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Question

A block of mass m is kept over another block of mass M and the system rests on a horizontal surface (figure 8-E1). A constant horizontal force F acting on the lower block produces an acceleration F2 m+M in the system, and the two blocks always move together. (a) Find the coefficient of kinetic friction between the bigger block and the horizontal surface. (b) Find the frictional force acting on the smaller block. (c) Find the work done by the force of friction on the smaller block by the bigger block during a displacement d of the system.
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Solution

(a)
a=F2 M+m (given)

The free-body diagrams of both the blocks are shown below:




For the block of mass m,

ma=μ1R1 and R1=mgμ1=maR1=F2 M+m g

(b)
Frictional force acting on the smaller block,
f1=μ1R1=F2 M+m g×mg=mF2 (M+m)

(c) Work done, w = f1s [where s = d]
=mF2 M+m×d=mFd2 M+m

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