# Revolving Ball on String Problem

• PhysicsinCalifornia
In summary, the conversation is about a physics problem involving a 0.50-kg ball on a 1.5-m light cord revolving in a horizontal plane. The goal is to find the angle that the cord makes with the vertical, given that the ball is moving at 4.0 m/s. The conversation includes various attempts and suggestions for solving the problem, including the use of trigonometric identities and equations.
PhysicsinCalifornia
Another physics question for all you smart people out there

A 0.50-kg ball that is tied to the end of a 1.5-m light cord is revolved in a horizontal plane with the cord making a certain degree with the vertical. If the ball is moving at 4.0 m/s, how can I find the angle that the cord makes with the vertical?

This one is a toughie!

I worked on this a couple of hours, but I keep on running into the same dead ends, could anyone give us some pointers?

(This is the direction I've been trying to go with no luck)

Fx = Tsin(theta) = m((v^2)/r)
Fy = Tcos(theta) - Fg = 0

What does $r$ stand for in your equation?

Well, of course. I meant what value does $r$ take in your equation.

EDIT: Because, you know, it's not 1.5 m.

Last edited:
PhysicsinCalifornia said:
(This is the direction I've been trying to go with no luck)

Fx = Tsin(theta) = m((v^2)/r)
Fy = Tcos(theta) - Fg = 0
So far, so good. As I think Berislav was trying to point out, r depends on $\theta$: rewrite r in terms of the length and the angle. Also, realize that $F_g = mg$.

Then just eliminate T and solve for the angle. Hint: You may need to use a trig identity.

(Note: We can't tell where you got stuck, since you only showed the first step in your solution.)

Well,

I got up to where

tan(theta)sin(theta) = 1.088

I just need to find (theta) now.

Any help?

Thanks

Maybe this will help:
$$\sin^2\theta / \cos\theta = (1 - \cos^2\theta)/ \cos\theta$$

Yea, that was my next step.

**New info**

I was informed by my friend that I should use the half-angle identity for this!

I don't know how to answer this problem yet, but I'm getting there

Use what I gave you in post #7 and solve for $\cos\theta$. (Rewrite the expression as a quadratic equation in $\cos\theta$, then solve it.)

## 1. What is the "Revolving Ball on String Problem"?

The "Revolving Ball on String Problem" is a physics problem that involves a ball attached to a string, which is then attached to a fixed point. The ball is set in motion and revolves around the fixed point due to the tension in the string.

## 2. What factors affect the motion of the ball in this problem?

The motion of the ball is affected by a few key factors, including the length of the string, the mass of the ball, and the speed at which the ball is set in motion. These factors can impact the tension in the string and the centripetal force acting on the ball.

## 3. How does the tension in the string change as the ball revolves?

The tension in the string is constantly changing as the ball revolves. At the point where the ball is at its lowest point, the tension is at its maximum, while at the highest point, the tension is at its minimum. This is due to the varying centripetal force acting on the ball.

## 4. What is the relationship between the ball's speed and the tension in the string?

The speed of the ball has a direct impact on the tension in the string. As the speed increases, the tension in the string also increases. This is because a higher speed requires a larger centripetal force to keep the ball in its circular motion, resulting in higher tension in the string.

## 5. Can this problem be applied to real-life situations?

Yes, the "Revolving Ball on String Problem" can be applied to real-life situations, such as a ball attached to a string being swung around in a circle. This problem is also relevant in understanding the motion of objects in circular orbits, such as planets revolving around the sun.

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