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Grade: 11
        A body takes time reach the bottomof an inclined plane of angle theta with the horizontal.if the plane is made rough time taken now is 2t.the coefficient of friction of the rough surface is
2 years ago

Answers : (1)

Arun
23506 Points
							Dear student

Angle of incline = θ.
Initially it is a smooth surface.
Let the mass be m. Gravity g.
Initial velocity = u = 0.
acceleration down the incline = a = g sinθ
time taken = T.
So length of incline = s = 1/2 * g sinθ * T²  ...(1)
When there is dynamic friction of coefficient = μ,
friction force = f = μ N = μm g Cos θ
a = (sin θ - μ Cos θ) g  
Time taken is = 2 T
So we get: s = 1/2 * g (sinθ - μ Cos θ) * (2T)²    ...(2)
From (1) and (2) , we get
Sin θ = (sinθ - μ cosθ) 4
μ = Tanθ  * 3/4
 
Regards
Arun (askIITians forum expert)
2 years ago
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