I'm really wanting to get into physics more and I've had this question for a while. I do know a bit about rocketry as I think it's pretty cool but I'm still struggling to understand how Newton's 3rd law applies on a more microscopic level. In a rocket, propellant is used to produce often very hot gas going very fast. This gas then exits through a rocket nozzle. Newton's 3rd law says that this gas moving with a lot of force away from the rocket will cause the rocket to experience an equal and opposite force thus allowing the rocket to liftoff. I'm curious where the actual collisions happen as the rocket seems to just eject the exhaust without the particles "hitting" anywhere to allow the force to occur. If anything needs clarifying I'd be happy to try!
How is Newton’s 3rd law applied in rocket propulsion
conservation-lawsfree-body-diagrammomentumnewtonian-mechanicsrocket-science
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I'm not sure where that picture is coming from, but it's misleading at best and here's why.
Let's say that the rocket expels some stuff (like the flaming gases in the picture), then the force of the rocket on that stuff will be $-F$, say. By Newton's third law, the force of that stuff on the rocket will be $F$. Now let's consider the system consisting of the rocket plus the box. The net external force on this combined system is $F$ because there is nothing external to the system exerting a force on either the rocket or the box besides the gases. Assuming the rocket and the box are in rigid contact, the acceleration of each object equals the acceleration of the whole system which is given by Newton's second law as $$ a = \frac{F}{m_\mathrm{rocket} + m_\mathrm{box}} $$ Now consider the system consisting of only the box. The only external force on this system is the force $f$ of the rocket on the box, so that acceleration of the box must also satisfy $$ a = \frac{f}{m_\mathrm{box}} $$ Combining these results gives $$ f = \frac{m_\mathrm{box}}{m_\mathrm{rocket}+m_\mathrm{box}}F $$ and therefore $$ f < F $$ In other words, the contact force between the rocket and the box is less than the contact force between the gaseous exhaust and the rocket!
If someone ever says "free expansion does no work" all they mean is that it does no work on the vacuum, which is pretty obvious in retrospect. This is because 19th century experimenters and 21st century high schools find it easiest to talk about gas properties in terms of pistons pushing on containers of gas. If the piston is replaced by nothingness, well clearly no work will be extracted from the system.
This doesn't mean the gas doesn't do anything. Think of it this way: First, you have a closed container, sitting in vacuum and containing a gas with some nonzero pressure $P$ inside. The force on the walls is the same in all directions, no matter the shape of the container, but for simplicity you can picture it as a cube with side length $s$. Each wall will have a force $Ps^2$ pushing on it.
Now remove one wall. There will no longer be any force acting on it (your "free expansion" principle), but until the gas is fully evacuated there will be a force on the opposite wall. So your container has a net force in the opposite direction from the gas expulsion lasting for some time. Momentum is conserved; rockets work.
On the side, students who memorize contextless phrases and key words ("free expansion," "time dilation," "entropy is always increasing," ...) will almost certainly apply them incorrectly. One always needs to understand context: What has no work done? Whose perspective says time is dilating? Physics is not about magic combinations of words that one can invoke like some sort of incantation.
Best Answer
There are two ways to think about it, depending on how you want to think about gases. You can think of gasses as having a pressure. When a rocket is burning, there is a very high pressure inside the rocket. That pressure pushes gas downward, but also pushes up on the rocket.
The other approach is to think of individual molecules of gas. They aren't just going straight down. They bounce around with thermal energy (they're very hot). Those gas molecules sometimes collide with the rocket, imparting momentum to the rocket.
Both are valid ways of thinking about a rocket motor, it just depends on how you want to treat them. Sometimes its best to think of the gasses as a fluid. Other times its best to think of it as a bunch of particles. But both have a rationale for why the rocket goes upward.