Time it takes to lift a sofa with power

[Capncanada]

Homework Statement

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?

Homework Equations

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

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..

 

[SammyS]

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

 

[Capncanada]

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?

 

[SammyS]

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

What is power?

 

[Capncanada]

Power is work over time.

 

[SammyS]

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

 

[Capncanada]

The potential energy increases..

 

[SammyS]

Right.

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

 

[Capncanada]

Found it, I need to gain a better grasp for what my units are. Thank you for getting me started on it. I found the PE=mgh and that is the work done.

t=w/p gets me my answer.

 

[SammyS]

Yup. That's it.