A 72.7 kg student runs up the stairs of a football stadium to a height of 11.9 m above the ground in 10.1 s.
(a) What is the power of the student in kilowatts?
Fs = m*g = 72.7kg * 9.8N/kg = 712.5 N. =
Force of the student.
P = F * d/t = 712.5 * 11.9/10.1 = 839.4
J./s = 839.4 Watts = 0.8394 Kilowatts.
To calculate the power of the student, we need to use the formula:
Power = Work / Time
The work done by the student can be calculated using the formula:
Work = Force * Distance
In this case, the force is equal to the weight of the student, which can be calculated using the formula:
Weight = Mass * Gravity
where the mass of the student is given as 72.7 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 72.7 kg * 9.8 m/s^2
Weight = 711.46 newtons
Now, let's calculate the work done:
Work = Force * Distance
Work = 711.46 N * 11.9 m
Work = 8466.574 J
Finally, we can calculate the power:
Power = Work / Time
Power = 8466.574 J / 10.1 s
Power = 837.375 W
To convert this to kilowatts (kW), we can divide by 1000:
Power = 837.375 W / 1000
Power = 0.837 kW
Therefore, the power of the student is approximately 0.837 kilowatts.
To find the power of the student, we need to use the formula:
Power = Work / Time
First, let's find the work done by the student. The work done is equal to the force applied multiplied by the distance moved.
The force applied can be found using Newton's second law:
Force = Mass x Acceleration
Acceleration can be calculated using the equation:
Acceleration = Change in velocity / Time
Since the student is running up the stairs, their velocity increases from 0 to a final value.
To find the change in velocity, we can use the formula:
Change in velocity = Final velocity - Initial velocity
The initial velocity is 0 since the student starts from rest, and the final velocity can be found using the equation:
Final velocity = Distance traveled / Time
Plugging in the values:
Distance traveled = 11.9 m
Time = 10.1 s
Final velocity = 11.9 m / 10.1 s
After calculating the final velocity, we can find the change in velocity and the acceleration:
Change in velocity = Final velocity - Initial velocity
Acceleration = Change in velocity / Time
Next, we can calculate the force applied by multiplying the mass of the student by the acceleration:
Force = Mass x Acceleration
The mass of the student is given as 72.7 kg.
Now that we have the force applied by the student, we can calculate the work done:
Work = Force x Distance
Finally, we can find the power by dividing the work done by the time taken:
Power = Work / Time
To convert power to kilowatts, divide the power by 1000.
Now we have all the steps to find the power of the student in kilowatts.