Question

A 790N person runs up a flight of 40 stairs (.25m for each step) in 20 seconds, and then down 10 steps in 5 seconds. How much total mechanical work is completed? How much total mechanical power is generated? Show all work.

Answer 1

Person moves up 40 stairs and then go down by 10 steps

So total steps that person moves up will be

$N = (40 - 10) = 30 steps$

Each step is of height 0.25 m

so total height raised

$H = 30 \times 0.25 = 7.5 m$

Total mechanical energy consumed

$E = mgH$

here we know that

$mg = 790 N$

$E = 790 \times 7.5 = 5925 J$

Total mechanical power generated will be

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

$P = \frac{5925}{(20 + 5)}$

$P = 237 W$

so its total power will be 237 Watt