Energy Problem with Spring, Gravity, and Friction

[FettuccineAlfredo]

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+W_f = U_g2+U_s2+K₂
Allow the point that the elevator touches the spring to be y=0

The Attempt at a Solution

1/2*m(v₁)²+F_fd=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

 

[gneill]

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##?

 

[Doc Al]

I didn't check your calculation, but realize that the work done by friction is negative. (As will be y₂.)