When you toss a coin inside a moving train, the coin will have the same initial horizontal velocity as the train. Therefore, its horizontal motion will match that of the train. However, vertically, the coin will experience the same acceleration due to gravity as it would if the train were stationary. As a result, the coin will follow a curved path due to its horizontal and vertical motion combined, and it will land back inside the train. This is because both the train and the coin are subject to the same gravitational acceleration, regardless of the train’s horizontal motion.
The concept of physics that explains this scenario is the principle of “inertia” and the independence of vertical and horizontal motion. Inertia refers to the tendency of an object to maintain its state of motion unless acted upon by an external force. In this case, the horizontal motion of the coin is the same as that of the train due to inertia.
Additionally, the concept of “projectile motion” explains how the coin’s vertical motion is independent of its horizontal motion. The vertical motion is determined by the force of gravity acting downward, causing the coin to follow a parabolic trajectory. Since the coin and the train experience the same gravitational force, the coin falls back inside the train as if it were stationary.
When tossing a coin inside a moving train, the key concept of physics involved is **relative motion** and **inertial reference frames**.
1. **Relative Motion**: The motion of the coin is observed differently depending on the reference frame from which you’re observing it. To someone inside the moving train, the coin appears to move vertically (up and down) in relation to their position, assuming the train is moving with constant velocity and there are no other forces acting on the coin. This is because the coin has the same horizontal velocity as the train at the moment it is tossed.
2. **Inertial Reference Frames**: According to the **principle of relativity** (a cornerstone of Einstein’s theory of special relativity), the laws of physics are the same in all inertial reference frames, meaning the motion of the coin inside the train behaves the same as it would inside a stationary room, from the perspective of someone inside the train. However, from the perspective of an observer outside the train (such as someone standing on a platform), the coin would follow a curved trajectory. This is because, from the perspective of the outside observer, the coin has both the forward velocity of the train and its vertical motion due to the toss.
So, while the coin appears to move up and down inside the train (in the train’s reference frame), it follows a more complex parabolic path when viewed from outside the train, due to the combination of its initial horizontal velocity (the same as the train’s) and its vertical motion.