What Is the Speed of the Elevator in a Rectilinear Pulley System?

[crazyman27]

Homework Statement

Both motors are drawing in the cord at a constant rate of 8 m/s. Determine the speed of the elevator.

Homework Equations

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The Attempt at a Solution

Using an equation of constraint I got 4Xe - Xb - Xc = constant (Xe being the distance from the roof of the shaft to the elevator, Xb being the distance from the roof of the shaft to an arbitrary point on the left-most cord, and Xc being the distance from the roof of the shaft to an arbitrary point on the right-most cord).

Differentiating this with respect to time gives 4Ve - Vb - Vc = 0 and subbing in 8m/s for Vb and Vc gives the speed of the elevator to be 4m/s. This isn't the solution however, not sure where I went wrong.

Any help appreciated.

 

[hikaru1221]

How do you get this one: 4Xe - Xb - Xc = constant?
If I were you, I would express the lengths of the strings connected to B and C (there are discrete 2 strings if you look carefully) in terms of Xe and d, where d is the distance between the middle fixed pulley and the pulley which is connected to neither the shaft nor the elevator.

 

[crazyman27]

How do you get this one: 4Xe - Xb - Xc = constant?
If I were you, I would express the lengths of the strings connected to B and C (there are discrete 2 strings if you look carefully) in terms of Xe and d, where d is the distance between the middle fixed pulley and the pulley which is connected to neither the shaft nor the elevator.

Thanks hikaru1211. I figured it out, I wasn't interpreting the pulley system correctly.