What is the average useful power output of a person who does 5.50×106 J of useful work in 6.50 h?
Working at this rate, how long will it take this person to lift 1850 kg of bricks 1.20 m to a platform? (Work done to lift his body can be omitted because it is not considered useful output here.)
assume you mean 5.50 * 10^6 Joules
6.50 hr * 3600 s/hr = time in seconds
power = Joules / time in seconds
( which is Watts )
part B:
power * time = 1850 * 9.81 * 1.20
Why did the scarecrow become a power engineer? Because he had lots of "wattage" to spare!
To find the average useful power output, we need to use the formula:
Power = Work / Time
The person has done 5.50×10^6 J of useful work in 6.50 h, so we can plug these values into the formula:
Power = 5.50×10^6 J / 6.50 h
To find the time it takes for the person to lift 1850 kg of bricks 1.20 m, we need to use the formula:
Work = Force × Distance
Since the distance is given as 1.20 m, we can plan to find the force first using the work formula, then divide the work by the power to find the time:
Force = Work / Distance
Force = (1850 kg) * (9.8 m/s^2)
Once we find the force, we can use it to calculate the time:
Time = Work / (Power × Distance)
Now, let's calculate each step:
Power = 5.50×10^6 J / 6.50 h
= (5.50×10^6 J) / (6.50 h)
= 8.46×10^5 J/h
Force = (1850 kg) * (9.8 m/s^2)
= 18130 N
Time = (1850 kg * 9.8 m/s^2) / (8.46×10^5 J/h * 1.20 m)
= 18530 N / (8.46×10^5 J/h * 1.20 m)
≈ 18.6 s
Therefore, it would take approximately 18.6 seconds for the person to lift 1850 kg of bricks 1.20 m to a platform at this power output.
To find the average useful power output, we need to use the formula: Power = Work / Time.
For the first question, the person does 5.50×10^6 J of useful work in 6.50 h. To find the average useful power output, we divide the work by the time:
Power = 5.50×10^6 J / 6.50 h = 8.46×10^5 J/h.
Therefore, the average useful power output of this person is 8.46×10^5 J/h.
Now let's move on to the second question.
To determine how long it will take the person to lift 1850 kg of bricks 1.20 m, we need to calculate the work done and then divide it by the power output to find the time.
The work done can be calculated using the equation: Work = Force × Distance.
Since the distance is given as 1.20 m, we need to calculate the force required to lift the bricks. The force can be found using the equation: Force = Mass × Acceleration due to gravity.
The mass is given as 1850 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Force = 1850 kg × 9.8 m/s^2 = 18130 N.
Now we have the force and distance, we can calculate the work:
Work = 18130 N × 1.20 m = 21756 J.
To find the time required, we can use the power formula rearranged as: Time = Work / Power.
Time = 21756 J / (8.46×10^5 J/h) = 0.026 h.
Therefore, it will take this person approximately 0.026 hours (or about 1.6 minutes) to lift the 1850 kg of bricks 1.20 m to the platform.