Lift relative velocity problem.

[Legendon]

Homework Statement

motor is mounted on top of lift.
a)if p moves by y, what is the displacement of Pt A? Prove that V_p=-3V_a.
b)If motor unwidns cable at const rate 2m/s, what is vel of cable wrt lift.
Prove vel of lift is 0.5m/s

Homework Equations

The Attempt at a Solution

I can do part a. I have prob with part b. If motor releases cable at 2m/s, can i take it that pt p moves 2m/s. so V_a is 2/-3=-0.667. Since pt a is connected to the lift, the vel of cable wrt lift is 2+0.667=2.667.
But velocity of lift is 0.5 so the vel of cable wrt to lift is 2.5. This is getting confusing.

 

[Legendon]

anyone ?

 

[Legendon]

this is a better picture

 

[Simon Bridge]

Conservation of energy is your friend here.

What is the effective load on the motor?

What is the force exerted to move P a distance y?
Thus - what is the work done to do this?

What is the work done to raise the lift, and thus point A, a distance x?

The answer has a clue, and another method:
Unwinding the cable at 2m/s does not mean that P moves at 2m/s.
Remember that the motor moves with the lift. 2m/s is the rate the total length of cable increases.

You'll note that the answer, 0.5ms, is exactly a quarter of 2m/s.
How many cables are pulling on the lift?
If the total length of cable increases by 2m/s, how much does each length of cable increase by?