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

• Mr Davis 97
In summary, the textbook is saying that the forces on an object are equal in magnitude, but opposite in direction.
Mr Davis 97
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}##?

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.

## 1. What is Newton's Third Law?

Newton's Third Law, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. This means that when a force is applied to an object, the object will exert an equal force in the opposite direction.

## 2. How does Newton's Third Law relate to the sign of a force?

The sign of a force refers to its direction, either positive or negative. According to Newton's Third Law, if a force is applied in one direction, there will be an equal force applied in the opposite direction. This means that the sign of the force will be opposite to the sign of the reaction force.

## 3. Can the sign of a force be negative?

Yes, the sign of a force can be negative. This means that the force is acting in the opposite direction to its reference point. For example, if a force is acting to the left, its sign will be negative.

## 4. How does Newton's Third Law apply to everyday situations?

Newton's Third Law can be observed in many everyday situations. For example, when you walk, your foot exerts a force on the ground, and the ground exerts an equal and opposite force on your foot, allowing you to move forward.

## 5. Does Newton's Third Law apply to all forces?

Yes, Newton's Third Law applies to all forces, whether they are contact forces (such as pushing or pulling) or non-contact forces (such as gravity or magnetism). In all cases, there will be an equal and opposite reaction force.

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