# Why an internal force cannot move a closed system externally?

Suppose a large box with a man inside.He is standing on a side of the box which he calls as the 'floor'.(This immediately indicates that this is an accelerated frame of reference). Also assume there is vacuum inside as well as outside the box. Now he is going to walk over the floor to punch with his fist an adjacent side. And then he did punch the wall. Two questions come into my mind. They are:

1. While he is walking the distance on the floor towards the adjacent wall ,would the floor move in opposite direction according to Newton's 3rd law? (like a treadmill?)

2.When he punches the adjacent wall, would the wall move in the direction of punching with he himself getting recoiled away from the wall due to Newtons 3rd law?

It would be great if an explanation is also provided. Also does the law of conservation of momentum got to do anything in this scenario?

• Internal forces obey Newton's Third Law. So they cancel out each other. Thus have no effect on the object. – Global Jul 28 '18 at 8:15
• Possible duplicate of Will the box move? – sammy gerbil Jul 30 '18 at 13:50

## 2 Answers

Internal forces come in pairs.
Let particle 1 and particle 2 be part of a system.
If there is a force on particle 1 due to particle 2 then there will also be an equal in magnitude and opposite in direction force on particle 2 due to particle 1.
These two forces are a Newton Third Law pair. The resultant of these two forces is zero.

• @JulesKurianMathew In such a discussion you must first define the system you are dealing with. In that way internal and external forces can be differentiated. – Farcher Jul 28 '18 at 16:16

The fact that there is no resultant external force on the system means that its centre of mass obeys Newton's 1st Law - ie it remains in the same state of rest or uniform velocity. Individual parts of the system may move relative to each other due to internal forces, but the motion of the centre of mass of those parts does not change.

Yes this is a consequence of Newton's 3rd Law, and it is related to the conservation of momentum. If a system is composed of masses $m_1, m_2, m_3, ...$ and the positions of their centres of mass are $x_1, x_2, x_3, ...$ then the position $X$ of the centre of mass of this system is defined by $$m_1 x_1+m_2x_2+m_3x_3+ ... =(m_1+m_2+m_3+ ...)X=MX$$ where $M$ is the total mass of the system. If these objects move over time due to internal forces then their velocities are given by $$m_1 \dot x_1+m_2 \dot x_2+m_3\dot x_3+ ... =M\dot X$$ $$m_1 v_1+m_2v_2+m_3v_3+ ...=\text{constant}$$ because the velocity $\dot X$ of the centre of mass does not change unless an external force acts. (By definition the total mass $M$ of the system does not change.) The last equation is a statement of the conservation of momentum.