Question

Peter’s body supplies a force of 500 N to run up a 10-m hill in 10 s. How much power is involved in Peter’s run up the hill? Explain and show your work. First solve for work. Then solve for power.

Answer 1

Answer: 500 Watts

Explanation:

Power $P$ is the speed with which work $W$ is done. Its unit is Watts ($W$), being $1 W=\frac{1 Joule}{1 s}$.

Power is mathematically expressed as:

$P=\frac{W}{t}$ (1)

Where $t$ is the time during which work $W$  is performed.

On the other hand, the Work $W$ done by a Force $F$ refers to the release of potential energy from a body that is moved by the application of that force to overcome a resistance along a path.  It is a scalar magnitude, and its unit in the International System of Units is the Joule (like energy). Therefore, 1 Joule is the work done by a force of 1 Newton when moving an object, in the direction of the force, along 1 meter ($1J=(1N)(1m)=Nm$  ).

When the applied force is constant and the direction of the force and the direction of the movement are parallel, the equation to calculate it is:  

$W=(F)(d)$ (2)

In this case, we have the following data:

$F=500 N$

$d=10 m$

$t=10 s$

So, let's calculate the work done by Peter and then find how much power is involved:

From (2):

$W=(500 N)(10 m)$ (3)

$W=5000 J$ (4)

Substituting (4) in (1):

$P=\frac{5000 J}{10 s}$ (5)

Finally:

$P=500 W$