The upper portion of an inclined plane of inclination a is smooth and the lower portion is rough. A particle slides down from rest from the top and just comes to rest at the foot. If the ratio of the smooth length to rough length is 3:4, what is the coefficient of friction?
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Explanation:
Using kinematics equation for distance travelled in smooth region
v2=02+2a1S1a1=gsinα;S1=m⇒v2=2gsinαm
The ball comes to rest after traveling distance in rough region, applying kinematics equation for distance travelled in rough region
02=v2+2a2S2v=2gsinαma2=μgcosα−gsinαS2=n
⇒gsinαm=2×μgcosα−gsinα×n
dividing equation by gcosα
tanαm=(μ−tanα)n
μ=nm+ntanα
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