A cannonball firing from a cannon is often given as an example of Newton's third law. The explanation goes like this: The cannon exerts a force on the cannonball and thus the cannonball exerts an equal but opposite force on the cannon. The ball accelerates rapidly and the cannon recoils in the opposite direction, but with much less acceleration than the cannonball because the cannon is much heavier (Newton's second law).
I am confused by this explanation. The cannon is fired when an explosive charge is detonated, causing a sudden and immense increase in pressure. Is it not this pressure that causes the rapid acceleration of the cannonball and the recoil of the cannon, not an action–reaction between the cannon and the cannonball? If no cannonball is present when the charge is detonated, then the pressure dissipates much more quickly and the recoil is smaller but still present (at least going by this question on Quora), which seems to also go against the action–reaction explanation.
Or am I talking nonsense? I suspect – or rather hope – that the above paragraph is correct but incomplete. I am sure Newton's third law (or the conservation of momentum) plays a fundamental role, but I am struggling to come up with a satisfactory explanation.
Best Answer
For purposes of this model, we can consider the expanding gas from the explosion to be part of the cannon, or as an intervening object between the cannon and the ball. So the gasses exert a force on the ball. The ball exerts a force back on the gasses. This is transferred to the cannon.
You could also imagine or build a (toy) "cannon" with a spring mechanism to propel the ball, rather than an explosion. You'd see very similar results.
In any case, the deeper point, which you will soon learn, is that momentum is a conserved quantity. Regardless of what mechanism applies the force on the ball and the cannon, after the ball is flying free the cannon must end up with as much backwards momentum as the ball has forward momentum.
Because air and exhaust gasses from the explosion are expelled from the cannon. These gasses have mass and carry momentum, therefore they exert a reaction force on the cannon just as a ball does.