Question

A girl weighs 58kg and runs up a staircase 52m high in 23seconds. Find her minimum power output

Answer 1

Given,

The mass of the girl, m=58 kg

The height of the staircase, h=52 m

The time she takes to run up the staircase, t=23 s

The work the girl does to climb up the staircase is equal to the change in the potential energy of the girl.

Thus the work done is given by,

`W=\text{mgh}`

Where g is the acceleration due to gravity.

On substituting the known values,

`\begin{gathered} W=58*9.8*52 \\ =29.56*10^3\text{ J} \end{gathered}`

The power output is equal to the rate at which the work is done

Thus the power output is given by,

`P=(W)/(t)`

On substituting the known values,

`\begin{gathered} P=(29.56*10^3)/(23) \\ =1285.22\text{ W} \end{gathered}`

Thus the maximum power output is 1285.22 W