The upper half of an inclined plane of inclination

Asked by admin @ 10/08/2021 in Physics viewed by 294 People

the upper half of an inclined plane with inclination (theta) is perfectly smooth while the lower half is rough a body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

Answered by admin @ 10/08/2021

For upper half which is smooth, the acceleration is g×sin(a).

Since the object starts from rest the final velocity when it reaches the end of upper half

is √( g×l×sin(a) ).

For the lower part the acceleration is ( g×sin(a) - μ×g×cos(a) ) due to friction

Since the object comes to rest when it reaches the bottom of inclined plane

we use the relation " u^2 + 2αs = 0 ", where α is acceleration.

Hence ( g×l×sin(a) ) = -2 ( g×sin(a) - μ×g×cos(a) ) (l/2)

Solving for μ we will get μ = 2 × tan(a)

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The upper half of an inclined plane of inclination

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