A piece of cardboard is kept perpendicularly on a horizontal surface by attaching it to one end of a spring. The other end of the spring is attached to the wall. An arrow of mass M = 0.021 kg is shot at the cardboard target. As a result, it gets attached to the cardboard and compresses the attached spring by a distance s = 0.060 m before stopping. Given that the coefficient of kinetic friction between the cardboard and the horizontal surface is μk = 0.30, the spring constant is k = 120 N/m and the piece of cardboard has a mass m = 0.788 kg, calculate the fraction of the initial kinetic energy of the arrow that is lost during the collision between the arrow and the cardboard, considering only the immediate aftermath of the collision, without considering other dissipative effects.
