Final answer:
The person uses a power of 214.5 Watts while climbing three floors of a building when their mass is 76 kg, climbing a total height of 15 m, and taking 52 s to do so.
Step-by-step explanation:
To calculate how much power is used when a person with mass M = 76 kg climbs N = 3 floors with each of height H = 5 m in a total time of T = 52 s, we use the formula for power:
P = (Work done) / (Time taken)
The work done by the person in climbing the floors is equivalent to the change in gravitational potential energy, which can be found by:
Work done = (Mass) × (Gravitational acceleration) × (Height climbed)
- Mass = 76 kg
- Gravitational acceleration = 9.8 m/s²
- Total Height climbed = 3 floors × 5 m/floor = 15 m
- Time taken = 52 s
Calculating the work done:
Work done = 76 kg × 9.8 m/s² × 15 m = 11154 J (Joules)
Now, calculating the power:
Power = 11154 J / 52 s = 214.5 W
So, the person uses a power of 214.5 Watts while climbing the three floors.