Final answer:
A perfectly flexible, uniform cable suspended freely from two points assumes the shape of a catenary, not a parabola. The tension in the cable is consistent with Newton's third law, being equal throughout provided the cable's weight is negligible. Suspension bridges demonstrate the catenary curve, not a parabolic shape.
Step-by-step explanation:
The statement is false; a perfectly flexible, uniform cable suspended freely from two points not in the same vertical line does not form a parabola. Instead, such a cable assumes the shape of a catenary. The tension in such a cable is due to the force that is parallel to the length of the cable, which is consistent with Newton's third law. This law states that the forces between two interacting objects are equal in magnitude and opposite in direction. In a suspended flexible cable, the tension is the same throughout the cable, provided its weight is negligible.
However, when a cable has a uniform weight along its length, the curve it forms is a catenary, which is different from the parabolic shape a thrown object follows under the influence of gravity. In context, suspension bridges use heavy cables that distribute weight evenly along their length and visibly sag into a catenary curve, proving that even under uniform weight distribution, the shape is not parabolic.