Thursday, July 20, 2017

newtonian mechanics - Why does Newton's Third Law work for fields?


Newton's 3rd law goes like this: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.


I find the law intuitive in some cases, for instance, when a moving particle collides with a stationary particle. Since momentum is conserved in the collision (assuming its elastic), some momentum of the moving particle is transferred to the stationary particle. As a result, the momentum of the moving particle decreases upon collision, an effect of the "equal and opposite force" exerted by the stationary particle.


But when it comes to gravitational (and electric) fields, Newton's Third Law seems to hold because of the equation $F=G\frac{m_1m_2}{r^2}$. Also the previous example wouldn't make sense because the total momentum/kinetic energy of objects in a field is always changing (not conserved). Edit: The momentum is conserved, because the system here includes the earth which also experiences a force of equal magnitude. the system should be a closed system for momentum to be conserved.


The justifications for Newton's Third Law seem to vary from case to case. Would there be any way to relate the two above cases and other cases?




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