# Falling elevator energy conservation

The cable of an elevator of mass M = 1640 kg snaps when the elevator is at rest at one of the floors of a skyscraper. At this point the elevator is a distance d = 36.4 m above a cushioning spring whose spring constant is k = 13600 N/m. A safety device clamps the elevator against the guide rails so that a constant frictional force of f = 12724 N opposes the motion of the elevator. Find the maximum distance by which the cushioning spring will be compressed.

(1/2)kx^2=Spring energy
K=(1/2)mv^2
U=mgh
Vf^2=Vi^2+2a(X-Xi)

F=ma
mg-Ff=ma
a=2.05 m/s^2

Vf^2=Vi^2+2a(X-Xi)
Vf^2=0+2(-2.05)(-36.4)
Vf=12.22 m/s

(1/2)kx^2=(1/2)mv^2
(1/2)(13600)x^2=(1/2)(1640)(12.22^2)
x= 4.24 m (that didn't work)

(then I tried this)
(1/2)kx^2=(1/2)mv^2+mgh
x=10.20 m (still wasn't correct)

Related Introductory Physics Homework Help News on Phys.org
What energy changes are taking place when the elevator falls?

TSny
Homework Helper
Gold Member
Don't forget that the friction force continues to act while the spring is compressing.

Potential energy is being converted to kinetic energy. So with that, (1/2)mv^2=mgh. Would the final equation be (1/2)kx^2=mgh?

The friction force is acting over a distance throughout the process of the elevator falling and compressing the spring. So the friction force is doing work against the falling elevator.
(1/2)kx^2=mgh-Ffd?

Ok, looking good.
Are h and d the same?
How are they related to the initial height you are given.
Hint : think what happens to the spring.

h is the initial height and d is the initial height + the distance the spring compresses when the elevator hits it. Thus Ffd=Ff(h+x), right?

Yes, good.

Awesome! Thank you!

TSny
Homework Helper
Gold Member
h is the initial height and d is the initial height + the distance the spring compresses when the elevator hits it. Thus Ffd=Ff(h+x), right?
Does the force of gravity also act through the entire distance h+x?

Yes it does. So will mgh be mg(h+x) instead?

TSny
Homework Helper
Gold Member
Yes, I think that's right.