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Q.

A body is moving down a long inclined plane of angle of inclination θ. The coefficient of friction between the body and the plane varies as μ=0.5x, where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by x=N tan⁡ θ . The value of N is

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Detailed Solution

The acceleration of the body down the plane is gsin⁡ θ−μgcos ⁡θ=g(sin ⁡θ−μcos⁡ θ)=g(sin ⁡θ−0.5 x cosθ). Therefore, the body will first accelerate up to x <2 tan θ. The velocity will be maximum at x =2 tan θ, because for x > 2 tan θ, the body starts decelerating.
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A body is moving down a long inclined plane of angle of inclination θ. The coefficient of friction between the body and the plane varies as μ=0.5x, where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by x=N tan⁡ θ . The value of N is