What is the average useful power output of a person who does 5.90×106 J of useful work in 7.90 h?
I got 207 W
Working at this rate, how long will it take this person to lift 2400 kg of bricks 1.30 m to a platform? (Work done to lift his body can be omitted because it is not considered useful output here.)
This is the part I need help with, please. Thanks!
a. My answer: 207.5 J/s = 207.5 W.
b. Work = F*d = Mg*d = 2400*9.8 * 1.3 = 30,576 Joules.
T = 30,576J. * 1s./207.5J. = 147.4 s.
To find the average useful power output, you need to divide the total useful work done by the time taken. In this case, the total useful work done is given as 5.90×10^6 J, and the time taken is 7.90 hours.
To find the average useful power output, use the formula:
Average Power = Useful Work Done / Time Taken
Plugging in the given values:
Average Power = 5.90×10^6 J / 7.90 h
Now, simplify the expression:
Average Power = (5.90×10^6 J) / (7.90 h) = 7.468 × 10^5 J/h
Therefore, the average useful power output is approximately 7.468 × 10^5 J/h, which is approximately 207 W (since 1 W = 1 J/s).
To answer the second part of your question, we need to calculate the time it takes to lift 2,400 kg of bricks by 1.30 m using the average power output of 207 W.
The formula to calculate work is:
Work = Force × Distance
Since the work done to lift the person's body is not considered useful, we can omit it. Therefore, we'll only consider the work done on the bricks.
The force required to lift the bricks can be calculated using the formula:
Force = Mass × Acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Plugging in the given values:
Force = 2400 kg × 9.8 m/s^2
Now, calculate the force:
Force = 23520 N
Next, calculate the work done on the bricks using the formula:
Work = Force × Distance
Plugging in the given values:
Work = 23520 N × 1.30 m
Now, calculate the work done on the bricks:
Work = 30576 J
To find the time required to do this work with an average power output of 207 W, use the formula:
Time = Work / Average Power
Plugging in the given values:
Time = 30576 J / 207 W
Now, calculate the time required to lift the bricks:
Time = 147.83 seconds
Therefore, at an average power output of 207 W, it would take approximately 147.83 seconds to lift 2,400 kg of bricks by 1.30 m to the platform.