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 ?

1 Answer
Steve J.
Jul 6, 2018

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#.

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