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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

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

Grade:12

2 Answers

hunaid
13 Points
6 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
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the answer to your question.
 
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

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