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**1. Homework Statement**

A bullet of mass m and speed v passes completely through a pendulum bob of mass

M. The bullet emerges on the other side of the pendulum bob with half its original

speed. Assume that the pendulum bob is suspended by a stiff rod of length L and

negligible mass. What is the minimum value of v such that the pendulum bob will

barely swing through a complete vertical cycle

**2. Homework Equations**

m

_{1}v

_{1i}

^{2}+ m

_{2}v

_{2i}

^{2}= m

_{1}v

_{1f}

^{2}+ m

_{2}v

_{2f}

^{2}

w=Δk+Δp

k = 1/2mv

^{2}

p = mgh

**3. The Attempt at a Solution**

initial kinetic energy of bullet = potential energy of bob @ max height + final kinetic energy of bullet

1/2mv

^{2}= Mg2L + 1/2 m(1/2v)

^{2}

1/2mv

^{2}- 1/8 mv

^{2}= 2MgL

3/8mv

^{2}=2MgL

v

^{2}= (16MgL)/(3m)

v = 4[(MgL)/(3m)]^(1/2)

Answer is [4M(gL)^(1/2)]/m

The key sets

1/2MV

_{b}

^{2}= Mg2L

if V

_{b}= velocity of the bob, then at max height the bob is not moving hence velocity is 0 and all of the energy that the bob carried at the bottom is now potential energy.

and then solves via the equation:

mv = MV

_{b}+ mv/2

initial momentum = momentum of bob + momentum of bullet after going through bob

If everything that I have said about the professors method is true, then I feel like I am beginning to understand why the professors way works, but why doesn't my method come to the same conclusion.

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