Final answer:
To calculate the power output for a 50.0 kg student climbing 5.00 m up a rope in 12.3 seconds, the work done is first determined by multiplying mass, gravitational acceleration, and height. This work is then divided by the time taken to find the power output, resulting in approximately 199.2 watts.
Step-by-step explanation:
To calculate the student's power output, we can use the formula for power (P), which is the work done (W) divided by the time (t):
P = W/t
Since work done is equal to the gravitational potential energy gained, which is weight (force due to gravity) × height, and weight is mass × gravitational acceleration (g = 9.8 m/s²), the work calculation can be expressed as:
W = mass × g × height
For a 50.0 kg student climbing 5.00 m, this becomes:
W = 50.0 kg × 9.8 m/s² × 5.00 m
= 2450 J (Joules)
Given that it takes the student 12.3 seconds to climb the rope, the power output can be calculated as:
P = 2450 J / 12.3 s
≈ 199.2 W (watts)
Therefore, the student's power output while climbing the rope at a constant speed is approximately 199.2 watts.