Gravity

Apr 2008
13
0
Ireland
Hi all, I'm just looking a little direction here, not the answer, so if anyone can help, that would be great.

In a current assignment I have, I need "to obtain an expression for ga in terms of Newtons' universal gravitational constant G, the radius of te asteroid Ra and the density of the rock. And hence, determine Ra. (The volume of a sphere of radius R = 4/3*Pi*R^3)."

We are given the density of the rock, and told that an experiment was done on the asteroid which shows it takes a small object 4.20 seconds to fall 1 metre.

If anyone can point me in the right direction, that would be great! I think I have a mental block on this one, I just can't seem to find my way.

Cheers
Sean


PS - I put this in the wrong section, I meant to put it in the College section. Sorry.
 
Last edited:
Apr 2008
11
2
Pittsburgh, PA
Hi all, I'm just looking a little direction here, not the answer, so if anyone can help, that would be great.

In a current assignment I have, I need "to obtain an expression for ga in terms of Newtons' universal gravitational constant G, the radius of te asteroid Ra and the density of the rock. And hence, determine Ra. (The volume of a sphere of radius R = 4/3*Pi*R^3)."

We are given the density of the rock, and told that an experiment was done on the asteroid which shows it takes a small object 4.20 seconds to fall 1 metre.

If anyone can point me in the right direction, that would be great! I think I have a mental block on this one, I just can't seem to find my way.

Cheers
Sean


PS - I put this in the wrong section, I meant to put it in the College section. Sorry.
Since you know the acceleration due to gravity on the asteroid(you can find this, by finding velocity of the rock after 1 second using the kinematic motion equations) \(\displaystyle x_{f}=x_{0}+v_{0}t+\frac{1}{2}at^2\) \(\displaystyle (v_{0}=0)\)Solve for a, and you should get \(\displaystyle a=-.113\), you can set \(\displaystyle .113=F/m_{1}\)

You know the formula for gravitational force is \(\displaystyle F_{G}=G\frac{m_{1}m_{2}}{r^2}\)

So, since you know the densities of the two objects, you can rearrange the density formula and solve for mass so it reads \(\displaystyle m=D*V\) and replace the two m's in the formula with the densities. (m1, the mass of the small rock will cancel) and now you can see where to go from there. I can help you a little further, if you need.
 
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Apr 2008
13
0
Ireland
Hi,

Cool, thanks for the help..I think the way forward is bit clearer.

Sean