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anonymous
 4 years ago
An elevator cable breaks when a 920kg 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)?
anonymous
 4 years ago
An elevator cable breaks when a 920kg 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)?

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0I'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
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