Finding Speed of Object Under Central Force: Equations & Solution

[postfan]

Homework Statement

An object of mass M moves under the influence of an attractive central force F = - A r^4 \hat{r} where \hat{r} is a unit vector in the radial direction.
If the object is in a circular orbit of radius R , find its speed v as a function of M,A, and,R.

Homework Equations

a=v^2/r

The Attempt at a Solution

I rearranged the above equation to v=sqrt(ar). I know that the radius is R but I don't know what the acceleration is. Help!

 

[rude man]

What is the force necessary to keep a mass M in circular motion with radius R?

Equate this force with the given force.

 

[postfan]

I don't understand what you are saying.

 

[jhosamelly]

You need to think about the centripetal force.

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

That is the force needed to keep an object in circular motion. Equate this with your central force.

 

[D H]

$F = - A r^4 \hat{r}$

You also know the constant A, the radius R, and the mass M. So what's the acceleration?

 

[postfan]

I still don't understand. Could you please give me a hint?

 

[D H]

F=ma. Divide the force by the mass.