How Do You Calculate Elevator Motion and Energy After a Cable Snap?

[vtech]

elevator problem - urgent help!

The cable of the 1800 kg elevator snaps when the elevator is at rest at the first floor, where the cab bottom is a distance d = 3.7 m above a cushioning spring whose spring constant is k = 0.15 MN/m. A safety device clamps the elevator against guide rails so that a constant frictional force of 4.4 kN opposes the motion of the elevator.

(image attached - i don't know how to make it embedded, sorry)

(a) Find the speed of the elevator just before it hits the spring._____ m/s
(b) Find the maximum distance x that the spring is compressed.______ m
(c) Find the distance that the elevator will bounce back up the shaft._____m
(d) Using conservation of energy, find the approximate total distance that the elevator will move before coming to rest._____m


--------------------

alrite let's see...

a) I've gotten the first answer by dKinetic + dPotGrav (or Ug) + E thermal (from friction) = 0 from conservation of energy... solve for V final from the kinetic part... 7.37ms-1

b) i believe it should be -1/2mv^2 - mgS + 1/2kS^2 + F(of friction)*S = 0 but I'm not sure if I'm getting the signs wrong... should my answer be negative because its compressing or not?... not getting the right answer... help please!

c) now i need my result from b) as x and is it 1/2kx^2 = mg(d up) + Friction(s +d up) solve for (d up)... Note: not sure if should just use answer from b) times the friction force or is it friction * (d up)... instead of what my equation says...?

d) to be honest I'm sorry but i have no clue to this one... and without b) and c)... I'm having trouble understanding it...

i hope some1 can help me out?! thanks in advance!

 

[Randomphyre]

Hmm, I am stuck on c) and d) too. but i can help you on b) you have it right but use the velocity you got in a) and if you have a TI-86 or higher just use solver to find distance from the quadratic equation you get.

I used: .5kS^2=.5mv^2-(force of friction)S+mgS

 

[vtech]

question?

i solved the quadratic, but is it the negative s because its in compression or not?...

i got either 0.90 or -0.72... I'm thinking its the positive... but i only have 1 try left... which one did u use? just want to make sure!

 

[Randomphyre]

It is .9

but your equations for C and D don't work (I did the same thing as you did in C and the answer was wrong) so try it yourself and if it is still wrong were going to have to brainstorm.

 

[vtech]

actually, ur right... friction only acts during d up... my original equation had friction acting at (s + d up)

it should be:

1/2kx^2 = mg(d up) + Friction(d up)

 

[vtech]

other ?

hey randomphyre, i was wondering... have u gotten around to ch8 #66 part (c)... any clues? its the crates falling on the conveyor belt...

energy supplied by motor?

 

[Randomphyre]

haha can get all the other parts except that. Its got me stumped too.

 

[vtech]

did u get d) for the elevator?

Ugrav (as a function of S + dup) = Uspring (as a function of S) + F(friction) L

solve for L... i thought it made sense... but i didn't get the right answer!... wut do u think??