A toy train has magnetic couplers whose maximum attractive...

A toy train has magnetic couplers whose maximum attractive force is 0.2 lb between adjacent cars. What is the maximum force $P$ with which a child can pull the locomotive and not break the train apart at a coupler? If $P$ is slightly exceeded, which coupler fails? Neglect the mass and friction associated with all wheels.

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Key Concepts

Newton’s Second Law

Newton’s Second Law tells us that the net force on each car equals the mass of that car multiplied by its acceleration. In the context of the train, the force applied by the locomotive must accelerate all the cars. Each coupler transmits the force required to accelerate the cars behind it, so understanding how the applied force is divided among the cars is critical.

Free?Body Diagram Analysis and Tension Distribution

By constructing free-body diagrams for the locomotive and each subsequent car, we see that the forces (or tensions) in the couplers are not all equal. The coupler closest to the locomotive is responsible for pulling all the following cars and thus bears the greatest load. This analysis helps determine that the maximum force that can be applied without breaking any coupler is limited by the capacity of the weakest link, which is the first coupler.

Weakest Link Principle in Linked Systems

In any chain of connected elements with limited strength, the failure occurs at the point subject to the highest stress — the weakest link. In the train, when a pulling force slightly exceeds the maximum allowable force, it is the coupler transmitting the full force necessary to accelerate the remainder of the train (the one immediately behind the locomotive) that will fail first.

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