# Tension in a String just before it breaks (Circular Motion)

1. Oct 22, 2007

### parkskier

1. The problem statement, all variables and given/known data
A 120 g ball on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor. The string suddenly breaks when it is parallel to the ground and the ball is moving upward. The ball reaches a height of 650 cm above the floor. What was the tension in the string an instant before it broke?

2. Relevant equations
Vf^2-Vi^2=2aS

3. The attempt at a solution
I used the above equation to find the intial velocity when it breaks away from the string. Here's how I set that up:

(0)^2-(Vi)^2=2(-9.8)(.45)

This yielded: Vi= 2.969 m/s
Now my problem is how do I use this velocity to find the tension of the string just before it breaks?

2. Oct 22, 2007

### bob1182006

Draw the FBD and see what forces are acting on the ball and where the Tension fits in.

also you're missing one important equation:

$$\vec{a}=\frac{\vec{v}^2}{R}$$

3. Oct 22, 2007

### parkskier

Okay, so my FBD looks like this:

Tension<------
....................|
....................|
....................V
..................mg

So...the only force in the x direction is Tension. The force of tension is F=ma, so using the equation you gave me I get my a to be 14.691 m/s^2, then multipling by the mass I get the Force of Tension to be 1.76, but this isn't right. Is there some way I need to incorporate the weight into the equation, I'm sure there must be.

4. Oct 22, 2007