# A 2.0- kg piece of wood slides on the surface. The curved sides are perfectly smooth, but the rough horixontal bottom is 30 m long and has a kinetic f

A 2.0- kg piece of wood slides on the surface. The curved sides are perfectly smooth, but the rough horixontal bottom is 30 m long and has a kinetic friction coefficient of 0.20 with the wood. The iece of wood starts fromrest 4.0 m above the rough bottom (a) Where will this wood eventually come to rest? (b) For the motion from the initial release until the piece of wood comes to rest, what is the total amount of work done by friction?
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Laith Petty
a) Use work-energy relation to find the kinetic energy of the wood as it enters the rough bottom
${U}_{1}={K}_{2}$

Now apply work-energy relation to the motion along the rough bottom
${K}_{1}+{U}_{1}+{W}_{other}={K}_{2}+{U}_{2}$
${\mu }_{k}mgs=78.4$
, then solve for s

b) Friction does -78.4 J of work