Physics Problem of the Week: Calculating Power Required to Lift an Object

Problem: If a mass of 10.0 kg needs to be lifted 10.0 meters upwards in 5.00 seconds, what will be the average power required?

Solution: Two formulas are needed here. The first is the formula for power:

P(av) = ∆W / ∆t    (W = work and t = time)

But to calculate the average power we will need to calculate the amount of work done. Noting that:

∆W = F · ∆s  (where s = displacement)

we conclude that the work done (since displacement is vertical) is used to overcome the weight of the object, therefore the gravitational potential energy change is equal to the work done!

∆W = m · g · ∆h (where m = mass, g = 9.81 m/s^2, and h = height) 

Thus, ∆W = (10.0 kg)(9.81 m/s^2)(10.0 m) = 981 Joules

Using this energy in the average power equation above, we see

P(av) = (981 J) / (5.00 s) = 196 J / s = 196 Watts 

For a video similar to this topic, see

https://www.youtube.com/watch?v=zt1noaXrJ14

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