Calculating Work and Speed of Elevator with Broken Cable

[Trizz]

Homework Statement

An elevator cable breaks when a 798 kg elevator is 28.9 m above a huge spring (k = 8.00 multiplied by 104 N/m) at the bottom of the shaft.

(a) Calculate the work done by gravity on the elevator before it hits the spring. I got 226009 which is right

(b) Calculate the speed of the elevator just before striking the spring. I got 23.8 which is right

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

I need help with C!

Homework Equations

PEgr = mgh
PEel = 1/2kx^2

The Attempt at a Solution

I don't have my work in front of me right now but I got 2.28 and 2.38 and they were each wrong. I'll edit this later if i find my work

 

[Trizz]

I remember now... I did it quadratically.

My final set up was

4.00e4 x^2 + 7828 x - 226009

 

[rl.bhat]

PEel = 1/2kx^2
It should be
mg(h+x) = 1/2kx^2

 

[Trizz]

mg(h+x) = 1/2kx^2 so would it be 7820(28.9+x) = 1/2(8*10^4)(x^2)

then... 226009 + 7820x = 40000x^2

or... -40000x^2 + 7820x + 226009 = 0

then would x be 2.47?I'm only clarifying because I have one chance left to get it right

 

[rl.bhat]

Your answer is correct.

 

[Trizz]

thank you so much