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shrutij
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Homework Statement
A 0.211 kg shoe is dropped onto a vertically oriented spring with a spring constant of 102 N/m. The shoe becomes attached to the spring upon contact, and the spring is compressed 0.117 m before coming momentarily to rest.
If the speed of the shoe just before impact is doubled, what is the maximum compression achieved by the spring?
The Attempt at a Solution
Before this question, I figured out the speed the shoe was traveling at just before it hit the spring to be 2.08 m/s, which was correct. I also figured out the work done by the spring force to be -0.698 J and the work done by the weight of the shoe to be 0.242 J.
I know that when speed doubles, K.E. quadruples, which means the net work done must increase by 4 as well.
Wnet= Wgrav+Wspring=0.242 -0.698=-0.456 J.
I found the new K.E. to be 1.826 J (with doubled speed).
When I equate KE to Wnet, I get a quadratic: m*g*x -0.5*k*x^2= -1.826 J (new K.E.)
Is there no other way other than solving this quadratic to get to the new compression?
HELP, please!