Question
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
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
Answers
GPT 3.5
To calculate the work done by each crane, we need to know the formula for work:
Work = force x distance
Since the two cranes are synchronized and able to divide the load equally, each crane will lift half of the total weight.
Weight of the concrete beam = 120 MT
Weight of beam lifted by each crane = 120 MT / 2 = 60 MT = 60,000 kg
Now, we need to calculate the force exerted by each crane. We can use the formula:
Force = mass x acceleration due to gravity
Mass = 60,000 kg
Acceleration due to gravity = 9.8 m/s^2
Force exerted by each crane = 60,000 kg x 9.8 m/s^2 = 588,000 N
Next, we need to calculate the distance each crane lifts the beam. The beam is initially lifted from the floor to a height of 7.5 meters, so the distance each crane lifts the beam is:
Distance = 9 m - 7.5 m = 1.5 m
Finally, we can calculate the work done by each crane:
Work = Force x Distance
Work done by each crane = 588,000 N x 1.5 m = 882,000 N-m = 882 kJ
Therefore, each crane does 882 kJ of work to lift the beam up to 9 meters.
Work = force x distance
Since the two cranes are synchronized and able to divide the load equally, each crane will lift half of the total weight.
Weight of the concrete beam = 120 MT
Weight of beam lifted by each crane = 120 MT / 2 = 60 MT = 60,000 kg
Now, we need to calculate the force exerted by each crane. We can use the formula:
Force = mass x acceleration due to gravity
Mass = 60,000 kg
Acceleration due to gravity = 9.8 m/s^2
Force exerted by each crane = 60,000 kg x 9.8 m/s^2 = 588,000 N
Next, we need to calculate the distance each crane lifts the beam. The beam is initially lifted from the floor to a height of 7.5 meters, so the distance each crane lifts the beam is:
Distance = 9 m - 7.5 m = 1.5 m
Finally, we can calculate the work done by each crane:
Work = Force x Distance
Work done by each crane = 588,000 N x 1.5 m = 882,000 N-m = 882 kJ
Therefore, each crane does 882 kJ of work to lift the beam up to 9 meters.