A massless spring with spring constant k hangs vertically from a ceiling, initially at its relaxed length. A mass m is then attached to the bottom Fig. 5.30 and is released. (a) Calculate the potential energy I of the system, as a function of the height y (which is negative), relative to the initial position. 32 Conservation of energy and momentum (b) Find yo, the point at which the potential energy is minimum. Make a rough plot of V (v). (c) Rewrite the potential energy as a function of z = y - yo. Explain why your result shows that a hanging spring can be considered to be a spring in a world without gravity, provided that the new equilibrium point, yo, is now called the "relaxed" length of the spring