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 spring constant of the spring. Take g = 10 m/s ^2 .

Step-by-step solution

Let the coefficient of kinetic friction between the block and the incline be . During the downward motion, the block travels a total distance s₁ = 4.8 + 0.2 = 5 m before coming to a momentary halt. Applying the work-energy theorem from the initial position to the point of maximum compression: W_ gravity + W_ friction + W_ spring = K mg s₁ 37^ - mg s₁ 37^ - 1 2 k x^2 = 0 Substituting m = 2 kg , g = 10 m/s ^2 , s₁ = 5 m , x = 0.2 m , 37^ = 3 5 , and 37^ = 4 5 : 2 10 5 3 5 - 2 10 5 4 5 = 1 2 k (0.2)^2 60 - 80 = 0.02k