Finding work for lifting a chain with winch on top of a building

In summary, the problem involves a winch on top of a building, with a chain of length 95 m and a mass per unit length of 1.2 kg/m hanging from it. The task is to find the work done in reeling up 60 m of the chain. The equation used is W = FxD, with F = μLg according to some examples. The final answer should be 42200 Joules, but the attempted solution resulted in 28252.8 Joules. The challenge lies in determining the correct value for L, which is the length of the chain that needs to be reeled up.
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Homework Statement



A winch is positioned on top of a building, a distance 70 m above ground level. A chain of length 95 m and a mass per unit length of 1.2 kg/m hangs from the winch along the side of the building. Find the work done (in Joules) in reeling up 60 m of the chain.

Homework Equations



W=FxD

F=μLg (according to a few examples)

The Attempt at a Solution



hmm i followed a few examples seeing if it can help me get to the right answer
ok so i know that
dW=F*dy F=μLg
so μ=1.2, g=9.81, L=(70-y) ...got that from the equation but not too sure about L
...if i put that together to solve for W
W=∫ μLg dy from 0 to 60 ...60 because its reeling it up by 60
then i do all the integral magic and i get 28252.8
but the answer is suppose to be 42200 >_<

i used most of the number except for the length of the chain...not too sure what to do with it... i thought i can use to for my limits 95-60 and 95-70 but...i think that's just saying I am only lifting its 25m to 35m =/hope i got the right idea...thanks
 
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  • #2
this one may be easier to balance work & potential energy (ps i didn't go through all the working)
 

1. How do you determine the weight of the chain and winch needed for lifting on top of a building?

The weight of the chain and winch needed for lifting on top of a building depends on several factors, including the weight of the object being lifted, the height of the building, and the type of winch being used. A professional engineer or contractor will need to assess these factors and calculate the appropriate weight capacity for the chain and winch.

2. What safety precautions should be taken when using a winch to lift a chain on top of a building?

It is important to follow all safety guidelines and precautions when using a winch to lift a chain on top of a building. This includes ensuring the winch is properly secured and stable, using appropriate personal protective equipment, and having a trained operator control the winch. It is also important to regularly inspect the equipment and follow proper lifting techniques to prevent accidents or injuries.

3. Can any type of winch be used for lifting a chain on top of a building?

No, not all winches are suitable for lifting chains on top of a building. The winch must have a sufficient weight capacity, be able to withstand the height and weight of the object being lifted, and have the necessary safety features. It is important to consult with a professional to determine the most appropriate winch for your specific needs.

4. Are there any specific regulations or permits required for lifting a chain with a winch on top of a building?

Yes, there may be specific regulations and permits required for lifting a chain with a winch on top of a building, depending on the location and type of building. It is important to consult with local authorities and obtain any necessary permits before beginning any lifting operations.

5. How do you ensure the chain and winch are properly maintained for safe lifting on top of a building?

Regular maintenance and inspections are crucial for ensuring the safety and effectiveness of the chain and winch when lifting on top of a building. This includes checking for any signs of wear and tear, lubricating moving parts, and replacing any damaged or worn components. It is also important to follow the manufacturer's recommended maintenance schedule and guidelines.

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