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A pendulum consists of a bob of mass M and a rigid rod of length ℓ with negligible mass. The bob is struck by a bullet of mass m. The bullet passes through the bob and emerges with a speed half that of impact. The shot causes the pendulum to swing through a complete circle, but the bob only barely passes the top of the circle. Find v, the impact speed of the bullet.

v

This is what I done so far:

(at beginning position h=0 therefore potential energy =0)

1/2mv

For pendulum to go in a verticular circular motion at min velocity F

then: mv

so plugging this in makes:

1/2mv

cleaning this up we have

v

Am I right in my thinking?. If not can someone explain where I went wrong and how to fix it?

A pendulum consists of a bob of mass M and a rigid rod of length ℓ with negligible mass. The bob is struck by a bullet of mass m. The bullet passes through the bob and emerges with a speed half that of impact. The shot causes the pendulum to swing through a complete circle, but the bob only barely passes the top of the circle. Find v, the impact speed of the bullet.

v

_{1}is speed of bullet before impact, v_{2}is speed of bobThis is what I done so far:

(at beginning position h=0 therefore potential energy =0)

1/2mv

_{1}^{1}= 1/2m(v_{2}/2)^{2}+Mg2l (since h at top = 2l)For pendulum to go in a verticular circular motion at min velocity F

_{c}= F_{g}then: mv

^{2}/l = mg => v^{2}= glso plugging this in makes:

1/2mv

_{1}^{2}= mv_{1}^{2}/8+M2v_{2}^{2}cleaning this up we have

v

_{1}^{2}= 2(mv_{1}^{2}+ 16Mv_{2}^{2})/8mAm I right in my thinking?. If not can someone explain where I went wrong and how to fix it?

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