Write an equation for the gravitational force between two objects

[stargirl17]

Homework Statement

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?

Homework Equations

Fg= Gm1m2/ r^2

The Attempt at a Solution

 

[rock.freak667]

The Attempt at a Solution

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

Homework Equations

Fg= Gm1m2/ r^2

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

 

[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?

 

[rock.freak667]

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?

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

 

[stargirl17]

oh so it would be b) 1/4?

 

[rock.freak667]

oh so it would be b) 1/4?

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

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

 

[stargirl17]

4 times as great

 

[rock.freak667]

4 times as great

Good, now just apply a similar method for number 4

 

[stargirl17]

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

 

[rock.freak667]

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

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.

 

[stargirl17]

isn't that the answer for 1?

 

[rock.freak667]

isn't that the answer for 1?

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

 

[stargirl17]

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

 

[jegues]

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

Edit: let me clarify this,

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

 

[stargirl17]

m/r2 : 1/r2