High School

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Two chains hold a 36.3 kg iron beam from the ceiling. If the beam is held stationary at 5.0 meters above the ground, how much work is done on the beam?

Answer :

The work done on the iron beam is 890.85 joules

To calculate the work done on the iron beam, we'll use the formula:

[tex]\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \][/tex]

Where:

- Force is the force exerted by the chains holding the beam.

- Distance is the vertical distance the beam is raised.

- θ (theta) is the angle between the force and the displacement. Since the force and displacement are in the same direction, cos(θ) = 1.

First, we need to find the force exerted by the chains. Since there are two chains, the total force is the weight of the beam divided by 2 (as each chain supports half of the weight):

[tex]\[ F = \frac{mg}{2} \][/tex]

[tex]\[ F = \frac{(36.3 \, \text{kg})(9.8 \, \text{m/s}^2)}{2} \][/tex]

[tex]\[ F = 178.17 \, \text{N} \][/tex]

Next, we calculate the work done:

[tex]\[ \text{Work} = (178.17 \, \text{N}) \times (5.0 \, \text{m}) \times (1) \][/tex]

[tex]\[ \text{Work} = 890.85 \, \text{J} \][/tex]

Therefore, the work done on the iron beam is 890.85 joules.

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Rewritten by : Barada