Question

What is the average power supplied by a 60.0 kg person running up a flight of stairs a vertical distance of 4.0 m in 4.2 s?

Answer 1

I found `560W`

Explanation:

Power is the rate at which work is delivered with time.
In this case, the work done by the person will be done against gravity (represented here by the weight of the person, `mg`) to raise him up to `h=4m`, or:

`W=mgh=60*9.8*4=2352J`

and the average Power will be:
`P=W/t=2352/4.2=560W`

Answer 2

The power supplied by the 60.0-kg person is 560 W.

Explanation:

Power is work done over time and is measured in watts, W . `1"W"=1"J/s"`. Work is force applied over a distance, and is measured in Joules, J . `1"J"=1 "N"*"m"`.

`P=(Fxxd)/t`

Given/Known
`F=mg=(60.0"kg"xx9.81"m/s"^2")=588.6 N"`
`d="4.0 m"`
`t="4.2 s"`

Unknown
`"Power": P`

Solution
Substitute the given/known values into the equation for power and solve.

`P=(588.6"N"xx4.0"m")/(4.2"s")`

`P=560("N"*"m")/s"="560"J"/"s"=560 "W"` (rounded to two significant figures)