As shown in the figure, a spring is fixed at the bottom end of an incline of inclination 37^ . A small block of mass 2 kg begins slipping down the incline from a point 4.8 m away from the spring. The block compresses the spring by 20 cm , comes to a momentary halt, and subsequently rebounds through a distance of 1 m up the incline. Determine the friction coefficient between the plane and the block. Take g = 10 m/s ^2

Step-by-step solution

Let the spring constant be k and the coefficient of friction be . During the downward motion, the block starts from rest and comes to a momentary halt after compressing the spring. The total distance moved down the incline is s₁ = 4.8 + 0.2 = 5.0 m . Applying the work-energy theorem for the downward journey: W_ gravity + W_ friction + W_ spring = K = 0 mg s₁ 37^ - mg s₁ 37^ - 1 2 kx^2 = 0 1 2 kx^2 = mg s₁ ( 37^ - 37^ ) --- (1) During the upward rebound, the block starts from rest at maximum compression and moves a