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December 20, 2014

December 20, 2014

Posted by **Anonymous** on Sunday, October 23, 2011 at 10:31pm.

(a) What initial speed must be given the ball so that it reaches the vertically upward position with zero speed?

(b) What then is its speed at the lowest point?

(c) What then is its speed at the point on the right level with the initial point?

(d) If the ball's mass were doubled, would the answers to (a) through (c) increase, decrease, or remain the same?

Can I start with h = L - L*cos(theta) = L(1 - cos(theta))? Where do I go from there?

- PHYSICS -
**drwls**, Monday, October 24, 2011 at 6:04am(a) Use conservation of energy. To reach the top with zero velocity

(1/2) M Vo^2 = M*g*L

Vo = sqrt(2 g L)

(b) At the lowest point,

(1/2)MV^2 = (1/2) M Vo^2 + M g L

V^2 = Vo^2 + 2 g L

= 4 g L

V = 2 sqrt(g L)

(c) What do you think? The P.E. is the same.

(d) Note that M does not appear in any of the answers above. What does that tell you?

- PHYSICS -
**Anonymous**, Monday, October 24, 2011 at 11:56amGot it, thanks very much!

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