Answer :
a) The work done by the student against gravity is approximately 1272.065 Joules. b) The power exerted by the student is approximately 2.62 Watts.
a) The work done by the student against gravity can be calculated using the formula:
Work = Force × Distance × cosθ
where
Force = mass × acceleration due to gravity = 118 lb × 32.2 ft/s^2 (acceleration due to gravity)
Distance = vertical height = 8 ft
θ = angle between the force and displacement vectors, which in this case is 0 degrees since the force and displacement are in the same direction.
First, we need to convert the student's weight from pounds to mass in slugs:
Mass = 118 lb / 32.2 ft/s^2 = 3.657 slugs
Now we can calculate the work done:
Work = (3.657 slugs) × (32.2 ft/s^2) × (8 ft) × cos(0°)
= 939.3548 ft·lb
To convert ft·lb to Joules, we can use the conversion factor:
1 ft·lb = 1.35582 J
Therefore, the work done by the student against gravity is:
Work = 939.3548 ft·lb × 1.35582 J/ft·lb
≈ 1272.065 J
b) Power is defined as the rate at which work is done. We can calculate the power using the formula:
Power = Work / Time
The time taken to climb the stairs is given as 8 minutes and 4.8 seconds, which we need to convert to seconds:
Time = 8 minutes × 60 seconds/minute + 4.8 seconds
= 484.8 seconds
Now we can calculate the power:
Power = 1272.065 J / 484.8 s
≈ 2.62 J/s or 2.62 Watts
To know more about Power, visit
https://brainly.com/question/11569624
#SPJ11
