To calculate the weight of the beam, we need to convert the mass into weight. The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity.
Weight = mass * acceleration due to gravity
Weight = 120 MT * 9.8 m/s^2
Weight = 1176 kN
(Note: 1 metric ton = 1000 kg = 9.8 kN)
The potential energy of an object is given by the equation:
Potential energy = weight * height
Potential energy when resting at the floor:
Potential energy = 1176 kN * 0 m
Potential energy = 0 kN-m
Potential energy when halfway the target height (3.75 meters):
Potential energy = 1176 kN * 3.75 m
Potential energy = 4410 kN-m
Potential energy when it is at 7.5 meters:
Potential energy = 1176 kN * 7.5 m
Potential energy = 8820 kN-m
To calculate the work done by each crane to lift the beam up to 9 meters, we need to calculate the change in potential energy. The work done is equal to the change in potential energy.
Work done = potential energy at final position - potential energy at initial position
Work done = (1176 kN * 9 m) - (1176 kN * 7.5 m)
Work done = 10,584 kN-m
Since the cranes are synchronized and the load is divided equally, each crane would have done half of the work.
Work done by each crane = (10,584 kN-m) / 2
Work done by each crane = 5292 kN-m
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 weight of the beam. Calculate the potential energy of the beam when resting at the floor. Calculate the potential energy of the beam when it is halfway the target height.
Calculate the potential energy of the beam when it is at 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.
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