Tension interaction

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Ropes, wires, strings, etc. are commonly used to provide force in everyday situations. A force provided by a rope or string is generally called a tension force.

Tension as a Force

Properties of Ideal Ropes

When discussing ropes, strings, etc. in this course, it will generally be that they have zero mass. In this case, their behavior is fairly simple. The important aspects can be summarized with two simple rules:

  1. A segment of a massless rope can only exert a tension force if it is stretched between two points of contact with other objects.
  2. If a massless rope is stretched between two points of contact with other objects, the tension force exerted by a given segment of the rope on the objects on either side will be equal in size and will point directly along the rope segment.

Tension as Constraint

Tension does not have an associated force law like gravitational or elastic restoring forces do. Instead, tension acts as a constraint. It will take on whatever value is necessary to keep the objects joined by the rope at the same separation.

Tension and Energy

Tension is a non-conservative force, and therefore has no associated potential energy. When tension is internal, however, it is a non-dissipative force, performing zero net work on the chosen system. The reason is that an ideal rope cannot stretch, which guarantees that the two interacting objects will undergo the same displacement. Thus, the work done on the two objects will cancel by Newton's Third Law.

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