I know that without presence of any "External" force momentum is always conserved. But how do we distinguish between "External" force and "Internal" force where all are "Force"?
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$\begingroup$ It depends on system choice. $\endgroup$– lucasCommented May 15, 2016 at 8:47
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1$\begingroup$ Please, describe in detail. $\endgroup$– AbsaedCommented May 15, 2016 at 9:25
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$\begingroup$ When you choose a system, you should determine its boundaries. A force is define as internal if it is inside the boundaries of the system. $\endgroup$– lucasCommented May 15, 2016 at 9:34
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$\begingroup$ But why momentum remains unchanged though there are internal forces acted upon the system? $\endgroup$– AbsaedCommented May 15, 2016 at 9:40
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2$\begingroup$ Because internal forces cancel each other. They are always two by two equal but opposite in direction. $\endgroup$– lucasCommented May 15, 2016 at 9:42
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2 Answers
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You define a system which you are interested in.
If there is no net external force acting on the system then linear momentum is conserved.
You can identify internal forces as they must occur in equal in magnitude but opposite in direction pairs - Newton's third law.
So you find a force in the system $\:\mathbf{f}_{12}\:$ which is the force on part $1$ of the system due to part $2$ of the system which has its equal in magnitude opposite in direction twin, $\:\mathbf{f}_{21}\:$ force on part $2$ of the system due to part $1$ of the system.
There is no such pairing of forces within the system for external forces which are forces on the system due to something outside the system so their Newton's third law pair would be a force on something outside the system due to force produced by system.
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$\begingroup$ But external force has also an equal reaction force according to newtons third law.So how we recognize? $\endgroup$– AbsaedCommented May 15, 2016 at 9:27
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$\begingroup$ You have missed the point. That reaction force will not be acting on part of the system it will be acting on something outside the system. As I wrote "so their Newton's third law pair would be **a force on something outside the system ** due to force produced by system.". $\endgroup$– FarcherCommented May 15, 2016 at 9:43
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$\begingroup$ @Absaed :---- On the part $\:k\:$ with linear momentum $\:\mathbf{p}_{k}\:$ and rate $\:\mathrm{d}\mathbf{p}_{k}/\mathrm{d}t=\overset{_{_{\bullet}}}{\mathbf{p}}_{k}$ $$ \mathbf{F}_{k}+\sum_{\jmath}\mathbf{f}_{k\jmath}=\overset{_{_{\bullet}}}{\mathbf{p}}_{k} \tag{01} $$ and $$ \sum_{k}\mathbf{F}_{k}+\underbrace{\sum_{k}\sum_{\jmath}\mathbf{f}_{k\jmath}}_{=\mathbf{0}}=\sum_{k}\overset{_{_{\bullet}}}{\mathbf{p}}_{k}=\overset{_{_{\bullet}}}{\mathbf{P}} \tag{02} $$ $\endgroup$– VoulkosCommented May 15, 2016 at 13:15
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For physical systems the external forces include 1. Applied Forces 2. Normal force of reaction 3. Force due to strings(tension) 4. Frictional forces between surfaces in contact Etc.
Whereas internal force include
1.Force due to gravity between masses 2.Magnetic force between magnetic bodies 3.Electrical force 4 spring force etc.
To identify force as internal and external one must define the system and its surrounding and then go for classification.
If parts of the same system exert forces on each other ,then they form pairs of internal forces
Internal forces operate such that the overall mechanical energy of a system does not change .
If we have a mechanical system the external forces are those which applies between part of a system and its surrounding/environment.
Some illustrations:
A batsman hits a cricket ball- the particles of the ball holding together are due to internal forces but the bat forcing the ball through a hit is external force on the ball.
If motion of a lift is our system then a person jumping or playing a ball, doing some exercises inside the lift is due to internal force only .
A vehicle is moving and parts of the vehicle are applying internal forces but the force of friction being applied by the road is external force on the vehicle. similarly the push of the vehicle on surface of the road and the normal reaction on it are external force .
It is a misnomer to look for internal force using Newton’s third law of action and reaction . As the pair of these forces act on different bodies and are external to them individually.
