A block of mass 2 kg is released from rest on a rough incline of…
Question
A block of mass 2 kg is released from rest on a rough incline of angle 37 degrees (use sin 37 = 0.6, cos 37 = 0.8) with coefficient of friction 0.25 between block and incline. After sliding 4 m down the incline the block contacts a relaxed light spring of stiffness 8 N/m placed along the incline. Taking g = 10 m/s^2, find the maximum compression of the spring (in metres).
Step-by-step solution
The net force pushing the block down the incline (gravity minus friction) is F = mg(sin theta - mu cos theta) = 2*10*(0.6 - 0.25*0.8) = 20*(0.6 - 0.2) = 8 N, constant throughout the slide.
From release to maximum compression x, the block descends a distance (d + x) = (4 + x) along the incline and momentarily stops, so all the net work goes into the spring: F(d + x) = (1/2) k x^2 => 8(4 + x) = (1/2)(8) x^2 => 8(4 + x) = 4 x^2 => 2(4 + x) = x^2 => x^2 - 2x - 8 = 0 => (x - 4)(x + 2) = 0 => x = 4 m.
Final answer4
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