# Gravitational force

1. Jan 10, 2010

### stargirl17

1. The problem statement, all variables and given/known data

1. Write an equation for the gravitational force between two objects that are separated by a distance r

2. Write an equation for the force to mass ratio (acceleration) on a planet with mass M and radius R.

3. What happens to the gravitational force between two objects if the masses remain constant while the distance between the two masses decreases to .5 the original separation distance? (circle your answer)

a. 1/2 as great as the original force.
b. 1/4 as great as the original force/
c. 2.5 times as great
d. 4 times as great
e. 25 times as great

4. The force between two planets is 2 X 107 N. What will be the force if the mass of one of the planets is doubled, the mass of the other planet is tripled and the distance between the planets is reduced to 3/4 the original value?

2. Relevant equations

Fg= Gm1m2/ r^2

3. The attempt at a solution

2. Jan 10, 2010

### rock.freak667

Before we can help, you need to post some attempt.

Since you have this, I think you can answer the first two parts and make an attempt at the 3rd part.

3. Jan 10, 2010

### stargirl17

i know the first one is the same as the equation. But i don't know how to do the others because i was on a field trip friday when the class went over this. could i have some hints or help?

4. Jan 10, 2010

### rock.freak667

For the third one, try replacing 'r' in the equation by 'r/2' and see how that relations to original force F(=GMm/r2)

5. Jan 10, 2010

### stargirl17

oh so it would be b) 1/4?

6. Jan 10, 2010

### rock.freak667

$$F'=\frac{GMm}{(\frac{r}{2})^2}$$

if you are dividing by (r/2)2, what does it become?

7. Jan 10, 2010

### stargirl17

4 times as great

8. Jan 10, 2010

### rock.freak667

Good, now just apply a similar method for number 4

9. Jan 10, 2010

### stargirl17

awesome thank you :)
can i have a hint about 2?

10. Jan 10, 2010

### rock.freak667

$$F=\frac{GMm}{r^2}$$

they want the force(F) to mass of a body ratio. Mass of the planet is M. Mass of the body is m.

11. Jan 10, 2010

### stargirl17

isn't that the answer for 1?

12. Jan 10, 2010

### rock.freak667

That's why you need to divide both sides by an 'm'

13. Jan 10, 2010

### stargirl17

oh ok cool. do u think i should just leave the answer as Fg/m= (Gm1m2/ r^2)/m

14. Jan 10, 2010

### jegues

a = fg/m = GM/(r^2) should be fine.

Edit: let me clarify this,

a = (fg) / (m) = (GM)/(r^2)

15. Jan 10, 2010

m/r2 : 1/r2