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Question

A plank with mass M=6 kg rests on top of two identical, solid, cylindrical rollers that have radius R=4 cm and mass m=2 kg. The plank is pulled by a constant horizontal force F of magnitude 6 N applied to the end of the plank and perpendicular to the axes of the cylinders (which are parallel). The cylinders roll without slipping on the flat surface. Also, there is no slipping between the cylinders and the plank.
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The total friction acting on the plank in newton is (answer upto two decimal places)

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Solution

Let ap be the acceleration of the plank.
For plank,
62ft=6aP ...(1)
For rollers,
ftfb=2×ap2 ...(2)
Also, τ=Iα
(ft+fb)R=mR22ap2 ...(3)
Solving equations (1), (2) and (3),
ft=1 N,fb=1 N,ap=23 m/s2
total friction on the plank=2ft=2 N

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