Work/spring: Work Done by Gravity & Spring Compression - 760 kg Elevator

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AI Thread Summary
The discussion revolves around calculating the work done by gravity, the speed of a 760 kg elevator just before it strikes a spring, and the compression of the spring after the elevator's fall. The work done by gravity was calculated as 215992 J, and the speed just before impact was found to be 23.8 m/s. For the spring compression, the initial approach using only spring work was incorrect; it must also account for gravitational potential energy. The correct approach involves combining both the gravitational work and the spring's work to find the total compression. The final solution for the spring compression was clarified to include both energy contributions.
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Homework Statement


An elevator cable breaks when a 760 kg elevator is 29 m above the top of a huge spring (k = 8.00 × 104 N/m) at the bottom of the shaft.
(a) Calculate the work done by gravity on the elevator before it hits the spring.


(b) Calculate the speed of the elevator just before striking the spring.


(c) Calculate the amount the spring compresses (note that here work is done by both the spring and gravity).


Homework Equations





The Attempt at a Solution


I got 215992 J for a, 23.8 m/s for b, and I need help with c. Thanks!
 
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Bones said:

Homework Statement


An elevator cable breaks when a 760 kg elevator is 29 m above the top of a huge spring (k = 8.00 × 104 N/m) at the bottom of the shaft.
(a) Calculate the work done by gravity on the elevator before it hits the spring.

(b) Calculate the speed of the elevator just before striking the spring.

(c) Calculate the amount the spring compresses (note that here work is done by both the spring and gravity).

Homework Equations



The Attempt at a Solution


I got 215992 J for a, 23.8 m/s for b, and I need help with c. Thanks

OK. What is the formula for Work done by the spring?

It will involve a "distance", and the problem is telling you to include that additional potential energy in addition to the kinetic energy to determine the total depression.
 
I took -215992 J = .5(-8.0x10^4)(d^2) and got 2.32 m which is not correct according to webassign.
 
I figured it out ;)
 
Bones said:
I took -215992 J = .5(-8.0x10^4)(d^2) and got 2.32 m which is not correct according to webassign.

Don't you also need the m*g*d term too?

I presume this is the correction you discovered?
 
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