Tension

Transmission of forces through ideal and real taut ropes, cables, and chains.

General idea of the topic

Tension is the force that a rope, cable or chain transmits between its ends when it is taut. It can only pull, never push, and in the ideal model, with a massless, inextensible rope, it has the same value everywhere along the rope and only changes direction when passing over a frictionless pulley.

Because tension is an unknown that depends on what the rest of the system does, it is not computed with a direct formula: it is obtained from the equations of motion of the bodies the rope joins. That is why it is the bridge from one body to another in multi-body problems.

What the student is expected to understand

By the end, the student should be able to draw tension as a force pulling toward the rope from each end, set up the second law for each connected body and solve for it, checking that it comes out positive.

The student should also be able to identify when the ideal-rope approximation stops holding, for example with heavy or stretching ropes.

Recommended learning route

1. Tension in Ropes and Cables: studies tension in ropes and cables at equilibrium and in motion, with examples of suspended loads and connected bodies.

Physical criterion to acquire

The essential criterion is to draw each body separately and place the tension in the direction in which the rope pulls on it. If the tension comes out negative, the rope would be pushing, which is impossible: the system does not behave as assumed and the setup must be revised.

Connection with real problems

• cranes, elevators and suspension cables.
• pendulums and swings.
• pulley systems and counterweights.
• climbing ropes and towing.

Final goal of the topic

The final goal is to compute the tension in ideal ropes within systems at equilibrium or in motion and to recognise when the ideal-rope model is insufficient.