A 3.00-kg mass is fastened to a light spring that passes over a pulley. They pulley is frictionless, and its inertia may be neglected. The mass is released from rest when the spring is unstretched. If the mass drops 10.0cm before stopping, find (a) the spring constant of the spring and (b) the speed of the mass when it is 5.00cm below its starting point.
When the spring stops, there is no kinetic energy and the potential energy lost (M g X) equals the added potential energy of the spring, (1/2) k X^2.
(a) Since you know M = 3.00 kg, g = 9.8 m/s^2 and H = 0.100 mm, you can solve for the spring constant k.
(b) Use the enery conservation law and the fact that the energy stored in the spring is 1/4 as large when X = 5 cm, as it is at X = 10 cm.