A block of mass m , released from rest at the top of an incline, slides down a l

Question

A block of mass m , released from rest at the top of an incline, slides down a length s from a height h down to the ground. The coefficient of kinetic friction between the plank and the barrel is ?k . a) Derive an expression for the work done by the force of friction on the block, as it slides down a distance s. b) Derive an expression for the work done by the force of gravity on the block, as it slides down a distance s. c) Using the Work-Energy theorem, derive an expression for the change in kinetic energy of the block, between the beginning and end of its slide.

Explanation / Answer

assuming the incline does not move,
work done by friction = ND

= k X mgcos X s

cos = sqrt( 1- [h/s]^2 )

W.= k mg s( sqrt(  1- [h/s]^2 ) )

work done by gravity = mgh

chang in Ke =

mgh - W = 1/2mv^2

W= work done by friction.

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