Centre of mass of non-uniform rod

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Homework Help Overview

The discussion revolves around finding the center of mass of a non-uniform rod, where the mass increases linearly with distance from one end. The original poster describes the setup involving linear density and attempts to express the center of mass in terms of mass, length, and linear density parameters.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the integration of linear density and the challenges in eliminating a constant from the equations. There are inquiries about the correctness of calculations and the method of expressing mass in terms of linear density.

Discussion Status

The conversation includes attempts to verify calculations and clarify the integration process. Some participants have provided guidance on the relationship between mass and linear density, while others are exploring how to simplify the equations involved.

Contextual Notes

There is mention of a guideline regarding the posting of handwritten work, indicating a preference for typed submissions to facilitate discussion. This suggests a focus on clarity and accessibility in the problem-solving process.

carlyn medona

Homework Statement


The mass of non uniform rod increases linearly with distance from lighter end. If m is mass of the rod and l it's total length a the linear density at lighter end, then found the distance of centre of mass from lighter end

Homework Equations


I put λ= kx+a where lands is linear density k a constant and x the distance from lighter end and integrated but can't get the answer in terms of m l and a

The Attempt at a Solution

 
Physics news on Phys.org
Please show us what you did.
 
So how do I eliminate k from the equation
 

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Remember that m = ∫(kx+a)dx
 
I think I made a mistake in my first calculation , is this one right?
 

Attachments

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carlyn medona said:
I think I made a mistake in my first calculation , is this one right?
Yes this looks right.
 
Thanks for checking
 
carlyn medona said:
So how do I eliminate k from the equation

For future reference: you should not post images of handwritten work; actually take the time and trouble to type things out. Most helpers will not even look at all at such posted images, but you were lucky in this case to get a sympathetic reader. Please consult the post "Guidelines for students and helpers" by Vela, pinned to the start of this forum's file list.
 
Oops sorry for that.
 

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