Chapter 4.3, Problem 26PP

To determine

To calculate: The chemical energy converted in $10.0\text{ min}$ if the runner’s power is $400\text{ W}$ .

Answer to Problem 26PP

The chemical energy converted in $10.0\text{ min}$ is $\underset{\_}{\text{240,000 J}}$ .

Explanation of Solution

Given data:

Power of the runner as she runs, $P=400\text{ W}$

Time, $t=10.0\text{ min}$

Formula used:

Power Equation:

  $P=\frac{E}{t}$

Where $P$ is the power in watts, $E$ is the energy of the object in joules and $t$ is the time in seconds in which energy is converted.

Calculation:

As per the problem,

  $\begin{array}{l}P=400\text{W}\\ t=10.0\text{ min= (10}\text{.0 min)(60 s)=600s [1 min=60 s]}\end{array}$

Substitute the values of power and time in the rearranged power equation to get energy:

  $\begin{array}{l}P=\frac{E}{t}\\ E=Pt\\ E=(400\text{ W)(600 s)}\\ E=240,000\text{ J}\end{array}$

Conclusion:

The chemical energy converted in $10.0\text{ min}$ is $\underset{\_}{\text{240,000 J}}$ .