Question

PE: A 75 kg runner, runs up the Art Museum's stairs to a height of 13 m. Find either the work done by the runner, or the change in potential energy as the runner ran up the stairs. Extra: If the runner took 8 s to run up, what was the power used in watts?Please help.

Answer 1

Given:

The mass of the runner is m = 75 kg

The final height is h_f = 13 m.

The initial height is h_i = 0 m

The time taken is t = 8 s

To find the work done and power.

Step-by-step explanation:

The work done can be calculated by the formula

`\begin{gathered} W=\text{ change in potential energy} \\ =mgh_f-mgh_i \end{gathered}`

Here, g = 9.8 m/s^2 is the acceleration due to gravity.

On substituting the values, the work done will be

`\begin{gathered} W\text{ = 75}*9.8*13-75*9.8*0 \\ =9555\text{ J} \end{gathered}`

The power can be calculated as

`\begin{gathered} P=(W)/(t) \\ =(9555)/(8) \\ =1194.37\text{ W} \end{gathered}`