Circular Motion of a Marble: What Determines the Speed at a Given String Length?

[klc2006]

Homework Statement

You swing a marble with mass m attached to the end of a string in a horizontal circle as shown in the figure below. The angle that the string makes with the vertical is
θ = 37°.

(a) Find the speed of the marble when the string is 26.0 cm long.

Homework Equations

soh,cah,toa

Ar = v^2/r
4ii^2r/T

The Attempt at a Solution

I solved for the radius by using trig, but now I don't know what to do. Without mass or revloutions, I don't know how to solve form the speed.

 

[ehild]

Draw the free body diagram: What forces act on the marble? What is the resultant when the marble moves along a horizontal circle? You do not need the value of the mass: it will cancel.


ehild

 

[klc2006]

You have gravity and force of tension

 

[ehild]

Yes, and what is their resultant?

ehild

 

[klc2006]

I actually have no idea. I'm blanking out.

 

[NihalSh]

I actually have no idea. I'm blanking out.

if its moving in circle, then some force should be providing centripetal force. Here that force is horizontal component of tension. And since the ball isn't moving up or down, force of gravity should be balanced by some other force, namely vertical component of tension.

just as ehild said, making free body diagram would make it more clear.

 

[ehild]

I actually have no idea. I'm blanking out.

The resultant of the tension and gravity is equal to the (horizontal) centripetal force. How is it related to mg and the angle of the string with the vertical ?


ehild