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

Step-by-step explanation:

Power
`P` is the speed with which work
`W` is done. Its unit is Watts (
`W`), being
`1 W=(1 Joule)/(1 s)`.

Power is mathematically expressed as:

`P=(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=(5000 J)/(10 s)` (5)

Finally:

`P=500 W`