Table of Contents
What Is Tension?
Tension is a pulling force transmitted through a string, rope, cable, or similar one-dimensional continuous object. It is a contact force that acts along the length of the object, pulling equally on the objects at both ends. Tension is always a pulling force - ropes cannot push.
In physics problems, strings and ropes are often assumed to be massless and inextensible. Under these ideal conditions, the tension is the same throughout the entire length of the rope. In real situations, the rope's mass and elasticity can cause the tension to vary along its length.
Tension Formulas
Common Tension Scenarios
| Scenario | Formula | Key Insight |
|---|---|---|
| Hanging mass | T = mg | Tension equals weight |
| Elevator up | T = m(g+a) | Tension > weight |
| Elevator down | T = m(g-a) | Tension < weight |
| Free fall | T = 0 | Weightlessness |
| Atwood machine | 2m1m2g/(m1+m2) | Always between the two weights |
Worked Examples
Elevator accelerating upward
A 70 kg person stands in an elevator accelerating upward at 2 m/s². The tension in the cable supporting the person (normal force) is: T = 70(9.81 + 2) = 826.7 N. This is why you feel heavier when an elevator starts going up.
Frequently Asked Questions
Can tension be negative?
No. Tension is always a pulling force. If your calculation yields a negative tension, it means the rope has gone slack (no tension) and the physical setup needs to be re-examined. Ropes cannot push; they can only pull.
What is the tension in a rope at an angle?
When a rope supports a hanging mass at an angle theta from the vertical, the tension is T = mg / cos(theta). As the angle increases, the tension increases. At 60 degrees from vertical, the tension is double the weight.
How does rope mass affect tension?
For a heavy rope of mass M supporting a load m, the tension at the top is (m + M)g and at the bottom is mg. The tension increases linearly from bottom to top, as each point must support the weight below it.