The system shown in the figure consists of a block of 4.00 mass, which can move on a horizontal surface with a kinetic friction coefficient of 0.30, and which is attached to a spring with a force constate of 200 / by means of an ideal rope, passing through an ideal pulley. The system is initially at rest, with the spring relaxed until suddenly the block is struck to the right, such that instantaneously its speed becomes 178 /. Determine:
The initial mechanical energy of the system.
The velocity of the block when the spring momentarily returns to its relaxed state, after having reached its maximum elongation.