problem help please
Merritt E Adams
do we not get 2 balls of mass m coming out with the same initial
velocity?
--
Merritt E Adams
Northwestern University, Evanston, IL. USA
m-a...@nwu.edu
AndroclesInFlorida
"Merritt E Adams" <m-a...@nwu.edu> wrote in message
news:3BEA1281...@nwu.edu...
Momentum is conserved.
Momentum is mass multiplied by velocity. So you CAN get two balls with the
velocity of the 2m ball (which stops) OR you can get one ball with twice the
velocity of the 2m ball, or you can have 4 balls with half its velocity.
Dirk Van de moortel
> do we not get 2 balls of mass m coming out with the same initial
> velocity?
Never mind the non-answer of our house clown Androcles ;-)
We have conservation of momentum and conservation of kinetic energy
and we assume that all collisions are ideal and completely pass their
kinetic energy to the next ball.
So we have for incoming momentum (P) and kinetic energy (T):
P_in = 2m * v = 2mv
T_in = 1/2 * 2m * v^2 = mv^2
2 balls of mass m coming out with speed v:
P_2_m_v = 2 * m * v = 2mv
T_2_m_v = 2 * 1/2 * m * v^2 = mv^2
Which seems quite okay since both P and T are conserved.
Is there another solution?
Androcles' alternatives are impossible of course:
1 ball of mass m with speed 2v:
P_1_m_2v = m * 2v = 2mv
T_1_m_2v = 1/2 * m * (2v)^2 = 2mv^2 impossible
4 balls of mass m with speed v/2:
P_4_m_v/2 = 4 * m * v/2 = 2mv
T_4_m_v/2 = 4 * 1/2 * m * (v/2)^2 = 1/2mv^2 impossible
Let's see if there is another possibility:
n balls of mass m with speed kv:
P_n_m_kv = n * m * kv = nmkv
T_n_m_kv = n * 1/2 * m * (kv)^2 = 1/2 * nmk^2v^2
If we have conservation of P and T:
P_n_m_kv = P_in
T_n_m_kv = T_in
then we must have:
nmkv = 2mv
1/2 * nmkv^2 = mv^2
Solving for n and k:
n = 1 (one ball)
k = 2 (double speed)
So the only way to have things with mass m coming out,
is 1 ball with speed 2v
Where did you get the idea that this doesn't happen?
Dirk Vdm
Dirk Vdm
Dirk Van de moortel
"Dirk Van de moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote in message
news:hICG7.11911$XM4...@afrodite.telenet-ops.be...
Oops, silly mistake ;-)
This should be:
Solving for n and k:
n = 2 (two balls)
k = 1 (same speed)
So the only way to have things with mass m coming out,
is 2 ball with speed v, like you said.
Sorry...
Joe Fischer
: "Merritt E Adams" wrote:
:> Why when a 2m (m=mass) ball hits a series of balls all with a mass of m,
:> do we not get 2 balls of mass m coming out with the same initial
:> velocity?
: Momentum is conserved.
: Momentum is mass multiplied by velocity. So you CAN get two balls with the
: velocity of the 2m ball (which stops) OR you can get one ball with twice the
: velocity of the 2m ball, or you can have 4 balls with half its velocity.
What a wonderful way to teach physics, :-),
put on a clown suit and forget about kinetic energy,
then demonstrate with billiard balls how wrong you are. :-)
Please don't ask to drive one of my cars though,
to get my permission you have to know how compute stopping
distance in your head.
Joe Fischer
--
3
AndroclesInFlorida
"Joe Fischer" <grav...@shell1.iglou.com> wrote in message
news:3beb0...@news.iglou.com...
cradle in action :)
KE is simply the integral of the momentum. It isn't forgotten, just
unnecessary to answer the question.
Joe Fischer
: "Joe Fischer" wrote:
:> What a wonderful way to teach physics, :-),
:> put on a clown suit and forget about kinetic energy,
:> then demonstrate with billiard balls how wrong you are. :-)
:>
:> Please don't ask to drive one of my cars though,
:> to get my permission you have to know how compute stopping
:> distance in your head.
:
: Obviously you've never actually played pool or billiards,
: or seen Newton's cradle in action :)
Gee, no, I was born yesterday. :-)
: KE is simply the integral of the momentum.
Would you please explain that for me teacher,
I am beginning to develop an interest in physics.
: It isn't forgotten, just
: unnecessary to answer the question.
Why do they bother with unnecessary things?
Joe Fischer
--
3
Bilge
Re: problem help please to usenet:
>Obviously you've never actually played pool or billiards, or seen Newton's
>cradle in action :)
>KE is simply the integral of the momentum. It isn't forgotten, just
>unnecessary to answer the question.
You have to conserve both and the collision is approximately
elastic. Using p_i = p_f just gets you p_i = any combination of
m and v in the final state. Since the collision is elastic, the
condition KE_i = KE_f requires the both the mass x velocity in
the initial and final states to balance AND the mass x velocity^2
to balance. That is what constrains the combinations of outgoing
masses and velocities possible. In terms of shooting pool, that's
what allows you break the rack so that only one ball comes out
of the rack to hit the back rail and roll back into its original
spot (more or less), leaving the rack as it was without incurring
a scratch.
Dirk Van de moortel
"Bilge" <ro...@radioactivex.lebesque-al.net> wrote in message news:slrn9umut...@radioactivex.lebesque-al.net...
Bilge, can you please reply to my correction to my own reply
so Androbut cannot pretend not having seen it? Thanks ;-)
Dirk Vdm
Martin Hogbin
Correction noted.
Martin Hogbin
Dirk Van de moortel
"Martin Hogbin" <mar...@hogbin.org.uk> wrote in message news:1005337549.14652....@news.demon.co.uk...
> [snip]
> Correction noted.
Thanks Martin ;-)
Dirk Vdm
Stewart Gordon
news:fYpG7.31302$cF.25...@news1.rdc1.fl.home.com...
<snip>
> Momentum is conserved.
> Momentum is mass multiplied by velocity. So you CAN get two balls with the
> velocity of the 2m ball (which stops) OR you can get one ball with twice
the
> velocity of the 2m ball, or you can have 4 balls with half its velocity.
For this to work, we'd need that:
(a) the 2 or 4 balls start at the same point in space
(b) the balls are perfectly elastic
What's this to do with relativity, anyway?
Stewart.
--
My e-mail is valid but not my primary mailbox. Please keep replies on the
'group where everyone may benefit.
Bilge
Re: problem help please to usenet:
>
Sorry it took so long to note your correction. My isp outsources
news and picked the most miserable, crappy news service in existence
_that's_ _newsville_.com otherwise known as _vic.com_, let me repeat,
the people at this news service, vic.com aka newsville.com are totally
inept, idiots. Their news server doesn't support requesting news
articles by id, nor does it support much of anything -- because
it's running DNEWS on windows rather than innd on anything else.
Due to this piece of &#(! newsserver, I had to go through my
.newsrc file and _guess_ how many articles ago your article
appeared in the order their newsserver received it.
Verified that you've corrected your faux pas.
AndroclesInFlorida
"Stewart Gordon" <smjg...@yahoo.com> wrote in message
news:9sjut8$eth$1...@sun-cc204.lut.ac.uk...
> AndroclesInFlorida <marie...@home.com> wrote in message
> news:fYpG7.31302$cF.25...@news1.rdc1.fl.home.com...
> <snip>
> > Momentum is conserved.
> > Momentum is mass multiplied by velocity. So you CAN get two balls with
the
> > velocity of the 2m ball (which stops) OR you can get one ball with twice
> the
> > velocity of the 2m ball, or you can have 4 balls with half its velocity.
>
> For this to work, we'd need that:
> (a) the 2 or 4 balls start at the same point in space
> (b) the balls are perfectly elastic
>
> What's this to do with relativity, anyway?
relativity?
Dirk Van de moortel
"AndroclesInFlorida" <marie...@home.com> wrote in message news:9kkH7.42657$cF.36...@news1.rdc1.fl.home.com...
Heck, you gave the dumbest answer one can imagine.
Dirk Vdm