Center of Mass Movement in Work Integration

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SUMMARY

The discussion focuses on calculating the work done in lifting a 10-foot chain weighing 25 pounds from a hanging position to the ceiling. The participant correctly identifies that the weight per unit length of the chain is (5/2)Δx. The key challenge lies in determining the movement of the center of mass during the lifting process, as the entire chain must be considered rather than just the endpoints. The participant seeks clarification on the center of mass's initial and final positions relative to the ceiling.

PREREQUISITES
  • Understanding of calculus concepts, particularly integration
  • Familiarity with the concept of center of mass
  • Knowledge of work-energy principles, specifically Work = mgh
  • Ability to set up and evaluate definite integrals
NEXT STEPS
  • Study the concept of center of mass in continuous distributions
  • Learn how to set up integrals for work done on variable weight objects
  • Explore examples of lifting chains and cables in physics
  • Review calculus techniques for solving work problems involving integration
USEFUL FOR

This discussion is beneficial for students in calculus courses, particularly those struggling with work problems involving variable weights and center of mass calculations. It is also useful for educators looking for examples to illustrate these concepts in a classroom setting.

Jet1045
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I posted this question in the calculus section but i guess that's the wrong place, so here is my question:

1. Homework Statement

Alright, so my calc class isn't getting easier and we started doing 'work' problems, and I'm just not getting it. Here's the question: A 10ft long weighs 25lbs and hangs from a ceiling. Find the work done in lifting the lower end of the chain to the ceiling so that its level with the upper end.

2. Homework Equations



3. The Attempt at a Solution
Alright, so for the interval of [0,10] you would divide it into n subintervals of length Δx.
The weight of the piece would be (25/10)Δx which is simplified to (5/2)Δx

So in class we did an example similar to this but it only involved lifting the cable to the top of the roof, where as this question you are taking the bottom and lifting it to meet the other end at the roof. So i don't think it is as simple as taking the integral from 0 to 10 of (5/2)x like it is for just lifting a chain to the top of the roof.
ANy help would be greatly appreciated. :)
 
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Work = mgh,


what distance does the center of mass move? Where is the center of mass before and after the move in relation to the ceiling?
 

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