Proving Two Bodies Moving Together are One System

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Discussion Overview

The discussion centers on the conditions under which two bodies moving together can be considered as one system, particularly in the context of applying forces to them. It explores theoretical aspects of motion, force equations, and the role of friction in determining whether the bodies accelerate together or not.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how to prove that two bodies moving together can be treated as a single system, presenting a scenario with two blocks on a frictionless surface.
  • Another participant suggests that if the applied force is small, static friction allows the blocks to stick together and move with equal acceleration, while larger forces lead to sliding and unequal accelerations.
  • Some participants clarify that the assumption of frictionless conditions is critical to the discussion, and they express interest in how friction relates to the movement of the blocks.
  • There is a discussion about the implications of pushing one block and how it affects the other, with a focus on the equations of motion for both blocks treated as a single system.
  • One participant introduces the idea that if the accelerations were different, it would lead to physical consequences, such as one block losing contact with the other or stretching occurring if they are connected by a rope.
  • Another participant emphasizes that the assumption of equal acceleration is an approximation valid for rigid bodies, questioning the conditions under which this holds true.

Areas of Agreement / Disagreement

Participants express varying views on the role of friction and the conditions under which the blocks can be treated as a single system. There is no consensus on the implications of different forces or the nature of the interaction between the blocks.

Contextual Notes

The discussion involves assumptions about friction, the nature of the surfaces, and the physical properties of the blocks, which are not fully resolved. The equations presented depend on these assumptions and the definitions of forces involved.

Kartik.
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How do we say(or prove) that when two bodies are moving together , they can be considered as one system?

Suppose we have two blocks of wood kept on a friction less surface side by side and you apply a force on anyone of them. I suppose from left to right, then the force equations for each block would be

F - FBA -F1= MAAA
FAB= MBAB

And we say that both blocks will move with same accelerations.(Is this right?)

F1 is the force or say resistance which block B gives to A when a Force F is applied(does this force exist?)

Can we prove the accelerations equal? Or its something else?
 
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If the applied force F is small, the blocks stick together (static friction), and their accelerations are equal. If you know the coefficient of static friction μs, you can calculate the maximum force for which this is true.

If the applied force is larger than this, the blocks start to slide against each other (kinetic friction), and their accelerations are not equal.
 
jtbell said:
If the applied force F is small, the blocks stick together (static friction), and their accelerations are equal. If you know the coefficient of static friction μs, you can calculate the maximum force for which this is true.

If the applied force is larger than this, the blocks start to slide against each other (kinetic friction), and their accelerations are not equal.

How do you relate friction with the movement of the blocks?
The case i took is on a friction less plane and assuming no friction between the blocks
And i would really like you to answer the few questions i wrote in those brackets
 
jtbell said:
If the applied force F is small, the blocks stick together (static friction), and their accelerations are equal. If you know the coefficient of static friction μs, you can calculate the maximum force for which this is true.

If the applied force is larger than this, the blocks start to slide against each other (kinetic friction), and their accelerations are not equal.
You seem too be assuming that one of the blocks is on top of the other. If two blocks are side by side (as said in the initial post), and you push on one, so that it pushes on the other (not said in the initial post but if not, one block would have moved independently of the other) then, yes, the two blocks move together, at the same acceleration. If one block has mass m and the other mass M, then together they will move with acceleration a= F/(m+ M).
 
HallsofIvy said:
You seem too be assuming that one of the blocks is on top of the other. If two blocks are side by side (as said in the initial post), and you push on one, so that it pushes on the other (not said in the initial post but if not, one block would have moved independently of the other) then, yes, the two blocks move together, at the same acceleration. If one block has mass m and the other mass M, then together they will move with acceleration a= F/(m+ M).

Like for the two blocks if you write the force equations the equations would be

For both the blocks considered as a single system -
F = (M+m)a

And for just the block on which the force is applied
F-N = ma1

and we say that a = a1; my questions is why?
 
It is actually an approximation good for rigid bodies.
If the accelerations were different, on of two things will happen:
If the pushed body has lower acceleration, the first one will travel a larger distance than the first one. The pushed body being in the way, it (or both) will have to stretch to make room
If the pushed body has higher acceleration, it will loose contact with the pushing body.

Same idea applies to a rope. We assume the rope is inextensible so the bodies connected with a rope under tension have same acceleration (otherwise the rope will have to change its length).
If you allow for elasticity of rope or bodies, then the accelerations are not necessarily equal.
 
HallsofIvy said:
If two blocks are side by side (as said in the initial post)

Sorry, I missed that. :blushing:

Carry on...
 
Kartik. said:
Like for the two blocks if you write the force equations the equations would be

For both the blocks considered as a single system -
F = (M+m)a

And for just the block on which the force is applied
F-N = ma1

and we say that a = a1; my questions is why?
Because they both represent the same thing- the acceration of that block!
 

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