Newton's Third Law textbook -- question about the sign of a force

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Discussion Overview

The discussion revolves around the interpretation of Newton's Third Law, specifically the relationship between the forces exerted by two objects on each other, as described in a textbook. Participants explore the implications of vector versus scalar representations of forces and the potential ambiguities in their descriptions.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants question whether the textbook's statement of ##F_{AB} = F_{BA}## is correct, suggesting it should be ##F_{AB} = -F_{BA}## if considering vector directions.
  • Others propose that the textbook may be referring to magnitudes of forces, which are equal, rather than their vector representations.
  • It is noted that many introductory textbooks use boldface or arrows to denote vector quantities, while unadorned italics may represent scalar magnitudes.
  • Some participants highlight that the phrase "opposite in direction" is often assumed, leading to a focus on magnitudes in discussions of Newton's Third Law.
  • A later reply discusses the role of diagrams in indicating the direction of forces and how they relate to the coordinate system used in calculations.
  • One participant emphasizes that in practical situations, the sign of a force is either provided or can be determined, suggesting that an arbitrary sign can be assigned to unknown forces without affecting the final outcome.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of force representations in Newton's Third Law. There is no consensus on whether the textbook's statement is correct or how to best represent the forces involved.

Contextual Notes

The discussion reveals potential ambiguities in the representation of forces as vectors versus scalars, and the reliance on diagrams for understanding directionality. Participants acknowledge that the interpretation may depend on the context and conventions used in specific problems.

Mr Davis 97
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Imagine that I am pushing on a wall. Then my textbook says that by Newton's third law, ##F_{AB} = F_{BA}##, where I am B and the wall is A. Isn't this wrong? Shouldn't it be that ##F_{AB} = -F_{BA}##?
 
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Mr Davis 97 said:
Shouldn't it be that ##F_{AB} = -F_{BA}##?
Sure, if they are using ##F## to represent the forces as vectors. Perhaps they were just talking about the magnitudes of the forces, which are equal.
 
Doc Al said:
Sure, if they are using ##F## to represent the forces as vectors. Perhaps they were just talking about the magnitudes of the forces, which are equal.
Ah, I see. I guess it can get kind of ambiguous.
 
Most introductory textbooks use boldface or arrows on top to denote vectors: $$\mathbf{F}_{AB} = -\mathbf{F}_{BA}\\{\vec F}_{AB} = - {\vec F}_{BA}$$ versus unadorned italics for magnitudes (scalars): $$F_{AB} = F_{BA}$$
 
Newton's Third Law: For every force acting, there is an equal and opposite force acting. Equal in magnitude, opposite in direction.
Since the "opposite in direction" is often taken as a given, other descriptions generally concentrate on the magnitude, and so FAB = FBA.
 
Mr Davis 97 said:
Ah, I see. I guess it can get kind of ambiguous.
If there is a diagram showing the opposite arrows, they are often meant to indicate the convention for positive direction of each force individually. So the later math doesn't use vectors in one coordinate system, but factors for the indicated unit vectors. A negative result then indicates that the force is opposite to its arrow in the diagram.
 
The thing is, for a given object (free body diagram) that force only applies once. If you stick with the data you've been given in any question or practical situation, the sign of any force is either given or is calculable. You can give an 'unknown' an arbitrary sign and the calculation will produce the correct sign eventually.
 

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