# 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 ?

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

$\text{work} = F \cdot d \cdot \cos \theta$

The force, $F$, would be vertical (opposing gravity) and the displacement, $d$, is horizontal. Therefore the angle between them, $\theta$, is ${90}^{\circ}$.

$\text{work} = F \cdot d \cdot \cos \theta = F \cdot d \cdot \cos {90}^{\circ} = F \cdot d \cdot 0 = 0$

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 $20 , 000 \text{ } l b \cdot m$.