The figure shows a ball with mass m attached to a thin rod with length L and neg

Question

The figure shows a ball with mass m attached to a thin rod with length L 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 in the horizontal position as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertical position with zero speed there. (Use any variable or symbol stated above along with the following as necessary: g.)

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

vleft = sqrt(2gL) Correct: Your answer is correct. m/s

(b) What is the ball's speed at the lowest point?

vbottom = sqrt(Vi^2 + 2gL)

Incorrect: Your answer is incorrect. m/s

(c) What is the ball's speed at the point on the right at which the ball is level with the initial point?

vright = vright

Incorrect: Your answer is incorrect. m/s

Explanation / Answer

a)Conserving energy between initial and final point,

0.5mv2=mgl

v=sqrt(2gl)

b)Conserving energy between initial and bottom point,

0.5mv2+mgl=0.5mv'2

v'=sqrt(v2+2gl)=2sqrt(gl)

c)Since they are at same height as initial point, speed is same as initial point.

v=sqrt(2gl)

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