Gravitational Force Between Two Identical Rods of Mass m and Length l

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Homework Help Overview

The discussion revolves around calculating the gravitational force between two identical rods, each with mass "m" and length "l", positioned in a straight line with a separation distance of "l". Participants are exploring the application of calculus and the concept of centers of mass in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to analyze the problem using calculus by considering small elements of mass. Some suggest using the centers of mass to simplify the calculation. Questions arise regarding the correct interpretation of the separation distance between the centers of the rods.

Discussion Status

The discussion is active, with participants providing different perspectives on the problem setup. There is an ongoing exploration of how to accurately determine the separation of the centers of mass, with some guidance offered on using practical examples to clarify the situation.

Contextual Notes

There is some confusion regarding the separation distance between the centers of mass of the rods, with varying interpretations being discussed. The problem context includes the challenge of applying calculus to a physical scenario involving gravitational forces.

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There are 2 identical rods of mass "m" and length "l" separated by a distance "l" in such a way that the 2 rods are in a straight line. Find the Gravitational force between these two rods.



Homework Equations





The Attempt at a Solution



I'm unable to analyse a calculus based strategy such as chosing the small elemnt of mass "dm" length "dx" and so on..
 
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peeyush_ali said:
There are 2 identical rods of mass "m" and length "l" separated by a distance "l" in such a way that the 2 rods are in a straight line. Find the Gravitational force between these two rods.



Homework Equations





The Attempt at a Solution



I'm unable to analyse a calculus based strategy such as chosing the small elemnt of mass "dm" length "dx" and so on..

Just use their centers of mass, and the gravitational force equation. Write that out for us.
 
so u mean to say that the interaction is nothing but...


F= Gm.m/4 l.l ??
 
peeyush_ali said:
so u mean to say that the interaction is nothing but...


F= Gm.m/4 l.l ??

Almost. What is the separation of the centers of mass in terms of l?
 
the situation is like this :

|<___________________>|
_____l_____ (l+l/2+l/2) _____l_____ the separation between the centres of the 2 rods is l+l/2 +l/2 =2l
 
peeyush_ali said:
the situation is like this :

|<___________________>|
_____l_____ (l+l/2+l/2) _____l_____


the separation between the centres of the 2 rods is l+l/2 +l/2 =2l

Two rods of length L have their centers of mass separated by L/2 or 2L? Why? Not.
 
the centres are separated by a length of 2l
 
peeyush_ali said:
the centres are separated by a length of 2l

If each rod is length L, then I don't think so. Just use a practical example. What if each rod is 1 meter long, and you stack them end-to-end. How far apart are the centers of the rods?
 

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