Calculus Work Rope problem helpp ?

In summary, the conversation discusses two problems related to calculating the work required for lifting objects using ropes. The first problem involves a mountain climber hauling up a 50M rope with a weight of 0.624 N/m. The work is calculated using the formula W=integral of 0.624xdx from 0 to 50. The second problem involves lifting a 5 lb bucket using a 20ft rope with a weight of 0.08lb/ft. The work is calculated using the formula W=integral of (.08)(20-x)dx from 0 to 20. The conversation also raises the question of when to use (L-x) in the formula and highlights the importance of setting up coordinates correctly
  • #1
zhao3738
1
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Calculus Work Rope problem helpp pleasezz!?

1.) A mountain climber is about to haul up a 50M length of hanging rope. How much work will it take if the rope weighs .624 N/m?

The Work on the rope is W= integral of 0.624xdx from 0 to 50.

2) A 5 lb bucket is lifted from the ground into the air by pulling in 20ft of rope at aconstant speed. The rope weighs 0.08lb/ft. How much much work was spend lifting the bucket and rope.

Just the work on rope = integral of (.08)(20-x)dx from 0 to 20.

My question is how come the work in question one is not 0.624(50-x), and question to is. When do you use the (L-x)? thank you
 
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  • #2


1) This should be in homework help
2) It all depends on how you set up coordinates. Does x=0 at the bottom? Does x=0 at the top? Somewhere inbetween? Is x+ going up? Is x+ going down? Coordinates are a convention, you can set them up HOWEVER you'd like.
 

1. What is the "Calculus Work Rope problem"?

The Calculus Work Rope problem is a classic physics problem that involves calculating the amount of work required to lift a rope with a given length and weight. It is often used as an example in calculus courses to demonstrate the application of integrals.

2. How do you approach solving the "Calculus Work Rope problem"?

To solve the Calculus Work Rope problem, you first need to draw a diagram and label all the given information, such as the length and weight of the rope. Then, you can use the formula W = F*d to calculate the total work required, where W is work, F is force, and d is distance. Finally, you can use calculus techniques, such as integration, to determine the exact amount of work.

3. What are the key concepts involved in solving the "Calculus Work Rope problem"?

The key concepts involved in solving the Calculus Work Rope problem include work, force, distance, and integration. Work is the measure of energy required to move an object, force is the push or pull applied to an object, distance is the length of the rope, and integration is a calculus technique used to find the total work.

4. Are there any real-life applications of the "Calculus Work Rope problem"?

Yes, there are many real-life applications of the Calculus Work Rope problem. For example, it can be used to calculate the work required to lift heavy objects, such as construction materials or equipment. It can also be applied in engineering to determine the amount of work needed to move objects with pulleys or cranes.

5. Are there any tips for successfully solving the "Calculus Work Rope problem"?

Some tips for solving the Calculus Work Rope problem include drawing a clear and accurate diagram, labeling all the given information, and setting up the problem using the formula W = F*d. It is also important to pay attention to units and use appropriate calculus techniques to find the correct solution.

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