Question

Is the weight of a 100-pound weight for 200 meters is equivalent to carrying a 50-pound weight for 400 meters? Is the enrgy is equivalent ?

Answer 1

Yes, the work done is zero in both cases.

Explanation:

I assume the weights are carried horizontally. Since they do not gain any altitude, they have not gained any gravitational potential energy. Therefore, zero work is done carrying a mass horizontally.

The work formula is

`"work" = F*d*costheta`

The force, `F`, would be vertical (opposing gravity) and the displacement, `d`, is horizontal. Therefore the angle between them, `theta`, is `90^@`.

`"work" = F * d * costheta = F * d * cos90^@ =F * d * 0 = 0`

I hope this helps,
Steve

P.S. If the weights were carried the distance described up the side of a building, the answer would still be yes. But the work done on the 2 weights would both be `20,000" " lb*m`.