Final answer:
The tension in the towing chain, when towing a car on a horizontal road, must overcome friction and does not need to equal the car's weight. The car's weight is counteracted by the normal force, and in a state of constant velocity, the net force is zero.
Step-by-step explanation:
The relationship between the tension in the chain and the weight of the car during towing is not one of equality, contrary to the premise of the question. When a car is towed on a horizontal road with a horizontal chain, the tension in the chain does not need to equal the weight of the car. Instead, the tension must be sufficient to overcome any resistance to motion, such as friction, to maintain constant velocity.
In physics, Newton's second law dictates that the net force on an object in uniform motion (constant velocity) is zero. Therefore, in the horizontal direction, the tension in the chain must compensate for all horizontal forces acting against the motion of the car (like friction), not its weight. The force of gravity (weight) is acting downward and is balanced by the normal force from the road, hence they do not affect the horizontal motion.
If the car is being towed out of, for example, mud, each time the car moves forward, the chain is tightened to keep it straight, which can create large tension in the chain. The tension in such a scenario can indeed become very large if a force is applied perpendicular to the chain, but this is due to force multiplication through mechanical advantage, not because tension must equal weight. A flexible connector like a rope, chain, or cable can only exert forces parallel to its length, and tension is the force exerted along this length.