# Pendulum problems - determine speed of the ball

1. Nov 4, 2007

### logglypop

A ball is attached to a string with length of L. It swings in a horizontal circle, with a constant speed. The string makes an angle (theta) with the vertical, and T is the magnitude of the tension in the string.

1)Determine the Mass of the Ball.
2)Determine th Speed of the Ball.
3)Determine the Frequency of revolutions of the Ball.

1)
F=Tsin(theta)=ma
m= (Tcos theta)/g

2)
F= (mv^2)/a= Tsin(theta)
v^2= [ aTsin(theta) ] / m
v= square root of [ aTsin(theta) ] / m

3)
T= 2pi time square root of (l /g)
frequency= 1/t
frequency= 1/ [ 2pi time square root of (l /g) ]

I need comment about my solution. Thanks

2. Nov 4, 2007

### learningphysics

Looks good.

don't you mean F = mv^2/r =Tsin(theta) ? and what is r?

also, your final answer should not have m in it... you should write your answer in terms of the given values of L, theta and T.

Not sure about part 3 (might be right)... I think it's better to use your v value to derive the frequency. try to use the v value along with the circumference of the circle to get the frequency... might come out to what you have above, in which case you've double checked your answer.

3. Nov 4, 2007

### logglypop

I got new approach on number 2

Tcos(theta)- mg= 0
T= mg/[cos(theta)]

F=Tsin(theta)
F= mg/[cos(theta)] * sin(theta) subtitute for T
F=mgtan(theta)

F=(mv^2)/r r=Lsin(theta)
mgtan(theta)=(mv^2)/ Lsin(theta)
v= square root of gLtan(theta)sin(theta)

4. Nov 4, 2007