A man starts pulling on the cord when the spring is in its unstretched state. The block has a mass of M . Given that the man exerts a constant force F , determine the kinetic energy of the block at the instant it passes through the equilibrium position.

Step-by-step solution

The equilibrium position of the block is reached when the net force acting on it is zero. At this position, the constant applied force F is balanced by the restoring force of the spring. F = kx₀ x₀ = F k According to the work-energy theorem, the net work done on the block equals its change in kinetic energy: W_ net = K The work done by the constant force F is: W_F = F x₀ = F ( F k ) = F^2 k The work done by the spring force is: W_s = - 1 2 k x₀^2 = - 1 2 k ( F k )^2 = - F^2 2k Since the block starts from rest, its