How does the counterweight affect elevator power?

[Janiceleong26]

Homework Statement

Homework Equations

P=Fv

The Attempt at a Solution

Since the elevator is rising at a steady speed, a=0, thus, the tension on the string equals to the weight of the elevator. I chose C as I thought just for the elevator case, it would be m1gv, but how does m2 affects the power of the system?

 

[stockzahn]

Answer C is not correct.

Imagine the movement within a finite time Δt (and therefore a change of position of Δh for both m₁ and m₂). What is the energy difference of the whole system during Δt?

 

[haruspex]

Since the elevator is rising at a steady speed, a=0, thus, the tension on the string equals to the weight of the elevator. I chose C as I thought just for the elevator case, it would be m1gv, but how does m2 affects the power of the system?

Yes, the motor is working at that rate in raising the elevator, but what is happening on the other side? How much power is being transferred, and which way, between the counterweight and the motor?

 

[Janiceleong26]

Answer C is not correct.

Imagine the movement within a finite time Δt (and therefore a change of position of Δh for both m₁ and m₂). What is the energy difference of the whole system during Δt?

Energy difference would be (m1-m2)gΔh ?

 

[Janiceleong26]

Yes, the motor is working at that rate in raising the elevator, but what is happening on the other side? How much power is being transferred, and which way, between the counterweight and the motor?

m2gv, and anti-clockwise? But I thought power is scalar? Does the minus sign comes from the velocity?

 

[stockzahn]

Energy difference would be (m1-m2)gΔh ?

Correct. And instead of distance and energy you need velocity and power - so what to do?

 

[Janiceleong26]

Correct. And instead of distance and energy you need velocity and power - so what to do?

Divide it by Δt and you will get velocity and (m1-m2)g is the force, so force times velocity gives power. I got it! Thanks!

 

[haruspex]

m2gv, and anti-clockwise? But I thought power is scalar? Does the minus sign comes from the velocity?

Even scalar values can have sign. If A does positive work on B then B does negative work on A.
If you take up as positive and gravity as -g then the motor does work at rate -m₁(-g)v on the elevator and at rate -m₂(-g)(-v) on m₂.

 

[Janiceleong26]

Even scalar values can have sign. If A does positive work on B then B does negative work on A.
If you take up as positive and gravity as -g then the motor does work at rate -m₁(-g)v on the elevator and at rate -m₂(-g)(-v) on m₂.

Oh I see, thanks. But why is there a negative sign before the mass?

 

[haruspex]

Oh I see, thanks. But why is there a negative sign before the mass?

Because m(-g) is the force from gravity. The motor has to supply an equal and opposite force, -m(-g).