# Query in Newton's Third Law and friction

So My main question is about Friction in Newtons third law

Consider a box on the floor , A force $$F$$ is applied to it on the east direction , the floor then applies an equal and opposite force on the west direction on the box which greatly reduces its Net Force

But My thinking is said Box should not move at all , because Friction is producing equal and opposite force on the box and hence it must remain stationary

What causes friction(kinetic friction in this sense) to take place is The applied force and hence if they are equal in magnitude then they must cancel out ?

• Why are you assuming the friction force always exactly cancels the applied force? Commented Mar 24, 2023 at 13:14
• so then if its not the equal force , then what would be the the pair of force for friction then it must act in opposite direction so it wouldnt make sense for the box to move with the same net force applied , since we are seeing some reduction in movement
– Razz
Commented Mar 24, 2023 at 13:16

You gave a reasonably accurate description of static friction, but then you said it was kinetic friction. In kinetic friction, the magnitude of the force is constant and in the direction opposing the motion, and not in any way determined by any other forces that might be acting on the box. So there's no reason to think it cancels an applied force - unless you're pushing the box at a constant speed. In which case the forces have to cancel to explain why the speed is constant.

• I kind of get it , but as i told about in the comment , like every force must have its opposite pair then what would the opposite pair of friction , during thinking it must cancel the impending force of friction as the opposite force is acting on the floor by box
– Razz
Commented Mar 24, 2023 at 13:21
• I think you've misinterpreted newtons third law. It is not "for every force acting on an object, another opposite force also acts on the same object." If that was newton's third law, then it would be impossible to ever accelerate anything, because it would be impossible to create a net force. Newton's third law is "if object A exerts a force on object B, then an equal and opposite force is exerted on object A from object B." So the opposite force is that the ground that the box moves along is also experiencing a force. Commented Mar 24, 2023 at 13:24
• I understand , thank you very much and sorry that you had to go through my constant bugging
– Razz
Commented Mar 24, 2023 at 13:49
• No problem at all. That's what this website is for. Commented Mar 24, 2023 at 13:50
• Do you mean friction force? Consider a simple scenario a box is placed above another box on the ground. Consider ground to be frictionless, but there is friction between two boxes. If you pull any of them, both will move. The friction force will act on the box on which force is not applied in direction of applied force while for the box on which force is applied, it is in the opposite direction.
– Fire
Commented Mar 24, 2023 at 13:51

Newton's third doesn't say that these two forces should be on the same object. If you have two objects, $$A$$ and $$B$$, one of the two forces could on $$A$$ and the other on on $$B$$. The law can also be stated as $$F_{A\rightarrow B}=-F_{B\rightarrow A}$$, where $$F_{A\rightarrow B}$$ means the force that $$A$$ exerts on $$B$$.

In your case, this does not mean the total force on the box is zero. There is a friction force on the box and there is an equal but opposite force on the floor.

The force pushing the box and the force of friction are not a third law pair, there is no reason why they must always be equal and opposite. They may happen to be equal and opposite, as in the case of a weak force pushing a box on a rough surface, in which case the net force is zero and the box doesn't accelerate anywhere. But they also may not be equal in magnitude, as in the case of a strong force pushing the box on a smooth surface, in which case the pushing force overcomes friction and accelerates the box. Since we can obviously push and accelerate a box, these two forces can't be a third law pair, since third law pairs by definition must always be equal and opposite.

You seem to misunderstand the third law. A third law pair acts between two objects - if A exerts a force on B, B exerts a force on A. The third law does not describe two forces acting on A. There are two unrelated third law pairs at work here. One is external the pushing force applying a force to the box, whose pair is the force the box applies back to whatever is pushing it. The other pair is the force of friction of the ground on the box, which is always equal and opposite to the force of the box on the ground.

In addition, that friction and applied force is not a third Newton law force pair (because they acts on the same body),- friction responds to normal force, which usually is perpendicular to external force applied.

Consider an external force, for example your hand, which pushes down a toy car with $$1KN$$, and car engine's forward force of $$10N$$, then of course in this scenario toy car will not move at all, because your hand produces great static friction which overcomes car's engine force.

You need to distinguish between kinetic friction and static friction. It is static friction the prevents the object from moving at all. Static friction is a variable force that matches the applied pushing force for a net force of zero, up until the maximum possible static friction force is reached. The maximum possible static friction force for a box of mass $$m$$ and the coefficient of static friction between the box and floor of $$\mu_s$$ is $$\mu_{s}mg$$.

When the pushing force reaches the maximum possible static friction force, the box "breaks free" and begins to slide. The friction force then transitions to kinetic (or dynamic or sliding) friction with a coefficient of kinetic friction of $$\mu_k$$ and a kinetic friction force of $$\mu_{k}mg$$ that is generally considered constant (i.e., independent of the pushing force). There is not a precise value of force for the transition from static friction to kinetic friction. You can see this in the friction plot at the following site: http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html#kin

The coefficient of kinetic friction is generally less than the coefficient of static friction (as shown in the link), meaning the kinetic friction force is generally less than the static friction force. Now consider the following two scenarios for the sliding motion of the box:

1. If the applied force that caused the initiation of sliding is maintained, the box will be subjected to a net force of $$(\mu_{s}-\mu_{k})mg$$ and the sliding box will accelerate.

2. If applied force is reduced to equal the kinetic friction force, the net force on the box will be zero and the box will slide with constant velocity.

Now consider the role of Newton's 3rd law.

The horizontal force the box exerts on the floor is equal and opposite to the horizontal force of friction the floor exerts on the box, per Newton's 3rd law. This applies to both (1) and (2) above.

The difference between (1) and (2) is that in (1) the pushing force on the box is greater than the opposing kinetic friction force on the box so the box slides and accelerates, whereas in (2) the two forces are equal and opposite so the box slides at constant velocity.

Hope this helps.