Train Paradox: Force & Curvature Explained

In summary, the conversation discusses the train paradox and its difference from the twin paradox. It is mentioned that the passenger on the train experiences a force, while the person waiting at the station does not. The physics behind this is the relativity of simultaneity, and there is no change in gravitational field. The passenger's age difference from the person waiting on the platform changes when they return, which is attributed to the acceleration and force exerted by the seat.
  • #1
ZealScience
386
5
I am thinking about train paradox here. The only difference between the passenger and the person waiting at the station is that the passenger is experiencing a force. They have exactly the same relative velocity and relative acceleration. The difference of this paradox from twin paradox is that there is no change in gravitational field here. So I assume that the force exerted by the chair also create a curvature that makes the RF of the passenger different from RF of the station. So what is the physics behind?
 
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  • #2
The passenger on the train isn't experiencing any force if the train is in uniform motion. The resolution isn't any form of force or curvature, it's the relativity of simultaneity.
 
  • #3
What train paradox are we talking about here? Can you give some background to your problem?
 
  • #4
Sorry, for the ambiguity.

I mean where the passenger travels and returns to the station and found out that his age difference from the person waiting on the platform for the whole journey has changed.

So if he returns there would be an acceleration and force acting on it by the seat.
 

FAQ: Train Paradox: Force & Curvature Explained

What is the train paradox and why does it occur?

The train paradox is a thought experiment that involves a train traveling along a curved track. It occurs because the train is constantly changing direction as it moves along the track, causing a change in its velocity. This change in velocity results in a force, known as centripetal force, which acts towards the center of the curve and allows the train to stay on the track.

How is force related to curvature in the train paradox?

In the train paradox, the force acting on the train is directly related to the curvature of the track. As the track becomes more curved, the force required to keep the train on the track increases. This is because the train needs to constantly change its direction to follow the curved track, and this change in direction requires a force.

What is the difference between centripetal and centrifugal force in the train paradox?

Centripetal force is the force that keeps the train moving along the curved track, while centrifugal force is the apparent outward force experienced by an object in a rotating frame of reference. In the case of the train paradox, the centrifugal force is often referred to as the "fictitious force" because it is not a real force, but rather a result of the train's change in direction.

Does the speed of the train affect the force and curvature in the train paradox?

Yes, the speed of the train does have an impact on the force and curvature in the train paradox. As the speed of the train increases, the force required to keep it on the track also increases. This is because a higher speed means a higher centripetal force is needed to counteract the train's inertia and keep it on the track.

How does the train paradox illustrate the principles of Newton's laws of motion?

The train paradox can be used to illustrate all three of Newton's laws of motion. The first law states that an object in motion will stay in motion unless acted upon by a force. In the train paradox, the train will continue to move along the track in a straight line unless acted upon by the centripetal force. The second law states that the force acting on an object is equal to its mass times its acceleration. In the train paradox, the force required to keep the train on the track increases as the mass or speed of the train increases. Finally, the third law states that for every action, there is an equal and opposite reaction. In the train paradox, the centripetal force acting on the train is countered by the centrifugal force acting in the opposite direction.

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