# What is tension?

Ropes pull on things! Learn how to handle that kind of force.

## What does tension mean?

All physical objects that are in contact can exert forces on each other. We give these

*contact forces*different names based on the types of objects in contact. If one of the objects exerting the force happens to be a rope, string, chain, or cable we call the force**tension**.Ropes and cables are useful for exerting forces since they can efficiently transfer a force over a significant distance (e.g. the length of the rope). For instance, a sled can be pulled by a team of Siberian Huskies with ropes secured to them which lets the dogs run with a larger range of motion compared to requiring the Huskies to

*push*on the back surface of the sled from behind using the normal force. (Yes, that would be the most pathetic dog sled team ever.)It's important to note here that tension is a pulling force since

**ropes simply can't push**effectively. Trying to push with a rope causes the rope to go slack and lose the tension that allowed it to pull in the first place. This might sound obvious, but when it comes time to draw the forces acting on an object, people often draw the force of tension going in the wrong direction so remember that**tension can only pull**on an object.## How do we calculate the force of tension?

Unfortunately, there's no special formula to find the force of tension. The strategy employed to find the force of tension is the same as the one we use to find the normal force. Namely, we use Newton's second law to relate the motion of the object to the forces involved. To be specific we can,

- Draw the forces exerted on the object in question.
- Write down Newton's second law $(a=\dfrac{\Sigma F}{m})$ for a direction in which the tension is directed.
- Solve for the tension using the Newton's second law equation $a=\dfrac{\Sigma F}{m}$.

We'll use this problem solving strategy in the solved examples below.

## What do solved examples involving tension look like?

### Example 1: Angled rope pulling on a box

A box of cucumber extract is being pulled across a frictionless table by a rope at an angle as seen below. The tension in the rope causes the box to slide across the table to the right with an acceleration of .

**What is the tension in the rope?**

First we draw a force diagram of all the forces acting on the box.

Now we use Newton's second law. The tension is directed both vertically and horizontally, so it's a little unclear which direction to choose. However, since we know the acceleration horizontally, and since we know tension is the only force directed horizontally, we'll use Newton's second law in the horizontal direction.

### Example 2: Box hanging from two ropes

A container of animal crackers hangs at rest from two strings secured to the ceiling and wall respectively. The diagonal rope under tension is directed at an angle from the horizontal direction as seen below.

**What are the tensions and in the two strings?**

First we draw a force diagram of all the forces acting on the container of animal crackers.

Now we have to use Newton's second law. There are tensions directed both vertically and horizontally, so again it's a little unclear which direction to choose. However, since we know the force of gravity, which is a vertical force, we'll start with

**Newton's second law in the vertical direction**.Now that we know we can solve for the tension using

**Newton's second law for the horizontal direction**.