Energy Problem with Spring, Gravity, and Friction

AI Thread Summary
The discussion revolves around calculating the final speed of an elevator after it compresses a spring while experiencing friction. The elevator initially travels at 30 m/s and encounters a frictional force of 20,000 N as it compresses the spring with a constant of 15,000 N/m over 0.8 m. The equation used combines kinetic energy, work done by friction, gravitational potential energy, and spring potential energy. A participant questions their calculation, arriving at a final speed of 30.03 m/s, and seeks clarification on variable definitions and the treatment of negative work done by friction. The conversation emphasizes the importance of correctly interpreting the variables and signs in the energy equation.
FettuccineAlfredo
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Homework Statement


An elevator is traveling at 30 m/s just as it touches a cushioning spring. The safety clamps engage at that moment and provide 20,000N of frictional force. The mass of the elevator is 3000kg and the spring constant is 15000 N/m. How fast will the elevator be traveling after the spring compresses 0.8m ?

Homework Equations


K1+Wf = Ug2+Us2+K2
Allow the point that the elevator touches the spring to be y=0

The Attempt at a Solution


1/2*m(v1)2+Ffd=mgy2+1/2*kx2+1/2*mv22
Manipulating this around and plugging in numbers gives an answer of 30.03 m/s for me. Am I missing something here?
Edit: d is just the distance along which friction occurs, -.8 m?
x is the compression of the spring, also .8m
y2 is the distance traveled by the elevator, so -.8m
 
Last edited:
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Hi FettuccineAlfredo,

Welcome to Physics Forums!

Can you define your variables used in the attempt at solution? For example, what distinguishes ##d##, ##x##, and ##y_2##?
 
I didn't check your calculation, but realize that the work done by friction is negative. (As will be y2.)
 

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