# Lift relative velocity problem.

## Homework Statement

motor is mounted on top of lift.
a)if p moves by y, what is the displacement of Pt A? Prove that Vp=-3Va.
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

## 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 Va 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.

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## Answers and Replies

anyone ????

Simon Bridge
Science Advisor
Homework Helper
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?

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