Dynamics midterm coming up don't understand pulley questions

[Faheema Baksh]

Determine the speed of the elevator if each
motor draws in the cable with a constant speed of 5 m>s.

Here is a link to the question and diagram. Scroll down to page 154. Its question 12-199.

http://www.mem.odu.edu/~bawab/ME205f/hwk12.pdf

I don't understand how to get the distances. Any help would be greatly appreciated.

 

[tiny-tim]

Welcome to PF!

Hi Faheema! Welcome to PF!

I don't understand how to get the distances.

There are motors at B and C, and the cables are disappearing into the motor mechanism …

so we can't measure the distance to the end of the cable!

So the book has chosen an arbitrary point on each cable, and measured the height of that instead. ​

 

[Faheema Baksh]

Thanks :) but this height that the book has chosen represents what exactly?

 

[tiny-tim]

Nothing!

It's arbitrary! ​

Can't you see from the diagram that they've cut each cable at a totally random point?

(and if they used some other point, that would only add a constant to the equations, which would cancel out in the end)

 

[Ken G]

Yes, it's not the length that matters, it's the rate of change of the length. Imagine that the points where they "cut" the cables are really just black lines marked on the rope. You know the rate of change of the height of the black marks is directly given by the motor speeds, so put the marks wherever you want, and proceed.