1

I have a question about the theory of relativity. I took a lesson on brilliant.org, maybe you have heard about this educational platform. And the example with the ball and the train is completely incomprehensible to me. Their theory states that if a train that is moving at a speed of 200 km/h collides with a stationary ball, then the ball will move at a speed of 400 km/h from the point of view of the observer. But I still don't understand why.

It seems to me that the ball would move with such a speed if it also moved at a speed of 200 km / h and then, upon collision, it began to move at a speed of 400 km / h. I apologize in advance for the stupid question.

link to lesson - https://brilliant.org/courses/puzzle-science/introduction-64/science-rules-3-diagrammar/1/

RC_23
  • 9,096
Алесандр Мерсер
  • 11
  • 1
    Consider the reference frame of the train, according to which the ball is moving towards the train. The train has essentially infinite mass in comparison to the ball, thus we can ignore any effect of the collision on it (if you don't want to ignore it then use conservation of the momentum). The problem now becomes equivalent to a ball hitting a wall, and we know that the result is that the ball gets rebounded with the same speed. Thus according to the train, the speed of the ball is 200. BuT the train itself was moving at 200, making the ball's speed 400 from a stationary perspective. – GedankenExperimentalist Mar 01 '23 at 19:52
  • Note that the link you provided is not accessible to everyone. As stated indeed this statement doesn't make sense, but it's not clear what exactly was communicated in this link... – Amit Mar 01 '23 at 19:53
  • 1
    @GedankenExperimentalist do not leave full answers in the comment, I suggest that you post it as an answer below – Mauricio Mar 01 '23 at 20:15
  • I do not have access, but the word relativity here refers to relative motion rather than Einstein's relativity. An excellent video to demonstrate relative motion is Frames of Reference on Youtube. – Ken Mellendorf Mar 01 '23 at 20:39
  • This is a different question, but the answer may help. Gravity Assist Analogy – mmesser314 Mar 02 '23 at 06:11

2 Answers2

1

As others have noted, this could be called "classical" or "Galilean" relativity, which is not what the Einstein theory is that most people associate with the word.

Assuming this is an ordinary elastic collision obeying Newtonian mechanics, the ball moves with twice the speed after the train impacts it for the same reason that a falling ball bounces off the ground and returns upward. If there is no energy loss, it bounces upwards with the same speed it impacted the ground, which is a change in velocity of 2 times the initial velocity (velocity is speed with a direction). So, if you go into a frame where the ball is stationary and the ground is moving toward the ball instead, after the impact the ball is moving away with twice the speed of the ground (draw some pictures and convince yourself that is true). In the train example, the train is the earth and the velocity is horizontal rather than vertical, but the principle is the same. A massive object hitting a stationary tiny object elastically causes the tiny object to move with twice the speed of the massive one.

The ability to change reference frames, between the one where the train is moving and the ball stationary and the one where the ball is moving and the train is stationary, is basically "the principle of relativity." However, this version of it is weak, it does not actually preserve all the laws of physics.

Poisson Aerohead
  • 2,013
  • (Galilean) relativity is still useful to these problems because it allows you to apply energy conservation law without knowing the larger mass or its change in velocity with respect to an initially comoving inertial frame. – g s Mar 01 '23 at 20:47
  • Yeah, fair enough, although when people say "theory of relativity" that is generally not what is meant. I clarified it a bit. – Poisson Aerohead Mar 01 '23 at 22:21
  • The fact is that this example explained the theory of relativity. And they considered this question from the point of view of the theory of relativity. – Алесандр Мерсер Mar 02 '23 at 08:11
1

According to the principle of (classical) relativity, the laws of mechanics are valid for all inertial frames of reference.

The train is moving with constant velocity, so it is an inertial frame. From the train's frame, there is a ball hitting it at 200 km/h. Supposing an elastic collision, the ball will bounce back with the same speed. The recoil of the train is supposed negligible due to its huge mass.

For a ground observer, a ball with a speed 200 km/h bigger than the train has 400 km/h.

Claudio Saspinski
  • 16,319