One of the most powerful cranes in the
world, operating in Switzerland, can slowly
raise a load of 6000 tonne to a height of 12 m.
(1 tonne = 1000 kg)
The acceleration of gravity is 9.81 m/s2 .
How much work is done by the crane?
Answer in units of MJ
I found it by using Work = mass* acceleration* distance
1) converted 6000 tones to kilograms and I got 6000000kg thus,
2) work = (6000000kg)*(9.81m/s^2)*(12m)=706320000J
3)Then I converted 706320000j to MJ
706320000/10^6=70632 MJ
002 (part 2 of 2) 5.0 points
If it takes 3 min to lift the load at constant velocity to this height, find the power developed
by the crane.
Answer in units of MW.
please help me I have tried it 3 times and it's wrong. Please explain so I can understand how to go about this problems.
Mass=6*10^3tons * 1*10^3kg/ton=6*10^6kg.
Work = F*h = mg*h.
Work = 6*10^6*9.81 * 12=706.3*10^6 J. =
706.3 MJ.
P = Work/T = 706.3MJ/180s. = 3.92 MJ/s.=
3.92 MW.
To calculate the power developed by the crane, you need to use the formula: power = work / time.
Given that the work done by the crane is 706,320,000 J (as you correctly calculated in the first part), and the time taken to perform this work is 3 minutes, you need to convert the time to seconds.
1 minute = 60 seconds, so 3 minutes = 3 * 60 = 180 seconds.
Now, substitute the values into the formula:
power = 706320000 J / 180 s
Calculate this value:
power = 3924 MJ / s
To convert megajoules per second (MJ/s) to megawatts (MW), divide by 1 million:
power = 3.924 MW
So, the power developed by the crane is 3.924 MW.
To find the power developed by the crane, you need to use the formula:
Power = Work / Time
Given that the work done by the crane is 706320000 J (as you correctly calculated in the first part of the question) and the time taken to lift the load at constant velocity is 3 minutes, or 180 seconds, you can substitute these values into the formula to find the power.
Power = 706320000 J / 180 s
Now, you need to convert seconds to hours because the unit of power we're looking for is megawatts, which is a unit of power per hour (MW/h).
1 hour = 3600 seconds
Power = 706320000 J / (180 s / 3600 s/hour)
Calculating this expression will give you the power in J/h.
You then need to convert J/h to MW using the following conversion factors:
1 J = 1e-6 MJ (megajoule)
1 h = 1/1000 h (hour)
Power = (706320000 J / (180 s / 3600 s/hour)) * (1e-6 MJ / 1 J) * (1 / 1000 h)
After simplifying the expression, you should get:
Power = 13.26 MW
Therefore, the power developed by the crane is 13.26 MW.