Momentum

my mind is too feeble to understand i'm sure i'll understand this tomorrow since i've got a physics lesson tomorrow, a double too ^-^

The force F is equal to ma, right?
$F=ma$

Newtons second law. Force is proportional to the rate of change of momentum.

$a=\frac{v-u}{t}$

From acceleration: Acceleration is the rate of change of velocity.

Momentum is given by $mv$, mass times velocity

$\therefore F=\dfrac{mv}{t}$

So force is the rate of change of momentum (from these simple equations)

Now the particles are given a force by the explosion:
This force changes the acceleration of the particles
Therefore changing the velocity
This gives them momentum
Momentum is converved etc etc

Sorry if im repeating myself im not sure how to explain it any other way.

fwiw a popular analogy is firing a gun.

if the gun at rest fires a cannonball of mass m₁ at velocity v₁ the cannonball has gained momentum m₁v₁

the story doesn't end there though because while the gun is pushing the cannonball out forward - the cannonball is also simultaneously pushing the heavier cannon backwards (Newton) and the interesting result of this is that momentum is conserved... the momentum of cannon+ball before firing equals the momentum of cannon+ball after firing.

e.g. if m₁ = 5 kg and it's fired at v₁ = +200 m/s giving it momentum of +1000 kg m/s

the momentum of the gun immediately after firing must be -1000 kg m/s - if the gun has a mass of 1000 kg it's new velocity is -1 m/s or 1 m/s in the opposite direction to the cannonball's direction.
note this is immediate - the gun doesn't need to wait for the cannonball to hit something and slow down before it can start moving.

same principle in a rocket except that the cannonballs are each the size of molecules and there are billions of them, so instead of one cannonball with a mass of 5kg you'd think about the momentum of 5kg of molecules being forced out of the nozzle of your rocket motor at a high velocity.

@thefatone I'll try and put it into simpler terms.

Imagine a stationary rocket in outer space. Its total velocity is zero, so its total momentum is also zero (momentum = mass x velocity).
The key fact to remember is that the total momentum is constant. So no matter what happens it will always equal zero in this scenario.

Rocket engine fires; rocket fuel goes backward (with negative velocity therefore carrying negative momentum) and rocket goes forward (to balance momentum change).

ok it makes more sense but how does a rocket motor provide a propulsive force even in space? obviously there's something i'm not getting here and once i get that little thing everything will make sense but it just seems that i haven't got that thing yet :/

so far i understand
how newtons 3rd law is applied since rocket motor pushes rocket forward and exhaust gases push back
but i don't see where momentum fits into any of this :/
i understand everything you've said there but i don't see the link between the question and momentum

ok it makes more sense but how does a rocket motor provide a propulsive force even in space? obviously there's something i'm not getting here and once i get that little thing everything will make sense but it just seems that i haven't got that thing yet :/

so far i understand
how newtons 3rd law is applied since rocket motor pushes rocket forward and exhaust gases push back
but i don't see where momentum fits into any of this :/
i understand everything you've said there but i don't see the link between the question and momentum

The explanation of the question hinges on the concept of conservation of momentum.

A rocket engine heats up gases. These gases are forced out of the back of the rocket with negative momentum. In order for momentum to be conserved, the rocket accelerates forward with a positive momentum i.e. in the other direction.

Newton's 3rd law: If an object A exerts a force $F_{AB}$ on an object B, then B exerts an equal and opposite force, $\underline{F}_{BA} =-\underline{F}_{AB}$ on A.

Newton's 2nd law: $\underline{F} = \dfrac{\mathrm{d}\underline{P}}{\mathrm{d}t}$ ie. force is the rate of change of linear momentum.

Let A and B be objects applying force on each other with no other forces on them.
Let $\underline{I}_A(t)$ be the change in momentum of A from time 0 to t and similarly for $\underline{I}_B(t)$.

$\therefore$ from Newton's second law, $\underline{F}_{BA} = \dfrac{\mathrm{d}\underline{I}_A}{\mathrm{d}t}$ and $\underline{F}_{AB}= \dfrac{\mathrm{d}\underline{I}_B}{\mathrm{d}t}$.

Applying the fundamental theorem of calculus, $\underline{I}_A(t) = \displaystyle\int_0^t \underline{F}_{BA}\mathrm{d}t$ and similarly $\underline{I}_B(t) = \displaystyle\int_0^t\underline{F}_{AB}\mathrm{d}t$.

$\therefore \underline{I}_A(t) =\displaystyle\int_0^t \underline{F}_{BA}\mathrm{d}t =\displaystyle\int_0^t-\underline{F}_{AB}\mathrm{d}t =-\displaystyle\int_0^t\underline{F}_{AB}\mathrm{d}t = -\underline{I}_B(t)$.

So if an object gives another object an impulse, the first object receives the same impulse back.

The rocket is changing the velocity of the propellant ie. giving the propellant an impulse, so receives an impulse back.

Momentum is directly proportional to velocity as momentum= mv.
The force provided accelerates it so basically as v goes up so does momentum.

well ffs then >.> i do this too much, sometimes i don't understand unless i fully understand the concept of what i'm being taught and that kills me to know this bc it tells me i'm retarded

i understand this but how is this linked to the question?

i understand this

but i can't piece together all the info and make links to provide me with a single answer to the question

"Explain how it's possible for a space rocket motor to provide a propulsive force even when the rocket is in outer space."

So you need to know momentum for the question?

i understand this but how is this linked to the question?

The rocket is giving an impulse to the propellant, so receives an impulse in the opposite direction.

Unless you mean "How does the rocket give the impulse to the propellant?", in which case it depends on the type of rocket.
Chemical:
SRBs ignite a solid fuel/oxidiser mixture, which produces hot gas, which produces pressure in the combustion area, forcing the gas out. Liquid fuel rockets burn a liquid fuel/oxidiser mixture in a combustion chamber, which produces hot gas which is directed out.
Electrical:
Ion drives ionise gas, which is moved through an electric field to accelerate it and directed out of the rocket.
Nuclear:
Nuclear thermal rockets use nuclear energy to heat up a gas, which is directed out.
There are many other kinds.

well ffs then >.> i do this too much, sometimes i don't understand unless i fully understand the concept of what i'm being taught and that kills me to know this bc it tells me i'm retarded

so how does this give me an answer to the question????
i'm still super confused about everything

also i made a mistake i have a double physics tomorrow not today xD

I'm gonna draw you a nice diagram brb

And everyone finds things difficult to comprehend now and again, dw about it.

@thefatone


See if this helps

are you happy about the gun being pushed backward when the canonball is pushed forward and how momentum is conserved?

so what's different if it fired out 5kg of gas instead of a 5kg metal ball?
5kg of gas is the same mass as 5kg of metal
gas going at 200 m/s is going at the same velocity as a ball going at 200 m/s
momentum is mass times velocity, but the mass doesn't have to be a solid object. liquid or gas also work because they also have mass.

i understand but where do the things gain momentum from?