An elevator with a mass of \(2000 \mathrm{~kg}\) rests at a level of \(6 \mathrm{~m}\) above the base of the elevator shaft. It is at a height of \(60 \mathrm{~m}\) when the cable holding it breaks. It falls freely to the base, where it is brought to rest by a strong spring. Assume \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\). Estimate:

(a) The potential energy of the elevator in its initial position

(b) The potential energy of the elevator in its highest position

(c) The work done in raising the elevator

(d) The kinetic energy and the velocity of the elevator just before it strikes the spring

(e) The potential energy of the spring when the elevator rests on it.