -10 N. Calculate the distance between the rocks. = 5.5 x 10 -10 N ( 6.67 x 10 -11 N m 2 /kg 2 )( 10.0 kg )( 40.0 kg ) r = 6.96 m r = FgFg G m 2 F g = 5.5 x 10 -10 N m 1 = 10.0 kg m 2 = 40.0 kg G = 6.67 x 10 -11 N m 2 /kg 2 r = ?