# Homework Help: Time it takes to lift a sofa with power

1. Oct 4, 2011

1. The problem statement, all variables and given/known data

Your sofa won't fit through the door of your new sixth-floor apartment, so you use a 1.18 kW motor to lift the 84.7 kg sofa 18.8 m from the street.

How much time does the lift take?

2. Relevant equations

KE_i+PE_i=KE_f+PE_f
(If forces are conserved? I'm not sure if so.)

3. The attempt at a solution

KE_i=PE_f
1/2mv^2=mgh
1/2v^2=gh
This leads to a dead end I think, velocity ends up being very large..

2. Oct 4, 2011

### SammyS

Staff Emeritus
Presumably, the sofa is lifted at a constant speed, so its kinetic energy doesn't change.

3. Oct 4, 2011

So conservation of energy would apply, so the Kinetic energy will equal the potential energy of the sofa at the top?

With the conservation equation how would I get to the units of time?

4. Oct 4, 2011

### SammyS

Staff Emeritus
I repeat, the Kinetic Energy doesn't change. It remains the same.

What is power?

5. Oct 4, 2011

Power is work over time.

6. Oct 4, 2011

### SammyS

Staff Emeritus
If the work doesn't go into increasing the K.E., then What form of energy is being increased as the piano is lifted?

7. Oct 4, 2011

The potential energy increases..

8. Oct 4, 2011

### SammyS

Staff Emeritus
Right.

So how much energy must the sofa gain to make it to the 6th floor?

9. Oct 4, 2011