ganeshie8
  • ganeshie8
The velocity of particle is \((v_x, v_y, v_z)\). As shown, the side of the cube is of length \(L\). Find the time taken for the particle to go from one wall to the opposite wall.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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ganeshie8
  • ganeshie8
|dw:1450170416631:dw|
ganeshie8
  • ganeshie8
basically we need to find the time taken by the particle to go from the left wall to the right wall
ganeshie8
  • ganeshie8
ignore gravity

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More answers

ParthKohli
  • ParthKohli
this is a great question and is a foundational one for the kinetic theory of gases
ganeshie8
  • ganeshie8
yes! also i think we assume that the collisions with walls are elastic
ParthKohli
  • ParthKohli
yeah, precisely. I think you know the answer to this already. not sure what you asked this for.
ganeshie8
  • ganeshie8
I have just started kinetic theory of gases, still not sure what the textbook is saying..
ParthKohli
  • ParthKohli
Consider the projection in the x-axis.\[T = \frac{distance}{speed} = \frac{L}{v_x}\]
ganeshie8
  • ganeshie8
aren't you assuming that the particle hits each wall with an angle 90 ?
ganeshie8
  • ganeshie8
|dw:1450171016975:dw|
ganeshie8
  • ganeshie8
it can take any random route in the cube right ?
ParthKohli
  • ParthKohli
sorry, I was away.
ganeshie8
  • ganeshie8
formula is just \(L/v_x\) right ?
ganeshie8
  • ganeshie8
assuming ofcourse \(v_x \lt\lt c\)
ParthKohli
  • ParthKohli
going from one wall to other will not change \(v_x\) along the way
ganeshie8
  • ganeshie8
why
ParthKohli
  • ParthKohli
conservation of momentum. even if there is a collision with another wall (maybe in the y-z plane or whatever) the momentum will be conserved along the x-direction as there are no forces acting on the ball in that direction|dw:1450171605831:dw|
ganeshie8
  • ganeshie8
omg! I se now.. yeah its easy... that is the reason textbook didn't even explain this... |dw:1450171593323:dw|
ParthKohli
  • ParthKohli
yes the significance of elastic collisions comes in when the ball collides with the wall we first considered we assume that e = 1 so the velocity just changes its sign
ParthKohli
  • ParthKohli
so basically we're assuming that there's no loss of kinetic energy and the speed remains the same.
ganeshie8
  • ganeshie8
Makes sense! so it takes \(2L/v_x\) to ame one round trip at any wall
ParthKohli
  • ParthKohli
yeah, you got it
ganeshie8
  • ganeshie8
By conservation of momentum, each collision transfers a momentum of \(2mv_x\) to the wall
ParthKohli
  • ParthKohli
ok so you now calculate the force, then the pressure, and I forget the rest :P
ganeshie8
  • ganeshie8
therefore the force on the wall due to this bouncing particle is given by \[F = \dfrac{\Delta p}{\Delta t} =\dfrac{2mv_x}{2L/v_x} = \dfrac{mv_x^2}{L} \]
ganeshie8
  • ganeshie8
you remember everything this is a derivation of rms speed of the atoms of a particular gas
ganeshie8
  • ganeshie8
need to massage above equation a bit and use ideal gas law looks easy, thanks :)
ParthKohli
  • ParthKohli
great stuff :)
Astrophysics
  • Astrophysics
I must say, that is a very good and easy derivation to follow
Astrophysics
  • Astrophysics
Is this from a chem textbook?
ganeshie8
  • ganeshie8
halliday book... fundamentals of physics
Astrophysics
  • Astrophysics
Oh interesting young and free also has this to nice stuff, I remember learning some of this in high school
ParthKohli
  • ParthKohli
i remember being glad that i was better than ganeshie at physics well now i can only be glad about being better than him at quadratic equations
Astrophysics
  • Astrophysics
Lol I wish I was better than ganeshie at something, |dw:1450172681187:dw| hehe nice read
Astrophysics
  • Astrophysics
One day I'll get ganeshie to just use this book
ParthKohli
  • ParthKohli
astro why do you love sears zemansky so much we all know halliday resnick is way better
ganeshie8
  • ganeshie8
young and freedman is a bit adnvanced book halliday is also advanced but he also spoonfeeds everything... ideal for me :)
ganeshie8
  • ganeshie8
also halliday matches closely with the walter lewin lectures
Astrophysics
  • Astrophysics
Fair enough, I did use a algebra physics book before which was pretty good, it was called...cutnell and johnson 9e |dw:1450172951146:dw|
ParthKohli
  • ParthKohli
looks like a poster of terminator
Astrophysics
  • Astrophysics
Haha yeah, it's pretty good actually
ParthKohli
  • ParthKohli
yeah, terminator is amazing
ganeshie8
  • ganeshie8
https://drive.google.com/file/d/0B6hjEAwn8lB-ZUE2T2IwTTdVNEU/edit
ganeshie8
  • ganeshie8
thats 8th edition
Astrophysics
  • Astrophysics
The problems are nice to, check it out if you have some free time you might like it
Astrophysics
  • Astrophysics
I've done quite a few from them xD
ganeshie8
  • ganeshie8
do u have 9th ed pdf ?
Astrophysics
  • Astrophysics
Yeah I should, lemme see
Astrophysics
  • Astrophysics
If you do problems from there I can also help u to, since I used to do them back in the day for school haha
ganeshie8
  • ganeshie8
im thinking of using that book for thermodynamics review...
Astrophysics
  • Astrophysics
Yeah I have it have to put it on gdrive ill shoot you a message and pk as well if hes interested
ganeshie8
  • ganeshie8
thank you :)
Astrophysics
  • Astrophysics
Np

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