Conservation of Energy Possibly

[Heisenberg.]

Homework Statement

The cable of an elevator of mass M = 3990 kg snaps when the elevator is a rest at one of the floors of a skyscraper. At this point the elevator is a distance d = 48.2 m above a cushioning spring whose spring constant is k = 21300 N/m. A safety device clamps the elevator against the guide rails so that a constant frictional force of f = 13784 N opposes the motion of the elevator. Find the maximum distance,x, by which the cushioning spring will be compressed.

Homework Equations

Uspring= (kx^2)/2
Ugrav=mgh
W=F*d=-U
Ffriction=mu*N

The Attempt at a Solution

Einitial=Efinal + deltaE
Einitial=mgh
Efinal=U + ((Ffriction*d) + (Ffriction*x))
mgh=(kx^2/2) + Ff*d + Ff*x
After plugging in numbers, I then set the equation equal to zero, then factored - I got an answer of 16.6 m for the value of x - the answer was incorrect - I went with the idea that it was a conservation of energy problem, I also added the work done by the frictional force -I'm not sure what I am doing wrong, or of any alternative method - please help!

 

[Heisenberg.]

im sorry to resort to this - but id at least like this to be viewed.. bump

 

[maladroit]

i'm working on it so you know that someone has seen it!

 

[Heisenberg.]

ah thank-you! there are rumors that I might have to not only find the work done by the frictional force but also the work done by gravity and the work done by the spring, I am not sure how to logically account for all that

 

[maladroit]

okay here are my thoughts...

you were right in thinking that this is a conservation of energy problem, or at least that is what I did too. we know that the work done by the spring is equal to 1/2kx², and we also know that work is defined as force times distance. you can solve for the force of the elevator (think weight and force of friction) as it moves over the distance(that is given too!) and solve for the x value. hopefully that is helpful!

 

[maladroit]

**solve for the x value where W=1/2kx^2!

sorry that was not very clear

 

[Heisenberg.]

well one, i thought that work is equal to the negative potential energy of the spring, two I am not sure how we can solve for the x value when you did not account for the spring constant

 

[maladroit]

k=spring constant so it is accounted for. the negative sign is correct, but you also have to take into consideration that you will be taking the square root of the magnitude of the work. the negative simply implies direction--the spring is being compressed.