The three freight cars are rolling along the horizontal...

The three freight cars are rolling along the horizontal track with the velocities shown. After the impacts occur, the three cars become coupled together and move with a common velocity $v$. The weights of the loaded cars $A, B,$ and $C$ are 130,000,100,000, and 150,000 Ib, respectively. Determine $v$ and calculate the percentage loss $n$ of energy of the system due to coupling.

Key Concepts

Conservation of Momentum

This concept states that the total momentum of a system remains constant if no external forces act on it. It is especially important in collision problems, where the momentum before and after the impact is equated, regardless of whether the collision is elastic or inelastic. It allows us to compute the final velocity of a coupled system by summing the momenta of the individual bodies.

Inelastic Collision

In an inelastic collision, objects stick together after impact and move as a single body. Although momentum is conserved in such collisions, kinetic energy is not; some of it is converted into other forms of energy, such as heat or sound. This concept is crucial to understanding why the final kinetic energy is less than the initial kinetic energy in the scenario.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated as one half of the mass multiplied by the square of its velocity. In collision problems, comparing the total kinetic energy before and after the collision helps in understanding the extent of energy transformation and loss during inelastic interactions.

Percentage Energy Loss

This concept involves quantifying the loss of kinetic energy in a collision by comparing the initial total kinetic energy to the final kinetic energy. The loss is often expressed as a percentage of the initial kinetic energy, indicating the proportion of energy that has been transformed into other forms due to the inelastic nature of the collision.

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