Work/energy question -> motion with gravitational, elastic and frictional forces?

Question

In a "worst-case" design scenario, a 2000kg elevator with broken cables is falling at 4m/s when it first contacts a cushioning spring at the bottom of the shaft. The spring is supposed to stop the elevator, compressing 2m as it does so. During the motion a safety clamp applies a constant 17000N frictional force to the elevator. As a design consultant, you are asked to determine what the force constant of the spring should be.

Answer 1

I guess you will have to work in terms of Conservation of Energy

Initial Kinetic energy = 0.5 * 2000 * 4^2

= 16000J

This whole energy is either lost or converted into heat/sound energy by friction when the spring is compressed.

Work done by friction = 17000 * 2 = 34000J

Work done by spring = 16000 - 34000

This is where I'm stuck...the frictional force is way too big for this question. The elevator will stop before compressing the spring to 2m.

Answer 2

all i learn about elasticity are from condoms