Doubt on the 3rd law of motion by Newton

Question

Let's say I am holding a pen still in air; logic says that I have applied a force equal to weight of the pen. But here comes the confusion: when I put a force mg upwards to resist the gravitational force of pen,then according to Newton's 3rd law of motion the pen should apply a force mg downward. Now its understood that this force is tolerated by our muscles but to tolerate force one must apply force against it. So to tolerate that force and ensure the hand holds the pen still in air, the muscles apply a force mg again which will resist the reaction force. So in total I have applied a force 2mg. How is this possible?

Answer 1

@Amit comment is correct.

You appear to be conflating the physical effort of the muscles involved with maintaining the position of the pen (which would be even more pronounced if you were maintaining the position of a heavy weight), with Newton's 3rd law.

Newton's 3rd law has nothing to do with the sources of the equal and opposite forces. The source of the upward force on the pen could just as well be a table that the pen rests upon.

Hope this helps.

Answer 2

I have found such concerns are addressed well with a change in wording. Stating Newton's 3rd law differently, forces always come in pairs. If there is a force of A on B, then there is always a force of B on A, of equal magnitude and opposite direction. Thinking of them as a pair rather than an action causing a reaction short circuits the logic that causes one to accidentally think that said reaction causes a re-reaction.

If your pen is pushing down on your hand, then your hand is pushing up on the pen. They come in pairs: one pen on hand, the other hand on pen. One does not cause the other, they just happen together.

Answer 3

Suppose weight was the only force acting on the pen. It would accelerate downward.

Suppose you hold your hand steady. Gravity pulls it down and you push it up equally hard.

Suppose you put a pen in your and and do not change the upward force. The downward force is now bigger because of the weight of the pen. Your hand and the pen will accelerate downward.

If you are holding a pen and your hand steady, these are the forces:

• The pen - weight and upward force from your hand. Equal and opposite
• Your hand - weight of your hand and the pen, and and equal upward force.

The pen does exert a downward force on your hand equal and opposite to the upward force your hand exerts on the pen.

Answer 4

Let's use observation to understand the situation. You can use an online simulation or just use your hands, but this time choos a heavier object. When you pick up the object, you can see your hand trembling in the air. Considering the air in the system is still, you can see the opposing force acting against the applied force on your hand and thus making your hand shake by moving it slightly downward. But see if comes back to it's position. What you think did it? There was a resistance in the work of that force. So, I say it is the frictional force (limiting friction to be exact) that is preventing the motion of your hand downward and that's why you are able to hold your pen. What your doubt about "2mg force being applied downward". No, the opposing force is applied on your hand while the applied force F(=mg) and mg is on the pen which is the thing in question. So, the mg from newton's 3rd law cannot be a part of the system since it is applied on the source of applied force and not just the system itself.