Question

An elevator cable breaks when a 920-kg elevator is 28 m above a huge spring (k=22.x 10^5 N/m) at the bottom of the shaft. Calculate the amount the spring compresses (note that work is done by both the spring and gravity.)
I already calculated the speed of the elevator just before striking the spring to be 23.4 m/s, and the work done by gravity on the elevator before it hits the spring to be 252, 448 J. How do I find x (spring compression)?

Answer 1

I'm pretty sure that what is necessary here is to notice that just before the elevator hits the spring it has total energy\[K+U=\frac12mv^2+mgx\]where x is the distance the spring will compress. Since all this energy is transferred to the spring we have\[\frac12mv^2+mgx=\frac12kx^2\]which is a quadratic that can be solved for x