Train, ball thrown, special relativity

In summary, the conversation discusses a question from a take-home exam regarding a train of length L moving at a speed of 3c/5 with respect to the ground and a ball being thrown from the back to the front at a speed of c/3 with respect to the train. The question asks for the time and distance covered in the train's frame, the ball's frame, and the ground's frame. It is mentioned that for the train and ball's frame, the situation can be treated as if stationary. For the ground's frame, relativistic velocity addition should be used to find the ball's velocity. The speaker apologizes for not providing enough information in their initial question and thanks the other person for their help.
  • #1
airfrek
2
0
This is a question off a take-home exam and I just need some help getting started on each part.

Homework Statement


A train of length L moves at speed 3c/5 with respect to the ground. A ball is thrown from the back to the front, at speed c/3 with respect to the train. How much time does this take, and what distance does the ball cover in the train's frame, the ball's frame, and the ground's frame?
 
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  • #2
For the train and the ball's frame you can treat this as if you were stationary and threw the ball.

For the ground's frame you need to find the ball's velocity, so you use relativistic velocity addition.

You will have to show some work from here on out if you want more help :)
 
Last edited:
  • #3
Yeah I'm sorry about that. This is my first time using something like this. I wasn't sure what I was supposed to do, but yeah I'll do a better job next time. Thank you for your help.
 

1. How does the speed of a train affect the ball thrown inside it?

The ball thrown inside the train will have the same speed and trajectory as it would if thrown outside the train. This is because the ball is in the same frame of reference as the train, and the train's speed does not affect its motion.

2. Can the ball thrown inside the train exceed the speed of light?

No, the ball cannot exceed the speed of light. According to Einstein's theory of special relativity, the speed of light is the maximum speed at which any object can travel. This means that the ball cannot travel faster than the speed of light, even if the train is moving at a high speed.

3. How does time dilation affect the ball thrown inside the train?

Time dilation, a concept in special relativity, states that time can appear to pass at different rates for objects moving at different speeds. This means that for an observer on the train, the time it takes for the ball to reach a certain point may appear longer compared to an observer outside the train. However, for the person throwing the ball, time will seem to pass at a normal rate.

4. Does the mass of the ball change when thrown inside a moving train?

No, the mass of the ball will remain the same regardless of the train's speed. According to special relativity, an object's mass does not change with its speed. However, its momentum and energy will increase as its speed increases.

5. How does the concept of relative simultaneity apply to throwing a ball inside a moving train?

Relative simultaneity is the idea that events that happen at the same time for one observer may not happen at the same time for another observer in a different frame of reference. In this case, the person throwing the ball and the person inside the train may not agree on when the ball was thrown due to their different perspectives and frames of reference.

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