First slide

Kinetic friction

Question

The upper half an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom. The coefficient of friction between the block and the lower half of the plane is given by

Moderate

A

µ = 2tanθ
B

µ = tanθ
C

µ = 2/tanθ
D

µ = 1/tanθ

Solution

For the upper half acceleration = gsinθ and v² = 0 + 2.gsinθ.l/2.....(1)
For the lower half retardation a = g(µsinθ - sinθ) and 0 = v² - 2.a.l/2....(2)
From (1) and (2): 2gsinθ.l/2 = 2.g(µcosθ - sinθ).l/2 ⇒ µ = 2tanθ.

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