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Ball + train collision

Anonymous Thu 02 Jul 17:48:40 2020 No.11860714 View Reply Original Report

Quoted By: >>11861098 >>11862796

Is this correct? This isn't my homework. This is something that was discussed on r9k and I think everyone got it wrong.

They said when a ball and train collide (elastically) and they're both initially going at 100 km/h in opposite directions, a bystander will see the ball bouncing back at 300 km/h. To me this is just wrong. Check pic for my explanation.

Anonymous

Anonymous Thu 02 Jul 2020 18:03:06 No.11860749 Report

Quoted By:

BUMPREE!

Anonymous

Anonymous Thu 02 Jul 2020 18:05:14 No.11860752 Report

Quoted By: >>11860762

Since you ask, I'll tell you. You are incorrect. "They" were right.

Anonymous

Anonymous Thu 02 Jul 2020 18:08:40 No.11860762 Report

Quoted By:

>>11860752

>you're wrong.

Millenia of science should result in better counter arguments than "no".

Anonymous

Anonymous Thu 02 Jul 2020 18:26:09 No.11860812 Report

Quoted By: >>11860868

Are you asking for a counter argument now? The original post just asked if it was correct.
The response to b) is unsupported. It conserves energy but it doesn't conserve momentum (as a vector). The correct way to do the calculation would be to actually solve the simultaneous conversation of energy and momentum equations, with the mass of the train as a parameter M, and look for the limit as M becomes large.

Anonymous

Anonymous Thu 02 Jul 2020 18:47:13 No.11860868 Report

Quoted By: >>11861086

>>11860812
>It conserves energy but it doesn't conserve momentum (as a vector).

I think it does.
System: train + ball.
Let's say the train is stationary and not moving. Ball hits it with momentum p. It bounces back with momentum -p.
This means the train basically gets a momentum of +2p.
Since the mass is so large it doesn't affect it in any way though.

Anonymous

Anonymous Thu 02 Jul 2020 19:10:42 No.11860967 Report

Quoted By:

How are these situations different:

>hitting the ball with a bat

>hitting the ball with a train going at 100 km/h

Anonymous

Anonymous Thu 02 Jul 2020 19:42:39 No.11861086 Report

Quoted By: >>11861126 >>11861223

>>11860868
The algebra for doing the elastic collision isn't that bad, if you use a few tricks.
(1) If two objects have masses M and m, and initial velocities a and b, and final velocities x and y, then: Ma + mb = Mx + my, and Ma^2 + mb^2 = Mx^2 + my^2.
(2) For any velocity v, you can easily see that M(a-v) + m(b-v) = M(x-v) + m(y-v). It's a bit more work to see that M(a-v)^2 + m(b-v)^2 = M(x-v)^2 + m(y-v)^2.
..continued..

Anonymous

Anonymous Thu 02 Jul 2020 19:46:04 No.11861098 Report

Quoted By: >>11861213

>>11860714
>not accounting for relativity
F-

Anonymous

Anonymous Thu 02 Jul 2020 19:53:14 No.11861126 Report

Quoted By: >>11861159 >>11861223

>>11861086
(3) In particular take v = (Ma+mb)/(M+m). Then M(a-v) = Mm(a-b)/(M+m) = -m(b-v).
(4) Hence 0 = M(a-v) + m(b-v) = M(x-v) + m(y-v). So (a-v) = -(m/M)(b-v) and (x-v) = -(m//M)(y-v)
..continued...

Anonymous

Anonymous Thu 02 Jul 2020 20:03:16 No.11861159 Report

Quoted By: >>11861223

>>11861126
(5) If we substitute in for (a-v) and (x-v), we get: (1 - (m/M))(b-v)^2 = (1 - (m/M))(y-v)^2.
(6) We conclude |b-v| = |y-v|, do either y = b, or y = 2v - b
(7) But v = (Ma + mb)/(M+m). In the limit as M increases to infinity , v goes to a, y equals either b or 2a- b. In the problem with the train, a = 100, b = -100, either the ball misses the train, and continues with velocity -100, or bounces and ends up with velocity 2*100 - (-100) = 300.

Anonymous

Anonymous Thu 02 Jul 2020 20:14:44 No.11861213 Report

Quoted By:

>>11861098

It says rel

Anonymous

Anonymous Thu 02 Jul 2020 20:16:40 No.11861223 Report

Quoted By: >>11861278

>>11861086
>>11861126
>>11861159

This looks awfully complex for something I thought would be intuitive.
t. beginner

Anonymous

Anonymous Thu 02 Jul 2020 20:20:45 No.11861241 Report

Quoted By:

>The ball is approaching the train at 200km/h (relatively) so it keeps that speed after the (purely elastic) collision, just redirected.

This is what I don't get.
Relative velocity is a conserved quantity even though the direction changes?
I think the direction changing changes everything and you have to recalculate the relative vel.

Anonymous

Anonymous Thu 02 Jul 2020 20:30:48 No.11861278 Report

Quoted By: >>11861400

>>11861223
The intuition here is just to work in the frame relative to the center of gravity. In that frame, for everything to be conserved, the magnitudes of the final velocities must equal the magnitudes of the initial velocities.

Anonymous

Anonymous Thu 02 Jul 2020 21:04:16 No.11861400 Report

Quoted By: >>11861465

>>11861278

My brain says this:
>ball is objectively going at 100 km/h in the start
>collision only changes its direction, doesn't give ball extra speed
>thus, guy viewing this will always see the ball going at 100 km/h

Anonymous

Anonymous Thu 02 Jul 2020 21:22:15 No.11861465 Report

Quoted By: >>11861510

>>11861400
What does your brain say if you start with the ball going 5 km/h? That is, substantially slower than the train?

Anonymous

Anonymous Thu 02 Jul 2020 21:36:22 No.11861510 Report

Quoted By:

>>11861465

Maybe it gains some momentum from the train but I have no idea how much.
The train is not accelerating either so there's probably not that much of a force.
Maybe the ball just gets stuck to the front of the train and stays there due to air resistance.

Anonymous

Anonymous Fri 03 Jul 2020 08:04:50 No.11862780 Report

Quoted By: >>11863339

I can't believe nobody can solve this problem

Anonymous

Anonymous Fri 03 Jul 2020 08:12:31 No.11862796 Report

Quoted By: >>11862849

>>11860714
wheres the mass details?

Anonymous

Anonymous Fri 03 Jul 2020 08:50:10 No.11862849 Report

Quoted By: >>11862876

>>11862796

They're probably not needed. Physics usually works with just letters M and m and the fact that M is much larger than m.

Anonymous

Anonymous Fri 03 Jul 2020 09:02:49 No.11862876 Report

Quoted By: >>11863095

>>11862849
op seemed to ask the pushback velocity, and you cannot calculate that without the masses of the two objects

op mentioned this question is asked in terms of elastic collision, which forces us to use Potential energy (mgh) and Kinetic energy (0.5mv2) in state 1 and state 2, or am i missing something? i dont even have half a clue how anyone could get 300 km/h , there is no data here kek

Anonymous

Anonymous Fri 03 Jul 2020 12:04:03 No.11863095 Report

Quoted By:

>>11862876
>i dont even have half a clue how anyone could get 300 km/h , there is no data here kek

I asked my friend who's an engineering student and he intuitively said 300 km/h. I have no idea how to prove this formally but his thought process was:

>1. Train sees the ball approach at the relative velocity of 200
>2. The ball bounces back at the same relative velocity of 200
>3. What the observer sees is the velocity of the train + the relative velocity of the ball (200), which is 300

Anonymous

Anonymous Fri 03 Jul 2020 14:48:21 No.11863339 Report

Quoted By:

>>11862780
Which problem? The physics problem has already been solved in the limit as the mass ratio goes to infinity. 300 km/h. The problem of getting OP's intuition to work right hasn't been solved, and probably requires some experiments with a well-equipped high school physics lab.

Anonymous

Anonymous Fri 03 Jul 2020 14:50:12 No.11863340 Report

Quoted By: >>11864232

>this thread
The absolute state of /sci/

Anonymous

Anonymous Fri 03 Jul 2020 20:52:27 No.11864232 Report

Quoted By:

>>11863340

What wrong bredda?

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