# Module 3 -- Tension Force

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.

#### Learning Goals

After completing this module, you should be able to:

• State the two important properties of the tension forces exerted by a segment of a massless rope.
• Describe the tension in a rope held at more than two points.
• Describe the tension in a rope that passes over a massless pulley.
• Correctly include tension forces arising from massless ropes in free body diagrams.

## Idealized Ropes

When discussing ropes, strings, etc. in this course, it will generally be assumed that they have zero mass and do not stretch. 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 secured between two points of contact on different 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 Force as a Constraint Force

Consider a box hanging from an ideal rope attached to the ceiling of an elevator. The elevator is accelerating upwards with an acceleration of magnitude a. The circumstance here is that the rope constrains the box to move upwards with the same acceleration as the elevator. We therefore know that the force of tension must be enough to cause this motion. Therefore we'll typically apply Netwon's second law to the box which will enable us to find an equation for the tension.

## Illustrative Examples

### Idealized Massless Pulleys

Pulleys are often used with ropes or strings. For now, when you see a pulley in a picture you should assume it is massless. This assumption implies that it will require no work to rotate or translate the pulley. In this approximation, the pulley only changes the direction of the rope. Later in the course, when we have learned about rotational motion, we will be able to discuss the effects of massive pulleys. Pulleys are commonly encountered in two qualitatively different types of situation.