A 70 kg man runs up a flight of stairs 3 m high in 2 seconds. What is the average power he expends?
Understand the Problem
The question asks to calculate the average power expended by a 70 kg man who runs up a flight of stairs 3 m high in 2 seconds. This involves calculating the work done against gravity and then dividing by the time taken.
Answer
The average power he expends is $1029 \, \text{W}$.
Answer for screen readers
The average power expended by the man is $1029 , \text{W}$.
Steps to Solve
- Calculate the potential energy gained
The potential energy gained ($PE$) is given by the formula $PE = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity (approximately $9.8 , \text{m/s}^2$), and $h$ is the height. Given: $m = 70 , \text{kg}$ $g = 9.8 , \text{m/s}^2$ $h = 3 , \text{m}$
$PE = 70 \times 9.8 \times 3$
- Calculate the potential energy
$PE = 2058 , \text{J}$
- Calculate the average power expended
Power ($P$) is the work done per unit time. Since the work done is equal to the potential energy gained, the average power is $P = \frac{PE}{t}$, where $t$ is the time taken. Given $t = 2 , \text{s}$
$P = \frac{2058}{2}$
- Calculate power
$P = 1029 , \text{W}$
The average power expended by the man is $1029 , \text{W}$.
More Information
The average power expended is approximately equal to the power of a small microwave.
Tips
A common mistake is to forget to use the correct units or to confuse mass with weight. Also, students might use the wrong formula for potential energy or power.
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