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Who has the most power?
I.) An Olympic cyclist, weighing 100 kg, bicycling 200 meters in 10 seconds.
II.) An Olympic weightlifter, lifting a mass of a 200 kg a height of 4 meters in 4 seconds.
III.) A laptop, having a resistance of 4 ohms, using 20 volts.
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Correct Answer: C. I and II
Solution: Recall power is energy over time. We will need to know what type of energy is used and then find it. Calculating the amount of energy comes down to remembering the formulas.
The Olympic cyclist exhibits kinetic energy.
[latex]K.E.=\frac{1}{2}mv^2,\ \Rightarrow K.E.=\left(\frac{1}{2}\right)\left(100\right){\left(\frac{200}{10}\right)}^2=20000\ {\rm J,\ }[/latex]
[latex]\Rightarrow {\rm P=}\frac{{\rm E}}{{\rm t}}?\left(\frac{{\rm 20000}}{{\rm 10}}\right){\rm =2000\ Watts}[/latex]
The Olympic weightlifter exhibits potential energy. Potential energy can be thought as the work of the force of weight. Work being distance times force.
[latex]P.E.=mgh,\ \Rightarrow P.E.=\left(200\right)\left(10\right)\left(4\right)=8000\ {\rm J}[/latex]
[latex]\Rightarrow {\rm P=}\frac{{\rm E}}{{\rm t}}?\left(\frac{{\rm 8000}}{{\rm 4}}\right){\rm =2000\ W}[/latex]
The laptop exhibit electrical power. Electrical power is current times voltage.
[latex]P=IV,\ V=IR\Rightarrow P=\frac{V^2}{R}\Rightarrow \frac{{20}^2}{4}=100\ {\rm W}[/latex]
Both Olympic athlete outperform the laptop at 2000 W.
2000 watts is thought to be the maximum power humans can achieve. Olympic level athletes push this limit every Olympic season.
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