A crane lifts a 432-kg steel beam vertically a distance of 62.8 m.How much work does the crane do on the beam if the beam accelerates upward at 2.5 m/s2?Neglect frictional forces, and express your answer in joules.
Question
A crane lifts a 432-kg steel beam vertically a distance of 62.8 m.How much work does the crane do on the beam if the beam accelerates upward at 2.5 m/s2?Neglect frictional forces, and express your answer in joules.
Solution
To calculate the work done by the crane on the beam, we can use the formula:
Work = Force x Distance
First, let's find the force exerted by the crane on the beam. We can use Newton's second law of motion:
Force = mass x acceleration
Given that the mass of the steel beam is 432 kg and the acceleration is 2.5 m/s^2, we can calculate the force:
Force = 432 kg x 2.5 m/s^2 = 1080 N
Now, we can calculate the work done by the crane. The distance the beam is lifted is given as 62.8 m:
Work = Force x Distance = 1080 N x 62.8 m
Calculating this, we find:
Work = 67704 J
Therefore, the crane does 67704 joules of work on the beam.
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