# Calculating Work for a Monkey Climbing a Chain

• peter0516
In summary, the problem involves a monkey attached to a 50-ft chain with a weight of 0.5 lb per foot and a 40-ft ceiling. The task is to find the amount of work the monkey does in climbing up the chain to the ceiling. The answer given by the teacher is 1087.5 ft-lb. The solution involves finding the mass as a function of height for the first 10 ft, and then for the remaining chain as the monkey climbs higher. After that, integration over height will give the final answer.
peter0516
Hard intergration problem!

1. A 20-lb. monkey is attached to a 50-ft. chain that weighs 0.5 lb.
per (linear) foot. The other end of the chain is attached to the
40-ft.-high ceiling of the monkey's cage. Find the amount of work the
monkey does in climbing up her chain to the ceiling.

Teacher said anwser is 1087.5 ft-lb

2. W= f(x)dx

3. i used w= from 0 to 40 .5x+20x...then took antiderivitve and got (1/4)x^2 + 20x=1200 ft-lb
what do i need to do after that i know i need to do the rope from 10 to 40 but idk the formulma

I see you posted it in two places. I suppose this is a homework problem?

I'll copy paste my reply from the other post.

As the monkey climbs up the mass he has to pull up becomes greater and greater, because he now also needs to lift a piece of the chain. Let's call the height z. The chain is 10 ft longer than the height of the roof. So for the first 10 meters the monkey has to climb every foot he needs to lift an additional 0.5 lb. So what is the mass as a function of z for the first 10 ft?

After those first 10 ft the entire chain is suspended in the air. From hat point on for every ft he climbs the length of the chain between the ceiling and the "bend" of the chain becomes shorter. Whereas the amount of chain between the the monkey and the "bend" becomes longer. Again you can express m in terms of z, but this time for every ft he has to climb there won't be 0.5 lb added but less. Think about it this way if the monkey reaches the ceiling both pieces of the chain will be 25 ft long. Now try to find both mass functions, after that its a simple integration over z.

## 1. What is a hard integration problem?

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Hard integration problems have many real-world applications, including physics, engineering, economics, and statistics. They are commonly used in modeling complex systems, analyzing data, and solving differential equations. In addition, they play a crucial role in the development of new technologies and scientific advancements.

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