# What is the tension as a function of theta

1. Mar 18, 2005

### amackeytexas

Need some help with this answer.
A mass m on the end of a string in length L. At the bottom it is given a push to a speed V. What is the tension as a function of theta, where theta is the angle from the intial position?

2. Mar 18, 2005

### Staff: Mentor

Start by identifying the forces acting on the mass. Then apply Newton's 2nd law, realizing that the mass is centripetally acceleration. Conservation of energy will come in handy as well.

3. Mar 18, 2005

### amackeytexas

Thanks. How close is this? mv^2/L=Tcos theta

4. Mar 18, 2005

### Staff: Mentor

Check it for $\theta = 0$. Does it make sense? (What forces act on the mass at that angle?)

5. Mar 18, 2005

### amackeytexas

forces at that angle are Tsin theta=mg

6. Mar 18, 2005

### clive

Hi makeytexas,

in order to find the corect answer you must take into account the energy's conservation law too:

$$\frac{m v_0^2}{2}=\frac{m v^2}{2}+m g L cos \theta$$

where $$v_0$$ is the initial speed.

The static equilibrium condition along the string direction would be

$$T=mg cos \theta + \frac{m v^2}{L}$$

.......

Last edited: Mar 18, 2005
7. Mar 19, 2005

### Staff: Mentor

That should be:
$$\frac{m v_0^2}{2}=\frac{m v^2}{2}+m g L (1 - cos \theta)$$

8. Mar 19, 2005

### clive

You're right Doc Al !

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