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## Homework Statement

An 8.0 lb block is suspended from a spring with a force constant of 3.0 lb/ in. A bullet weighing 0.10 lb is fired into the block from below with a speed of 500 ft/sec and comes to rest in the block.

a) Find the amplitude of the resulting simple harmonic motions

b) What fraction of the original kinetic energy of the bullet is stored in the harmonic oscillator?

## Homework Equations

F = -kx

m

_{1}v

_{1}= m

_{2}v

_{2}

v = x

_{m}* ω

ω = √(k/m)

U = 0.5 kx

^{2}

K = 0.5 mv

^{2}

g = 32.2 ft/s

^{2}

## The Attempt at a Solution

For a)

m

_{1}v

_{1}= m

_{2}v

_{2}

v

_{2}= m

_{1}v

_{1}/m

_{2}

v

_{2}= [3.1 x 10

^{-3}slugs * 500 ft/sec] / [0.248 slugs]

= ~6.17 ft/sec

So:

v = x

_{m}* ω

= x

_{m}* √(k/m)

x

_{m}= v * √(m/k)

= 6.2 ft/sec * √[0.25 slugs / (36.0 lbs/ft)] *

*I converted from 3.0 lb/in here*

= 0.52 ft

...I solved that correctly, right?

and for b)

U

_{i}= 0

K

_{i}= 0.5m

_{1}*v

_{1}

^{2}

= 0.5 * (3.1x10

^{-3}slugs) * (500 ft/s)

^{2}

= 388 ft-lb

K

_{f}= 0

U

_{f}= 0.5*k*x

^{2}

= 0.5 * (36.0 lb/ft) * (0.52 ft)

^{2}

= 4.87 ft-lb

...Now, I imagine that quite a lot of energy would be "lost" as heat due to friction (and other, more complicated forces that this problem doesn't quite take into account) but this seems like a rather large fraction lost. Do I have an arithmetic error? Or did I just use the wrong formula?