Here are the essential concepts you must grasp in order to answer the question correctly.
Conservation of Momentum
The principle of conservation of momentum states that in a closed system, the total momentum before an event must equal the total momentum after the event, provided no external forces act on it. In this scenario, the momentum of the train cars before they couple must equal the momentum of the combined train after the coupling occurs.
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Elastic and Inelastic Collisions
Collisions can be classified as elastic or inelastic based on whether kinetic energy is conserved. In this problem, the coupling of the train cars is an inelastic collision, where the cars stick together, and kinetic energy is not conserved, but momentum is. This distinction is crucial for calculating the final speed of the combined train.
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Intro To Elastic Collisions
Relative Velocity
Relative velocity refers to the velocity of one object as observed from another object. In this scenario, understanding the relative speeds of the train cars before they couple is essential for applying the conservation of momentum correctly. The fourth car's speed relative to the three-car train is key to determining the initial momentum of the system.
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Intro to Relative Motion (Relative Velocity)