Chapter 6, Problem 66P

To determine

Average power output of football player.

Answer to Problem 66P

Solution: $4\text{84}\text{.36}\text{W}$

Explanation of Solution

Given:

Distance along the stairs $=83\text{m}$

Angle of inclination $={33}^0$

Mass of player $=82\text{kg}$

Time taken $=75\text{s}$

Formula Used:

Work done against gravity $=\text{mg h}$

h : vertically upward displacement

Power $\text{=}\frac{\text{work}}{\text{time}}$

Energy supplied by man, can do work against gravity.

Calculation:

Work done against gravity =mg h

  

S= distance travelled along the stairs.

  $\begin{array}{c}h\text{ = (83 m) sin}\text{33}°\\ W\text{ = (82 kg)×(9}{\text{.8 m/s}}^{\text{2}}\text{)×(83 m)×sin}\text{33}°\\ \text{= 36326}\text{.77 J}\end{array}$

Power $\text{=}\frac{\text{work}}{\text{time}}$

  $\begin{array}{l}\text{= }\frac{\text{36326}\text{.77 J}}{\text{75 s}}\\ \text{= 484}\text{.36}\text{W}\end{array}$

Conclusion:

Player energy supplied is converted into gravitational potential energy of player plus earth as a system. Average power output of player $=4\text{84}\text{.36}\text{W}$ .