Calculating Gravity Using Angular Speed and Weight

[bodensee9]

Homework Statement

Suppose I tie a ball of mass M to a string of length L and I swing the ball on the string in a vertical fashion. If the speed at the top is V1 and the speed at the bottom is V2.
Would I have:

Let T = tension in string
(top) -T - Mg = -MV1^2/R
(bottom) T - Mg = MV2^2/R

So to find Mg (the force of gravity), I would add the 2 equations to get:

-2Mg = MV2^2/R - MV1^2/R.

But somehow that is wrong?
Thanks.

 

[method_man]

Are you talking about something similar to http://3.bp.blogspot.com/_2XJwgH8jh...CWmF3XojwI8/s400/physics+simple+pendulum.png"? If you do, you forgot to take the angle into consideration.

 

[rl.bhat]

When the ball is moving through the bottom with velocity V2 its kinetic energy = 1/2*m*v2^2. As it moves towards the top, its kE decreases but its PE increases. At the top, KE = 1/2*m*v1^2 and rise in PE = 2mgR.Apply conservation of energy to find mg.