Question

A 4.2×10³-N piano is wheeled up a 3.5-m ramp at a constant speed. The ramp makes an angle of 30.0° with the horizontal. Find the

work done by a man wheeling the piano up the ramp.

Answer 1

Approximately
`7.4 * 10^(3)\; {\rm J}`, assuming that the friction on the piano is negligible.

Step-by-step explanation:

Under the assumptions, no energy would be lost to friction. Hence, the work that the person exerted on the piano would be entirely converted into the gravitational potential energy (GPE) of the piano.

With an angle of elevation of
`30^(\circ)`, moving the piano up this
`3.5\; {\rm m}` slope would increase the height of the piano by
`(\sin(30^(\circ)}))\, 3.5\; {\rm m} = 1.75\; {\rm m}`.

The question stated that the weight of the piano is
`4.2 * 10^(3)\; {\rm N}`. Hence, the piano would have gained GPE of the amount:

`(4.2 * 10^(3)\; {\rm N})\, (1.75\; {\rm m}) = 7350\; {\rm J}`.

Therefore, the person would have exerted
`7350\; {\rm J}` of work on this piano.