#variable mass
orchid girder
limpid socket
orchid girder
dm/dt = rho A (v+u)
Mv+ Fdt = (M+dm)v - dmu
Fdt = dm(v-u)
F= rho A (v^2 -u^2 )
where am i going wrong
dark sapphire
Is it F = ρA(v+u)(2v+u) ?
orchid girder
got it nvm
dark sapphire
I did it like this
orchid girder
thoda sign ki galti
orchid girder
I did it like this
this is wrong tho
dark sapphire
this is wrong tho
Why?
orchid girder
applying impulse momentum theorem
Fdt= (M+dm)v - (Mv-dmu)
dark sapphire
applying impulse momentum theorem
Fdt= (M+dm)v - (Mv-dmu)
What's that theorem?
orchid girder
What's that theorem?
change in momentum = F.dt integration
dark sapphire
Ok....
orchid girder
yeah sure
orchid girder
applying impulse momentum theorem
Fdt= (M+dm)v - (Mv-dmu)
Fdt = dm(v+u) , substitute dm from first msg
dark sapphire
I did it like this
signal cairn
Now I have this doubt
??
signal cairn
where did steam come from
signal cairn
oh mbmbmb
dark sapphire
As in, it can be approximated as a fluid due to it being approximately continuous flow
signal cairn
F = Fth cuz constant velocity
signal cairn
applying impulse momentum theorem
Fdt= (M+dm)v - (Mv-dmu)
yeah isse ho jayga aage
signal cairn
I did it like this
oh
yeah there's some issue with that
the force from the stream particles is the thrust force
and whenever we use thrust force we use mdv/dt
instead of dP/dt
cuz it is designed in this way
dark sapphire
instead of dP/dt
Yes, but that's fine here since the mass of the stream itself isn't changing. It's assumed to be infinite
Oh I see your point nvm
signal cairn
Yes, but that's fine here since the mass of the stream itself isn't changing. It...
no momentum of the block
I didn't get this
dark sapphire
It's not going to be (v+u)² is what I meant.
signal cairn
uh can you please elaborate
@dark sapphire did you get the issue?
I think I got it
we can't apply impulse momentum on the block itself cuz it does nothing
we need to apply impulse momentum on M + dm system
and using thrust force
F - Fth = mdv/dt
since dv/dt is zero
F = Fth
and Fth = (v+u)dm/dt and dm/dt = pA(v+u)
so F = pA(v+u)^2
orchid girder
@dark sapphire can i close?
dark sapphire
<@763645886500175892> can i close?
Yes yes. Sorry
orchid girder
all clear?
white delta
<@763645886500175892> can i close?
Wait a min, please. 😅
orchid girder
alrr
white delta
Yes, but that's fine here since the mass of the stream itself isn't changing. It...
Yep, the velocity of the steam after impact is not zero relative to the plank no?
dark sapphire
Yep, the velocity of the steam after impact is not zero relative to the plank no...
Ye, I got it
white delta
That would mean rather than thrust force, it would have to be more like a k.t.g scenario?
dark sapphire
That would mean rather than thrust force, it would have to be more like a k.t.g ...
Pressure force is what I considered in the first place
white delta
Ye, I got it
No, that's my doubt 😅
dark sapphire
It's similar to a fluid rather than a Maxwell-Boltzmann distribution imo since they don't have intrinsic kinetic energy
Each microscopic particle is considered to be massless, but the whole has a mass
white delta
Hmm, collision of particles with the wall must be elastic no?
dark sapphire
As opposed to gases where we proceed with the assumption of massive particles.
dark sapphire
Hmm, collision of particles with the wall must be elastic no?
Inelastic here by definition, since there is accumulation.
dark sapphire
Oh but the coefficient of restitution isn't zero here is it? In the viewer frame.
I don't have paper on me, this is frustrating
No, it's zero nvm. They don't separate at all
white delta
Oh but the coefficient of restitution isn't zero here is it? In the viewer frame...
Yep, the coefficient of restitution is the thing that's bugging me...
dark sapphire
Yep, the coefficient of restitution is the thing that's bugging me...
The relative velocity of separation is zero here because they're moving together after collision right?
white delta
The relative velocity of separation is zero here because they're moving together...
I think that depends on what you assume, the vital information that's missing from the question.
dark sapphire
I think that depends on what you assume, the vital information that's missing fr...
Yeah, the accumulation isn't explicit here.
white delta
If the collision is taken to be elastic and dust particles very small, it is a ktg question. if inelastic and big particles, you can treat it like fluid.
dark sapphire
It could be a non-stick surface for all we know
white delta
@orchid girder ig you can close the thread now. 🙏
orchid girder
+solved @white delta