A 120-MT concrete beam is lifted from the floor by two tandem heavy lift cranes up to a target height of 7.5 meters.
Calculate the work done by each crane to lift the beam up to 9 meters given that they are synchronized and were able to divide the load equally.
To calculate the work done by each crane, we first need to determine the total work required to lift the beam 9 meters.
The work done is equal to the force applied multiplied by the displacement. In this case, the force is the weight of the beam, which is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2).
The mass of the beam is given as 120 MT (megatons), which is equal to 120,000 kg.
The distance lifted is 9 meters.
So, the total work done to lift the beam 9 meters is:
Work = Force x Displacement
= (mass x acceleration due to gravity) x (distance lifted)
= (120,000 kg x 9.8 m/s^2) x 9 m
= 105,840,000 joules
Since the two cranes are synchronized and divide the load equally, each crane contributes equally to the total work.
Therefore, the work done by each crane to lift the beam up to 9 meters is:
Work = Total Work / Number of Cranes
= 105,840,000 joules / 2
= 52,920,000 joules
So, each crane would have done 52,920,000 joules of work to lift the beam up to 9 meters.
To calculate the work done by each crane, we can use the formula:
Work = force x distance
Since the cranes are synchronized and divide the load equally, each crane will need to lift half of the total weight of the beam.
The weight of the beam is given as 120 metric tons (MT). Since there are 1000 kilograms (kg) in a metric ton, we can convert this weight to kilograms:
Weight = 120 MT x 1000 kg/MT = 120,000 kg
The target height is given as 9 meters, but we need to lift the beam up to 7.5 meters, which means the distance traveled for each crane is:
Distance = 9 meters - 7.5 meters = 1.5 meters
Now, we can calculate the work done by each crane:
Work = force x distance
Since each crane is lifting half of the weight, the force applied by each crane is half the weight:
Force = 1/2 x Weight
Work = (1/2 x Weight) x Distance
Calculating the work done by each crane:
Work = (1/2 x 120,000 kg) x 1.5 meters
Work = 60,000 kg x 1.5 meters
Work = 90,000 kilogram-meters (kg-m)
So, each crane would need to do approximately 90,000 kilogram-meters (kg-m) of work to lift the beam up to 9 meters if they are synchronized and divide the load equally.