Question

A 125-lb student races up stairs with a vertical height of 4.0 m in 5.0 s to get to a class on the second floor. How much power in watts does the student expend in doing work agains gravity?

Answer 1

The formula to find the power is

$P=\frac{W}{t}$

Where W represents the work done, which is the product between the force exerted and the distance traveled, W=Fd. In this case, the force is the weight of the student.

$F=mg$

Let's replace the mass and the gravity, knowing that 125 pounds are equal to 56.7kg.

$\begin{gathered} F=56.7\operatorname{kg}\cdot9.81m/s^2 \\ F=556.23N \end{gathered}$

Once we have the force, we can find the work done

$\begin{gathered} W=556.23N\cdot4m \\ W=2,224.92J \end{gathered}$

Now we can use the work done to find the power in Watts

$\begin{gathered} P=\frac{2,224.92J}{5\sec } \\ P=444.98W \end{gathered}$

Therefore, the power in Watts is 444.98.