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Work Energy Theorem Question I cant do

  1. Oct 27, 2003 #1
    I have no clue how to do b, c and especially d.


    The cable of the 1,800 kg elevator cab in Fig. 8-51 snaps when the cab is at rest at the first floor, where the cab bottom is a distance d = 3.9 m above a cushioning spring whose spring constant is k = 0.14 MN/m. A safety device clamps the cab against guide rails so that a constant frictional force of 3.6 kN opposes the cab's motion. (a) Find the speed of the cab just before it hits the spring. (b) Find the maximum distance x that the spring is compressed (the frictional force still acts during this compression). (c) Find the distance (above the point of maximum compression) that the cab will bounce back up the shaft. (d) Using conservation of energy, find the approximate total distance that the cab will move before coming to rest. (Assume that the frictional force on the cab is negligible when the cab is stationary.)
  2. jcsd
  3. Oct 27, 2003 #2
    Since this is homework, I will only give some hints, you're on your own for the rest ...

    Write down a work equation. The spring does some work (change in potential energy), the frictional force does some work (force through a displacement), this total work can be related to the kinetic energy by the work-energy theorem. You can solve for the compression of the spring.

    You can solve it in a manner analogous to (b).

    To come to rest, it has to shed all of its kinetic energy. The only way to dissipate that energy is through friction. If you assume all the energy loss (work) is frictional, you can solve for the total displacement.
  4. Oct 27, 2003 #3
    ok i got b and c


    but im still not getting d

    any chance you can give me an equation or something?

    more hints?

    thanks a bunch
  5. Oct 27, 2003 #4


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    Post what you've got, LD!

    Forum rules, and all...
  6. Oct 28, 2003 #5
    for b i got the following

    1800(9.81)(3.9) - 3600(3.9+x) = 1/2k(x)^2

    im not quite sure if that is completely correct. I think their might need to be an x in the first term so its


    and for c

    1/2k(x)^2 - 3600h = (1800)(9.81)h

    not sure if that is right either but i think it is, just plug in x from b

    and for d.....

    i still got nothing

    someone help please!
  7. Oct 28, 2003 #6
    You have to have something! Even if you don't have any clue where to go, you should just write things down, even random things, to get you started. Try to think of how you can you what you know to find what you want. Specifically, try to find a formula that contains your unknown. If you know how to find all the other variables, then you're done.
    For example, I randomly wrote down Wnet-nonconserv=[del]Emechanical. Of course, the nonconservative work is the work done by _____. The mechanical energy is given by _____.
  8. Oct 28, 2003 #7
    Ok, here's another hint: the fact that the elevator is bouncing up and down the whole time doesn't matter. The fact that there is a spring at all, doesn't matter. This is simply a problem concerning a body whose kinetic energy is continually being dissipated by a force of constant magnitude; whether the elevator is bouncing, spinning around, or doing a little dance doesn't change this fact. Think about how you'd find the total distance moved until it comes to rest if it were, say, a block sliding across a table.
  9. Oct 28, 2003 #8
    I got all of them except b now

    is my formula for b right?

    cuz i get the wrong answer
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