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# the upper half of an inclined plane with  inclination fi 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 coefficient of friction for the lower half is

hunaid
13 Points
3 years ago
suppose length of plane is L.
when block descends the plane, rise in kinetic energy = fall in potential energy = mgLsinθ ---eq (1)
work done by friction is :  μ*(reaction)*distance
0  + μ(mgcosθ )*(L/2)
=  μ(mgcosθ )*(L/2)
[work done against friction for the upper half of plane is zero]
Now work done = change in KE
mgLsinθ =  μ(mgcosθ )*(L/2)
tanθ =  μ/2
μ = 2tanθ
11 months ago
Dear student,

Suppose length of plane is L.
when block descends the plane, rise in kinetic energy = fall in potential energy = mgLsinθ ---eq (1)
work done by friction =  μ(mgcosθ )*(L/2)
Now work done = change in KE
mgLsinθ =  μ(mgcosθ )*(L/2)
tanθ =  μ/2
μ = 2tanθ

Thanks and regards,
Kushagra