1. Gravitation Problems Answers 1. Find the gravitational force of attraction between two elephants, one of mass 1.00 x 10 3 kg and the other of mass 8.00 x 10 2 kg, when they are separated by 5.0 m. F g = m 1 = 1000 kg m 2 = 800 kg r = 5.0 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 )( 1000 kg )( 800 kg ) ( 5.0 m ) 2 F g = 2.1 x 10 -6 N

2. 2. What is the gravitational force between a 90.0-kg man and his 35.0-kg dog when they are 3.0 m apart? F g = m 1 = 90.0 kg m 2 = 35.0 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 )( 90.0 kg )( 35.0 kg ) ( 3.0 m ) 2 F g = 2.3 x 10 -8 N

3. 3. The gravitational force between two rocks is 2.0 x 10 -4 N. They are separated by 2.0 m and one rock has a mass of 3.00 x 10 3 kg. Find the mass of the other rock. F g = 2.0 x 10 -4 N r = 2.0 m m 1 = 3.00 x 10 3 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 = 2.0 x 10 -4 N r = 2.0 m m 1 = 3.00 x 10 3 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 )( 3.00 x 10 3 kg ) ( 2.0 m ) 2 ( 2.0 x 10 -4 N ) m 2 = 4.0 x 10 3 kg

5. 4. Two spaceships are floating in space. Ship 1 has a mass of 2.00 x 10 4 kg and is 3.50 x 10 2 m away from Ship 2. The gravitational force between them is 2.5 x 10 2 N. Find the mass of Ship 2. F g = 2.5 x 10 2 N r = 350 m m 1 = 20 000 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 = 2.5 x 10 2 N r = 350 m m 1 = 20 000 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 )( 20 000 kg ) ( 350 m ) 2 ( 2.50 x 10 2 N ) m 2 = 2.3 x 10 13 kg Solve for m 2

7. 5. Two bowling balls each have a mass of 7.0 kg. The gravitational force of attraction between them is 2.5 x 10 -9 N. Find the distance between them. F g = 2.5 x 10 -9 N m 1 = m 2 = 7.0 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 G m 1 m 2 = r2r2 = m

8. F g = 2.5 x 10 -9 N m 1 = m 2 = 7.0 kg G = 6.67 x 10 -11 N m 2 /kg 2 r = ? 5. = 2.5 x 10 -9 N ( 6.67 x 10 -11 Nm 2 /kg 2 )( 7.0 kg ) 2 r = 1.1 m r = FgFg G m 2

9. 6. The gravitational force of attraction between two asteroids is 3.60 x 10 -6 N. The mass of one asteroid is 1.500 x 10 3 kg and the mass of the other is 6.500 x 10 3 kg. Find the distance between them. = 3.60 x 10 -6 N ( 6.67 x 10 -11 N m 2 /kg 2 )( 1500 kg )( 6500 kg ) r = 13.4 m r = FgFg G m 2 F g = 3.60 x 10 -6 N m 1 = 1500 kg m 2 = 6500 kg G = 6.67 x 10 -11 N m 2 /kg 2 r = ?