Velocity Problem of neutron star

[Cursed]

Homework Statement

A neutron star has a mass of 2.0 x 10³⁰ and a radius of 5.0 x 10³. Suppose an object falls from rest near the surface of the star. How fast would it be moving after it had fallen a distance of 0.010 m? (Assume that the gravitational force is constant over the distance of the fall, and that the star is not rotating.)

Homework Equations

(a) F=(G*m₁*m₂)/r²
(b) F=ma
(c) V²=V_o² + 2ax

The Attempt at a Solution

Using equation (a), I found the force to be about 1.068 x 10⁴³ N

Using equation (b), I found the acceleration to be 5.338 x 10¹²

Using equation (c), I found the velocity to be 231042.68 m/s after the object had fallen a distance of 0.01 m.

 

[Dick]

What's the question? b) looks fine. I don't see how you got a) since you didn't give a mass for the object. c) doesn't look correct numerically.

 

[Cursed]

What's the question? b) looks fine. I don't see how you got a) since you didn't give a mass for the object. c) doesn't look correct numerically.

Yeah, (c) didn't look right.

For (a), I squared the mass because I only had one mass given, and that was 2 x 10³⁰. Then I divided it by the distance squared, which I used 5 x 10³ for, and multiplied it by G.

F = (G*M²)/r²

 

[Dick]

If you did that then the force in a) is the force between two neutron stars with centers 5000m apart. For c), I don't mean that it's REALLY wrong, it just looks like somebody forgot a 2.

 

[Nabeshin]

Yeah you don't want to be doing any mass squaring on this one. What happens is you set F=ma in the Gm1m2/r^2 equation and the m of the falling object cancels out, so it's not needed to solve the problem.

 

[Cursed]

Now I'm confused. :s

So what equation(s) would I use to go about solving this?

 

[Dick]

If M is the neutron star mass and m is the mass of the object, F=G*M*m/r^2. (If they don't give you a value for m, that's all you can say). Since we also have F=m*a, a=G*M/r^2.