AP® Physics 1: Algebra-Based · Unit 2 · Topic 2.2
Tension and Ideal Strings
Tension is the pulling force transmitted through a stretched string or rope, equal in magnitude at both ends for an ideal massless string, always pulling inward along its length.
A string can only pull, never push. When you tie a rope between two objects and it goes taut, every tiny segment of that rope pulls on its neighbors equally in both directions, like a chain of people holding hands and leaning back. If the string is ideal, meaning massless and unstretchable, then Newton's second law tells you why the pull cannot change along its length: any difference in force from one end to the other would have to accelerate the string's mass, but it has none. So whatever pulls on one end pulls with the same strength on the other.
This is also why an ideal string can wrap around a frictionless, massless pulley without losing any tension. The pulley only changes the direction the force points, not its size. The string stays taut and the same internal pull runs through it from end to end, just redirected.
Tension problems almost always start with an object in equilibrium or with known acceleration, and a free-body diagram showing the rope's pull as a vector along the rope's direction. When ropes are angled, you break tension into horizontal and vertical components using sine and cosine, then apply Newton's second law separately on each axis. This setup connects directly to the rest of the unit: the same component method you use for angled tension shows up again with inclined planes, friction, and circular motion, where forces rarely line up neatly with the axes.
Key terms
- Tension
- The pulling force transmitted through a string, rope, or cable, directed along its length.
- Ideal string
- A string treated as massless and unstretchable, so tension is the same throughout its length.
- Equilibrium
- A state where the net force on an object is zero, so it does not accelerate.
- Free-body diagram
- A diagram showing all forces acting on a single object as vectors.
- Component
- The part of a force vector that acts along one axis, found using sine or cosine of its angle.
Watch it explained
- How it worksHow does an ideal massless string pass a force around a pulley without losing any of it?
- Worked exampleFind the tension in a rope holding a 15 kg lamp hanging motionless from a ceiling.
- Worked exampleFind the tension in each of two ropes at 40 degrees holding up a 200 N sign.
- Common mistakeWhy doesn't a rope pulled by two people at 100 N each carry 200 N of tension?
Check yourself
End of topic.