Work Done lifting a chain

In summary, to calculate the work done lifting a 25-ft chain over the side of a building, we can break the chain into smaller segments and use the formula Force = g * density * volume. The volume of each segment can be estimated using the formula (25 ft. * 4 lb./ft.) / N, where N represents the number of segments. By taking the limit as N approaches infinity, we can find the total work performed through integration.
  • #1
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How much work is done lifting a 25-ft chain over the side of a building? Assume that the chain has a density of 4 lb/ft. Hint: Break up the chain into N segments, estimate the work performed on a segment, and compute the limit as N approaches infinity as an integral.


(The small segment of the chain of length delta y located y feet from the top is lefted through a vertical distance y.)

Force = g*density*volume...?

whats the volume of a segment of the chain, I am having difficulty.


please help
 
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  • #2
Volume is wrong here. It has to be mass: ##(25ft. \cdot \;4 lb./ft.)/N##.
 

1. How is work done calculated when lifting a chain?

The work done when lifting a chain is calculated by multiplying the force applied to lift the chain by the distance the chain is lifted. This can be expressed as W = F x d, where W is work done, F is the force applied, and d is the distance the chain is lifted.

2. Does the weight of the chain affect the amount of work done?

Yes, the weight of the chain does affect the amount of work done. The heavier the chain, the more work is required to lift it. This is because the force required to lift the chain will be greater and the distance it needs to be lifted will also be greater.

3. How does the angle of lifting affect the work done?

The angle at which the chain is lifted can affect the work done. If the chain is lifted at an angle, the force required to lift it will be greater than if it was lifted straight up, resulting in more work being done. This is because the force must be applied in both the vertical and horizontal direction.

4. Is any work done when holding a chain in a fixed position?

Yes, there is work done when holding a chain in a fixed position. This is because even though the chain is not being lifted, a force must still be applied to counteract the weight of the chain. Therefore, work is still being done to maintain the position of the chain.

5. How can the work done be reduced when lifting a chain?

The work done when lifting a chain can be reduced by using a pulley system or by decreasing the weight of the chain. This reduces the force required to lift the chain and therefore reduces the amount of work done. Additionally, lifting the chain at an angle can also reduce the work done.

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