A block of mass m is connected rigidly with a smooth wedge (plank) by a light spring of stiffness k . If the wedge is moved with constant velocity v 0 , then find the work done by the external agent until the maximum compression of the spring.

Step-by-step solution

Let us take wedge + spring + block as a system. The forces responsible for performing work are spring force kx (←) and the external force F(→). Work Energy theorem for block + spring + plank relative to ground : Applying work-energy theorem, we have W ext + W sp = ΔK where W sp the total work done by the spring on wedge and block - 1 2 k x 2 and ΔK = change in KE of the block (because the plank does not change its kinetic energy) Then, W ext = 1 2 k x 2 + Δ K As the block was initially stationary and it will acquir