Rock hanging from ceiling swinging uniform circular motion

1. Feb 22, 2007

iamtheone

1. The problem statement, all variables and given/known data

A rock of mass 5.5kg is hanging from the ceiling moving in uniform circular motion. The radius of the orbit is .8m. The angle of the rope in comparison to if it were hanging straight down is 15 degrees outward.

What is the magnitude of the force of the cord on the mass? I already found out this is about 55.801 N

What is the magnitude of the acceleration of the rock?

What is the angular speed of the rock?

How many revolutions per second does the rock make?

2. Relevant equations

angular speed = v/r

f = ma

centripital accel = (v^2)/r

..others probably as well...

3. The attempt at a solution

*To get the magnitude of the acceleration of the rock:

Ftotal = Frope + Fweight = 109.701

plug in to F = ma, a=19.9457 (incorrect)

I'm guessing I need to include another force....or take the magnitude of both those force vectors added together? I don't know how to get the Frope force vector though.

Any help with thi swould be apreciated.

2. Feb 22, 2007

You mentioned centripetal acceleration, so there is a centripetal force, too.

3. Feb 22, 2007

iamtheone

i don't know how to calculate it. And I mentioned it merely because I THINK it applies.

4. Feb 22, 2007

Did you draw a free body diagram? What equations can you work out from the diagram?

5. Feb 22, 2007

iamtheone

I did, but I'm still pretty much clueless.

6. Feb 22, 2007

Well, regarding the second question, what kind of an acceleration does the rock possess?

7. Feb 22, 2007

iamtheone

centripetal, but i don't know the velocity, so I can't calculate that either...

8. Feb 22, 2007

Well, which equation did you use to obtain the force in the rope? Which equation can you use to obtain the magnitude of the centripetal force (and the velocity)?

9. Feb 22, 2007

iamtheone

I used Fcos(20) = mg -> which is just a version of f = ma

I can't find equations for the magnitude of the centripetal force or the velocity....which is very annoying. I've been looking in my book for a while now.

10. Feb 22, 2007

Can you find the magnitude of the centripetal force now?

11. Feb 22, 2007

iamtheone

that gives the acceleration....not force.

12. Feb 22, 2007

arildno

And force equals..?what?..*acceleration?

13. Feb 22, 2007

iamtheone

mass, but i can't calculate v - ive already tried this many times....i guess the question comes down to being able to calculate v.

14. Feb 22, 2007

arildno

The tension is given by T=mg/(cos(15)), not by mg/(cos(20)!

Now, what is the planar radial component of this tension?

15. Feb 22, 2007

denverdoc

well if v^2/r=a and R is known, then we need another eqn to solve for the a. You have Tension which you have calculated, what if you were to resolve that into x and Y components? edit: whoops didn't mean to butt in.