NOTE: 1 MJ = 106J.
One of the most powerful cranes in the
world, operating in Switzerland, can slowly
raise a load of 6000 tonne to a height of 8 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
work = force * distance
= 6000 * 1000kg * 9.81 * 8
= 470.88 * 10^6 J
= 471.88 MJ
Since the load moves at constant speed the force applied by the engine is equal to the gravity force. Therefore, the work is
W=F•h = m•g•h =6•10^6•9.8•8=
= 4.71•10^8 J=471 MJ
To find the work done by the crane, we need to calculate the amount of potential energy transferred.
The potential energy is given by the formula:
Potential Energy = m * g * h
where:
m = mass of the loaded object (in kg)
g = acceleration due to gravity (in m/s^2)
h = height (in meters)
First, we need to convert the mass of the loaded object from tonne to kg. We know that:
1 tonne = 1000 kg
So, the mass of the loaded object is:
mass = 6000 tonne * 1000 kg/tonne
mass = 6,000,000 kg
Now, we can calculate the potential energy:
Potential Energy = 6,000,000 kg * 9.81 m/s^2 * 8 m
Potential Energy = 470,880,000 J
However, the answer is required in megajoules (MJ). We can convert the potential energy from joules to megajoules by dividing it by 10^6:
Potential Energy in MJ = 470,880,000 J / 10^6
Potential Energy in MJ = 470.88 MJ
Therefore, the work done by the crane is 470.88 MJ.