Please write explanation for each step. Stopped Pendulum Consider the \"Stopped

Question

Please write explanation for each step. Stopped Pendulum Consider the "Stopped Pendulum" demonstration from lecture. As the pendulum swings, its string hits a peg located some distance h below the suspension point (see figure). If the length of the string is L, (a) show (or make a convincing and correct argument) that the pendulum bob will return to the height it was released from if it is released from rest from a height below the peg and air resistance is ignored, (b) derive an expression for the minimum distance h, in terms of L, such that the bob will swing around the peg in a complete circle when released from 6-90°. Peg

Explanation / Answer

a) A fixed peg does no work on the pendulum. Therefore, no energy is lost and pendulum will have enough energy to return to the same initial height it was released from.

b) radius of circle made by peg = L - h

velocity where tension is minimum,

v2 = g(L-h)

Now using conservation of energy,

mgh = 1/2mv2 + mgh

mgh = 1/2mg(L-h) + mg(L-h)

m, g will cancel out on both sides

h = 1/2(L-h) + (L - h)

h = 3/2 (L-h)

h = 3L/5

  

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