Posted by gallium on Wednesday, August 31, 2011 at 8:02pm.
work in the block=friction*distance
but friction force is mainly constant in the wood, so reducing the distance by 1/2 reduced the work absorbed by half
1/2 m 100^2 -1/2 m 10^2=friction work
so if friction work is halved, then that is added to the final KE.
final KE=1/2 m 10^2+1/2 (1/2 m 100^2-1/2 m 10^2)
final ke=1/2 m(10^2 + 1/2 10000 -1/2 100)
final ke=1/2m (50+5000)
1/2 m vf^2=1/2 m 5500
vf= sqrt 5500=75 m/s
check that work, I did it mostly in my head.
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