Tricky(?) Centripetal Motion Problem

[realslow]

Homework Statement

I whirl a 'tennis ball on a string' above my head (horizontally) with a period of 0.75 seconds. The ball has a mass of 150 g and the circular motion has a radius of 0.95 m. What is the downward angle of the string from the horizontal, the tension in the string, and the string length?

Homework Equations

Fc = 4π²mRf²

The Attempt at a Solution

Okay, I tried for very long to get to the answers .. with no success.
I think I am having trouble getting the situation set up.
I tried using like a banked curve situation to split into vertical and horizontal..
I think I can get Fc, but I am stuck after that :(
Please help!

 

[ehild]

First make a drawing. Show the forces. The resultant is equal to the centripetal force.

ehild

 

[Doc Al]

What forces act on the ball? Draw a free body diagram. What's the ball's acceleration?

Analyze horizontal and vertical force components using Newton's 2nd law.

 

[realslow]

Okay, thank you, I will try the question again!

 

[realslow]

Would the net force of the vertical component be 0?

 

[ehild]

Yes. But you need a long arm to whirl that ball above your head :)

ehild

 

[realslow]

Okay, I will consider that, thanks!
I'm really having trouble with this question..
For the horizontal component, does F_C = F_T - F_app in this case?

 

[ehild]

What is Fapp? Draw those forces. What forces act on the ball?

ehild

 

[realslow]

F_app would be Fgsinθ
The forces I drew were F_T, F_app, Fg and F_N
Maybe I'm not drawing the diagram right :( should I have two separate diagrams for horizontal and vertical? Because I'm only drawing one...

 

[ehild]

You have too many forces. Look at the ball. What forces act on it?

ehild

 

[realslow]

I know tension force is for sure, but isn't gravity working on it as well?

 

[realslow]

Oh I guess so, I just noticed your diagram hehe sorry :)

 

[ehild]

The resultant has to be equal to the centripetal force, and it is horizontal. Calculate the centripetal force. You need the angle of the thread with the horizontal. But it is the same as the direction of T. You have right triangles composed of the forces, find the angle. I go to sleep...

ehild

 

[realslow]

Alright, I will try once again! Thanks for the help :) Good night!

 

[ehild]

Alright, I will try once again! Thanks for the help :) Good night!

How are you getting on?

ehild

 

[realslow]

It's not going so well :( this question is really making me depressed *sighs*
I tried getting the angle, but I can't. I've tried getting two equations for the unknown angle, but I only ended up with one, so.. I'm at a dead end.

 

[ehild]

You see the forces in the picture: red for the tension, green for the force of gravity. Their resultant is the centripetal force, and it is horizontal. These three forces make a right angle. You can calculate the magnitude both of the centripetal force and gravity. How is related alpha to Fcp and G?

The other approach is decomposing the tension into vertical and horizontal components. The vertical component is of equal magnitude and opposite to G. The horizontal component is equal to the centripetal force.

You can calculate the centripetal force from the given data: period, radius, mass.

ehild

 

[realslow]

Ahh thank you so much! Many many thanks :D I finally got the correct answer!
However, I would really appreciate it if you could explain why the three forces made a triangle :) I'm thinking along the lines of vectors, but I'm not too sure..

 

[ehild]

Do you know how to add vectors?

ehild

 

[realslow]

Yes, I do :)
So I guess my vectors reasoning was pretty accurate then!
Thank you soooo much for your help!