# Energy and momentum - pendulums

1. Nov 16, 2008

### FrenchAtticus

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

A heavy ball swings on a string in a circular arc of radius 1m.
The two highest points of the ball's trajectory are Q and Q'; at these points the string is +/- 20 degrees from the vertical. Point P is the lowest point of the ball's trajectory where the string hangs vertically down. The acceleration of gravity is 9.8 m/s^2.

1.) What is the ball's speed at the point P? Neglect air resistance and other frictional forces.
2.) What is the magnitude of the ball's acceleration at the point P?
3.) What is the ball's speed at the point Q?
4.) What is the magnitude of the ball's acceleration at the point Q?

2. Relevant equations

mgh1 + 1/2mv1^2 = mgh2 + 1/2mv2^2

3. The attempt at a solution

9.8(1-cos(20)) + 1/2v1^2 = 0 + 1/2v2^2
0.591 + 1/2v1^2 = 1/2v2^2

How can I solve this with two unknowns?

2. Nov 16, 2008

### LowlyPion

Why do you think there are 2 velocities to consider?

PE at highest = KE at lowest

m*g*h = m*v2/2