Igcse Model Questions Vol1 2022 Physics Question 33

The diagram shows an inclined plane making an angle \(\theta = 30^{\circ}\) with the horizontal. A block of mass \(m = 2.0\,\text{kg}\) is attached to a spring of constant \(k = 150\,\text{N m}^{-1}\) that is fixed at the top of the plane. Initially the spring is compressed by \(x_0 = 0.10\,\text{m}\) from its natural length. The block is released from rest and slides up the plane, compressing the spring further. After moving a distance \(d = 0.25\,\text{m}\) up the plane the block momentarily comes to rest. (a) Calculate the work done by gravity on the block during this motion. (b) Determine the elastic potential energy stored in the spring when the block stops. (c) Find the total mechanical energy of the system at that instant. (d) If the whole motion takes \(t = 0.8\,\text{s}\), compute the average power supplied by the spring over the distance \(d\). Assume no friction.