Work and Energy - Mission WE2 Detailed Help

A horizontal force of 80 Newtons is applied to a 10-kg crate to move it horizontally a distance of 4 meters across a concrete floor at a constant speed of 2 m/s. The task requires 2 seconds. The power rating for the person applying the force is approximately _____ W.


 
Work (W) is calculated from knowledge of the force (F) that acts upon an object, the displacement (d), and the angle (Θ) between the F and d vectors. The formula is
 
W = F • d • cosine(Θ).
 

Power (P) is calculated from knowledge of the work done upon an object (W) and the time (t) required to do this work. The formula is

P = W / t


 
As is often the case in a power problem, the best strategy is to first calculate the work done; then use the work done and the time to calculate the power. See the two equations in the Formula Frenzy section.
The solution described above involves calculating the work from the force and the displacement and then calculating the power by dividing the work by the time. But what about the speed? Where does that come in? While it's not against the rules to ask a physics question with information that is not used in the solution, in this case the speed can be used. For a constant speed motion involving a force in the direction of motion (Theta = 0 deg.), the power can also be calculated using force and speed. The derivation of the equation is as follows:
P = W / t = F • d / t = F • (d/t) = F • v

So the power could be calculated in this situation as a force (F) multiplied by speed (v).


 

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