What is the average useful power output of a person who does 5.50×106 J of useful work in 6.50 h?
235 W correct answer
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.)
92.6 s correct
can someone give me the steps to achieve these answers?
6.5 h * 3600 s/h = 23400 seconds
so
5.5 * 10^6/2.34*10^4 watts
work done = m g h = 1850*9.81*1.2
power = work/time
235 = work/time
so
time = work/235
Sure! I can help you with that.
To calculate the average useful power output, we use the formula:
Power (P) = Work (W) / Time (t)
In this case, the work done is given as 5.50×10^6 J and the time is 6.50 hours. However, we need to convert the time to seconds (since power is measured in watts, which are joules per second).
To convert hours to seconds, we can multiply the given time in hours by 3600 (the number of seconds in an hour):
Time in seconds = 6.50 hours × 3600 seconds/hour = 23,400 seconds
Now we can calculate the average useful power output by dividing the work by the time:
P = 5.50×10^6 J / 23,400 s ≈ 235 W (rounded to three significant figures)
So, the average useful power output is approximately 235 watts.
Now let's move on to the second question: how long will it take this person to lift 1850 kg of bricks 1.20 m to a platform?
The work done in lifting the bricks can be calculated using the formula:
Work (W) = mass (m) × gravitational acceleration (g) × height (h)
The mass of the bricks is given as 1850 kg, the height is 1.20 m, and the gravitational acceleration is approximately 9.8 m/s^2. Substituting these values into the formula, we get:
W = 1850 kg × 9.8 m/s^2 × 1.20 m = 21,672 J
Now, we can use the formula for work to calculate the time taken (t) using the average power output (P):
t = W / P = 21,672 J / 235 W ≈ 92.6 s (rounded to two significant figures)
Therefore, it would take approximately 92.6 seconds to lift 1850 kg of bricks 1.20 m to the platform.
I hope this helps! Let me know if you have any further questions.