Solving the Pendulum Problem: Mass, Speed, Frequency and Trajectory

[ice97531]

Ok here is what I know:
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.

Determine the Mass of the Ball.
Determine th Speed of the Ball.
Determine the Frequency of revolutions of the Ball.
Suppose the strings breaks as the ball swings in its circular path. Describe the trajectory of the ball after the strings breaks but before it hits the ground.

Good luck.

 

[ice97531]

By the way...
I'm not just posting here cuase i don't want to do it
I've been working on it forever
This is the only part I can't figure out

 

[Jupiter]

The ball moves in a circle with uniform speed. So its acceleration is given by
$$a=\frac{v^2}{r}$$ where r is the radius of the circle.
You can find r rather easily.
There is only one force that can provide this acceleration and that is the tension T. Gravity acts down, and so it won't produce a centripetal acceleration. However, only the horizontal component of T will provide an acceleration. The vertical component acts up and merely counteracts the gravity. So,
$$F_{net}=Tsin\theta=ma$$
I mentioned that the vertical component of the tension counteracts gravity. This is true by Newton's second law.
$$mg=Tcos\theta$$
You can now find the mass and speed of the ball. The frequency is rather easy. You must know that
$$T=\frac{2\pi r}{v}=\frac{1}{f}$$

 

[ice97531]

I'm still a little confused
Tell me if my thinking is right

For the mass I got:
F=Tsin(theta)=ma
therefore:
(Tsin(theta)) / 9.8 = m

Is this right?

or do I use the cos instead of sin to find the mass?

 

[himanshu121]

it should be cos

 

[himanshu121]

For the last part the motion will be projectile with initial velocity which is in horizontal direction and tangentially to the circle