Question

How much power does a student of 25kg mass who climbed a stair with 20 steps and one step is 15cm high in 30s has? (Assume =10m/s2)?

Answer 1

To calculate the power exerted by the student while climbing the stairs, we first need to determine the work done and then calculate the power from that work.

1. **Calculate the total height climbed:**
- The height of one step = 15 cm = 0.15 m
- Total height for 20 steps = 20 steps * 0.15 m/step = 3.0 m

2. **Calculate the gravitational potential energy gained:**
The work done (or potential energy gained, \(PE\)) can be calculated using the formula:
\[
PE = mgh
\]
where:
- \(m = 25 \, \text{kg}\) (mass of the student)
- \(g = 10 \, \text{m/s}^2\) (acceleration due to gravity)
- \(h = 3.0 \, \text{m}\) (total height climbed)

Substituting the values:
\[
PE = 25 \, \text{kg} \times 10 \, \text{m/s}^2 \times 3.0 \, \text{m} = 750 \, \text{J}
\]

3. **Calculate the power:**
Power (\(P\)) is defined as the work done over time:
\[
P = \frac{W}{t}
\]
where:
- \(W\) is the work done (which is equal to the gravitational potential energy gained here, 750 J)
- \(t\) is the time taken (30 s)

Substituting the values:
\[
P = \frac{750 \, \text{J}}{30 \, \text{s}} = 25 \, \text{W}
\]

Thus, the power exerted by the student while climbing the stairs is **25 Watts**.