# Simple pendulum problem

1. Nov 22, 2007

### SciencePF

1. The problem statement, all variables and given/known data

A sphere of mass 0,5 kg bounces from 2 extreme positions like a pendulum. When it makes a 25º with vertical the sphere is 20 cm high from equilibrium position and the tension value is 5,5 N.

Find:

- Total acceleration
- Length of the wire
- velocity modulus in that position
- minimum value for the tension in the wire

2. Relevant equations
T-mgcos$$\theta$$=mv2/r
-mgsin$$\theta$$=ma

3. The attempt at a solution
5,5-0,5+10cos25=0,5v2/r
-0,5*10sin25=0,5at

in the previous expressions v2 is v square and at is tangential acceleration

I dont know how to find v or r (the lenght of the pendulum). Can you help? Thanks

2. Nov 22, 2007

### katchum

I think you could introduce: mgh = 1/2mv^2 to find v.
And somehow you use 20cm to calculate h.

3. Nov 22, 2007

### SciencePF

i think that your suggestion only gives v if the pendulum has started its motion from an angle that corresponds to h=20 cm.

4. Nov 22, 2007

### SciencePF

Hello, friends!
A great help would be if someone can say that this problem has a solution!

5. Nov 22, 2007

### Shooting Star

Drawing a diagram and dropping a perp on the vertical at the mean position from the bob when it's at 25 deg, r-20 = r*cos 25 gives you r, where r is the length of the pendulum. Now find v.

6. Nov 22, 2007

### SciencePF

Thanks very much to all :)