A sofa is mounted on rollers so that it moves with negligible friction. Pushing that sofa up a ramp from the street onto a moving van, a worker does 1600 joules of work on the sofa. Yet, the sofa gains only 100 joules of kinetic energy; it’s not moving too fast at the top of the ramp. A) How is this possible? B) Is energy conservation violated here? Please explain.Thanks
Rolling friction is less than the sliding friction
(A) It's possible, because the work done by the worker on the sofa is the kinetic and potential energy he gives the sofa. Since the sofa goes up a ramp, it definitely gains gravitational potential energy: The higher off the street it gets, the more “potential” it has to gain speed if it falls. (B) Energy conservation is not violated: Of the 1600 joules of work done by the worker on the sofa, 100 joules go into the sofa’skinetic energy while the other 1500 joules go into the sofa’s potential energy.
