# Difference Between Balanced and Unbalanced Forces

## Main Difference – Balanced vs. Unbalanced Forces

When we think of forces acting on a body, the forces could either be balanced or unbalanced. The main difference between balanced and unbalanced forces is that when the forces are balanced, the net force on the body is 0, whereas the net force acting on a body is not 0 if the forces are unbalanced.

## What are Balanced Forces

Forces acting on a body are balanced if their vector sum is 0, i.e. there is no net force acting on the body. According to Newton’s laws of motion, then, the body will not accelerate. This means that if the body is at rest it will continue to stay at rest and if the body is in motion, it will continue to move at the same speed in a straight line. If the body moves at the same speed but does not move in a straight line, then the forces on the body are not balanced and the body is accelerating.

### Balanced Forces – Examples

Let’s take a simple example. The dogs in the diagram below are both pulling at a piece of cloth. Suppose both dogs are pulling at the cloth with a force of 50 N in opposite directions, the two forces would cancel each other and the resultant or the net force would be 0. Here, the forces are balanced and the cloth would not move. Balanced Force_ Dogs playing tug-of-war

Think of a mug resting on the table. The fact that the mug does not move does not necessarily mean that there are no forces acting on the mug. There is always gravity acting on the mug, trying to pull it down (here we assume we are talking about a mug on Earth!), however gravity is cancelled out by an upwards reaction force exerted by the table on the mug. In other words, the forces are balanced and this is why the mug does not move.

### Coplanar Forces

Let’s take an example where a body being pulled by 3 coplanar forces (i.e. they all act along the same plane). If the body continues to stay at rest, then we know that the forces on it are balanced. In the diagram below, we have two forces $A$ and $B$ acting at right angles to each other and a third force $F$ acting at an angle $\theta$ to the vertical. If they are balanced, then we can work out a relationship between the two forces $A$ and $B$ and the angle $\theta$. First, taking the forces vertically, $A=F\mathrm{cos\:}\theta$.

Horizontally, we get $B=F\mathrm{sin\:}\theta$.

Dividing the first equation by the first, we get, $\frac{B}{A}=\mathrm{tan\:}\theta$

If three coplanar forces are balanced and they make different angles with each other, simply find components of each force along two perpendicular directions. Then the vector sum of the components along each direction should be 0.

## What are Unbalanced Forces

When we say forces on a body are unbalanced, we mean that there is a net resultant force. As usual, we find the resultant force by finding the vector sum of the forces. To indicate we are taking the sum or the resultant of forces, we write $F$ as $\Sigma F$.

According to Newton’s second law, if a resultant force of $\Sigma F$ acts on a body with mass $m$, then the body would undergo an acceleration of $a$ in the direction of the resultant force. Let’s take another tug-of-war as an example: this time between a human and a dog: Tug-of-war: Dog vs. Human

In the photo, the forces seem balanced. However, imagine what would happen if the dog pulled at the cloth with a force of 60 N while the woman pulled it with a force of 60.25 N in the opposite direction. Now, there will be an unbalanced force of 0.25 N towards the woman. If the mass of the shirt is 3 g, then the acceleration of the shirt towards the woman would be: $a=\frac{\Sigma F}{m}=\frac{0.25\:\mathrm{N}}{0.03\:\mathrm{kg}}=8\:\mathrm{m\:s^{-2}}$

## Difference Between Balanced and Unbalanced Forces

### Net Force

For balanced forces, the net force is 0.

For unbalanced forces, the net force is not 0.

### Acceleration

Balanced forces cause no acceleration.

Unbalanced forces cause acceleration.

Image Courtesy

“Tug of War” by PROgarlandcannon (Own work) [CC BY-SA 2.0], via flickr

“Tug of war” by PROCary Bass-Deschenes (Own work) [CC BY-SA 2.0], via flickr (Modified) 