Uniform Circular Motion of an object

[brutalmadness]

Homework Statement

A horizontal force of 210N is exerted on a 2.0kg object as it rotates uniformly on a horizontal plane with a radius of 0.9m. Calculate the speed of the object.

Homework Equations

I THINK the relevant equations for this problem are v=2\Pir/T and ar=v^2/r.

The Attempt at a Solution

v=2\pi0.9/?
ar=?/0.9

My biggest problem is that for the life of me, I can't figure out how to find either the T or the v. If I knew how to do that, I could figure out the problem. I've also drawn a diagram of the problem.

 

[Galileo's Ghost]

You won't need to find T. Use your equation for "ar" as you suggest, but remember Newton's Second Law... F = ma. Since you know the Force, v can be calculated. No T needed, but if you are curious, T can be calculated now that you know v!

 

[PhanthomJay]

Homework Statement

A horizontal force of 210N is exerted on a 2.0kg object as it rotates uniformly on a horizontal plane with a radius of 0.9m. Calculate the speed of the object.

Homework Equations

I THINK the relevant equations for this problem are v=2\Pir/T and ar=v^2/r.

The Attempt at a Solution

v=2\pi0.9/?
ar=?/0.9

My biggest problem is that for the life of me, I can't figure out how to find either the T or the v. If I knew how to do that, I could figure out the problem. I've also drawn a diagram of the problem.

All you need to know is that the radial acceleration (or centripetal acceleration ) is v^2/r, as you have noted. Then use Newton's 2nd law in the radial (centripetal) direction to calculate v, the tangential speed .

 

[brutalmadness]

In this case, would my F=m(a) be 2.0(210)?

I'm thinking I need to find "a" first... perhaps a=Fnet/m?

 

[Galileo's Ghost]

In this case, would my F=m(a) be 2.0(210)?

No...F = 210, m = 2.0, a is given by the equation you have stated...v^2/r

 

[brutalmadness]

Hmmm...

F=ma and a=v^2/r... F=m(v^2/r)

v^2/r=F/m

v^2=Fr/m

v=sqrtFr/m

v=sqrt 210(.9)/2.0

v= 9.7 m/s^2

 

[azatkgz]

Right!

 

[brutalmadness]

thank you guys so much :D