I don't quite get Newton's third law

[physgirl]

i don't quite get Newton's third law... :(

It sounds simple enough, F₁₂ = -F₂₁. However, I'm getting that mixed up with the second law now (ie. if there is a net F on the system, there will be acceleration).

For instance, say that there's a box, and the "F" vector is pointing to the right. However, there's another force (say, F₂) pointing to the left. If F is greater than F₂, then the box will accelerate to the right according to F-F₂=ma. Correct?

But... doesn't the Third law say that for any force acting on this box, there's always another "force" (opposite in sign, equal in magnitude) ALSO acting on the box? As in... in the above scenario, there's -F acting upon the box to counter F, and -F₂ acting upon the box to counter F₂... This confuses me, because this is implying that there's no net force on the system right? Because by the Third law, there's some force (-F₂₁) canceling out the force in interest (F₁₂)?!

Where's my misunderstanding coming from?

Thanks in advance for any input :)

 

[DylanB]

But... doesn't the Third law say that for any force acting on this box, there's always another "force" (opposite in sign, equal in magnitude) ALSO acting on the box?

Here is the confusion. Newton's 3rd law describes in the simplest case, two objects in contact with each other will exert equal and opposite forces on each other. For example, if the force F on your box is caused by your hand pushing the box to the right, then there will be an equal force from the box pushing on your hand (not the box) to the left.

 

[rcgldr]

Newton's third law takes into account the reaction force related to acceleration of an object. This reaction force does not cancel out the force that is causing the acceleration, it's just a reaction to the acceleration caused by a force.

 

[D H]

IBut... doesn't the Third law say that for any force acting on this box, there's always another "force" (opposite in sign, equal in magnitude) ALSO acting on the box?

Piling on Dylan's response, the third law counterpart to a force always acts on some other body. Moreover, third law pairs are always the same kind of force. For example, the Earth exerts a gravitational force on the Moon, and the Moon exerts an equal but opposite gravitational force on the Earth.

A more complicated example: Think of a sled sitting the ground. The forces acting on the sled are gravity (downward) and the normal force (upward). The net force acting on the sled is zero¹ as the sled isn't moving. This does not mean that gravity and the normal force are third law counterparts. Both forces act on the sled and the two forces are different kinds of forces. One is gravitational and the other is electrostatic repulsion. The third law counterparts of these forces are the gravitational force and electrostatic repulsion exerted by the sled on the Earth. This example can be made even more complex by adding a person pulling a sled with a rope. There are *lots* of third law pairs here.------------------------

¹From an inertial perspective, the sled is moving; it is sitting still on the rotating Earth. The sled undergoes uniform circular motion about the Earth's rotation axis. The gravitational and normal forces on the sled are neither equal in magnitude nor opposite in direction. The vector sum of the normal and gravitational force do not quite cancel.

 

[Asok]

the third law confusion.. well .. it can be explained like this... the force and the reaction which describe in the third law are acting on different objects.. one force act on the box and the other act on the the hand.. both are same and opposite in direction.. if you take the box alone only one force acts on it.. the reaction of that force acts on the hand.. so to the box apply F=ma then you can have one unbalanced 'F', hence the acceleraion by that force..

Another thing.. say you draw a box which is in stable on a table and you are marking the forces.. then probably you will mark 'mg' downwards and the reaction to the upward by the table.. but never get mixed up, those are not the force and the corresponding reaction which Newton says in his third law..the reaction for the 'mg' is unmarked force at the Earth's center of gravity which acts upwards.. and the 'reaction' for the 'reaction force' which acts from the table on the box, is the force which acts downwards and acts on the table from the box.. mmm. i think you better sketch this using four forces.. (you will have to draw the Earth's center too)