Work Energy Theorem Question I cant do

[Little Dump]

I have no clue how to do b, c and especially d.

Thanks

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.)

 

[Ambitwistor]

Since this is homework, I will only give some hints, you're on your own for the rest ...

Originally posted by Little Dump
(b) Find the maximum distance x that the spring is compressed (the frictional force still acts during this compression).

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.

(c) Find the distance (above the point of maximum compression) that the cab will bounce back up the shaft.

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

(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.)

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.

 

[Little Dump]

ok i got b and c

thanks

but I am still not getting d

any chance you can give me an equation or something?

more hints?

thanks a bunch

 

[enigma]

Post what you've got, LD!

Forum rules, and all...

 

[Little Dump]

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

1800(9.81)(3.9+x)

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!

 

[StephenPrivitera]

Originally posted by Little Dump

and for d...

i still got nothing

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 W_{net-nonconserv}=[del]E_mechanical. Of course, the nonconservative work is the work done by _____. The mechanical energy is given by _____.

 

[Ambitwistor]

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.

 

[Little Dump]

I got all of them except b now

is my formula for b right?

cuz i get the wrong answer