A 1.75 kg block at rest on a ramp of height h. When the block isreleased, it sli

Question

A 1.75 kg block at rest on a ramp of height h. When the block isreleased, it slides without friction to the bottom of the ramp, andthen continues across a surface that is frictionless except for arough patch of width 10.0 cm that has a coefficient of kineticfriction k=0.640. Find h such that the block'sspeed after crossing the rough patch is 3.50 m/s.

Explanation / Answer

The equation of motion for the block is         F = m g sin -k m g cos ==> a = g ( sin - k cos ) The speed of the block at the bottom of the inclined planeis v = 2 a L             = [ 2 * L * g ( sin - kcos ) ]             = [ 2 gL sin - 2gLk cos )]            = [ 2 gh - 2gLk cos )]             ( sin = h / L ) ==> h   = [(v2 / 2g) + Lk cos] Substitute all the values. I hope this helps you

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