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