Question

A 48 kg woman climbs a flight of stairs 12 m high in 30 s. How much power does she use?

Answer 1

To calculate the power used by the woman, we can use the formula for power, which is:

\[
\text{Power} = \frac{\text{Work}}{\text{Time}}
\]

First, we need to calculate the work done against gravity when she climbs the stairs. The work done (W) can be computed using the formula:

\[
W = m \cdot g \cdot h
\]

where:
- \(m\) is the mass (48 kg),
- \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)),
- \(h\) is the height (12 m).

Now, we can calculate the work done:

\[
W = 48 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 12 \, \text{m}
\]

Calculating this step-by-step:

1. Calculate \(48 \cdot 9.81\):

\[
48 \cdot 9.81 \approx 470.88 \, \text{N}
\]

2. Now multiply by 12 m:

\[
W \approx 470.88 \, \text{N} \cdot 12 \, \text{m} \approx 5666.56 \, \text{J}
\]

Next, we calculate the power by dividing the work done by the time taken (30 s):

\[
\text{Power} = \frac{5666.56 \, \text{J}}{30 \, \text{s}} \approx 188.85 \, \text{W}
\]

Thus, the power used by the woman while climbing the stairs is approximately **188.85 watts**.