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

The figure shows a ball with mass m = 0.405 kg attached to the end of a thin rod with length L = 0.516 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically up position, with zero speed there.

(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 11:56am
Got it, thanks very much!

## Answer this Question

## Related Questions

- Physics - The figure below shows a thin rod, of length L and negligible mass, ...
- physics - Figure 8-31 shows a ball with mass m = 1.0 kg attached to the end of a...
- Physics/Math - A thin rod, of length L and negligible mass, that can pivot about...
- Physics - A thing rod of length L and negligible mass, that can pivot about one ...
- physics - Two blocks, each of mass m, are attached to the ends of a massless rod...
- Physics - A 2.5 m rod of mass M= 4. kg is attached to a pivot .8m from the left ...
- Physics - A thin rod, of length L and negligible mass, that can pivot about one ...
- mechanics - The figure below shows a ball with mass m = 0.299 kg attached to the...
- Physics - A mass of 100g is attached to one end of a massless rod, 10cm in ...
- physics - A mobile is constructed from a thin rod of mass 50 g and length 50 cm...