In a time of 10s, a 70 kg student runs up 2 flights of stairs whose combined vertical height is 8.0m. compute the student's power output in doing work against gravity in (a)watts and (b)horsepower
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To compute the student's power output, we need to use the formula:
Power = Work/Time
In this case, the work is done against gravity while climbing the stairs. The work done against gravity is given by the equation:
Work = Force * Distance * cos(theta)
Where:
Force = mass * gravity
Distance = vertical height of the stairs
Theta (θ) = angle between the force vector (vertical direction) and the displacement vector (horizontal direction).
Here, the mass of the student is 70 kg, and the vertical height of the stairs is 8.0 m. To calculate the force, we need to know the value of gravity, which is approximately 9.8 m/s^2.
Let's calculate the power output:
(a) In watts:
1. Calculate the force: Force = mass * gravity
Force = 70 kg * 9.8 m/s^2
2. Calculate the work done against gravity: Work = Force * Distance * cos(theta)
Since the stairs are vertical, cos(theta) = 0, and the work becomes:
Work = Force * Distance * 0
3. Calculate the power output: Power = Work/Time
Since the work done is zero in this case, the power output will also be zero.
Therefore, the student's power output in watts is zero.
(b) In horsepower:
1 horsepower is equivalent to 745.7 watts. We can convert the power output from watts to horsepower:
Power (in horsepower) = Power (in watts) / 745.7
Since the power output in watts is zero, the power output in horsepower will also be zero.
Therefore, the student's power output in horsepower is zero.