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**A 2.8 kg block is dropped from a height of 5.8 m (above the top of the spring) onto a spring of spring constant 3955 N/m. Find the speed of the block when the compression of the spring is 15.0 cm.**

x=0.15m

k=3955N/m

m=2.8kg

E

_{initial mech}=E

_{final mech}

U

_{si}+U

_{gi}+K

_{i}=U

_{sf}+U

_{gf}+K

_{f}

U

_{si}=0 because the spring is uncompressed

U

_{gi}=???

K

_{i}=.5mv

_{i}

^{2}where [tex]V_i =sqrt(2g*5.8m)=10.868[/tex]

U

_{sf}=.5kx

^{2}

U

_{gf}=0 because I can set the height at that point to be 0

K

_{f}=.5mv

_{f}

^{2}where we're solving for v

How do I calculate the potential graviational energy? I'm guessing I need to find out how far the block would go if it were allowed to come to a rest, but I get an impossible to solve equation, or maybe I just don't remember what to do.

Block at rest:

U

_{si}+U

_{gi}+K

_{i}=U

_{sf}+U

_{gf}+K

_{f}

0+mgx + .5mv

^{2}

_{i}=.5kx

^{2}

x(mg-.5kx)=-.5mv

_{i}

^{2}

x(27.468-1977.5x)=-165.359

x=???

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