# Free Body Diagrams Tutorial

Free body diagrams (otherwise known as FBD's) are simplified representations in a problem of an object (the body), and the force vectors acting on it. This body is free because the diagram will show it without its surroundings; i.e. the body is 'free' of its environment. This eliminates unnecessary information which might be given in a problem.

Let's take this figure to be a pictorial representation of our problem: a sled on snow, with horses pulling it. First we will represent the sled (the 'body' in our problem) as a (really) simplified figure, a square resting on a flat surface.

In this tutorial, we will review some of the main forces which you will encounter in physics, and discuss their contribution to an FBD.

## Gravity

The first force we will investigate is that due to gravity, and we'll call it the gravitational force. We know that the acceleration due to gravity (if on Earth) is approximately $g = 9.8 m/s^2$.

The force, by Newton's Second Law is

$F_g = m g$

where $g$ is the acceleration due to gravity and m is the mass of the carriage. Let's add this to our diagram.

Note that the force vector, labelled $F_g$, points downward, as this is the direction in which the gravitation force acts.

Note also that this force is commonly called “weight”. This 'weight' ($mg$) is different from our everyday use of the word 'weight' (which is known in physics as 'mass').

## Normal Force

The normal force is one which prevents objects from 'falling' into whatever it is they are sitting upon. It is always perpendicular to the surface with which an object is in contact. For example, if there is a crate on the floor, then we say that the crate experiences a normal force exerted by the floor; and because of this force, the crate does not fall into the floor. The normal force on the crate points upward perpendicular to the floor.

It is called the normal force because “normal” and “perpendicular” mean the same thing.

The normal force is always perpendicular to the surface with which a body is in contact. For a body on a sloping surface (say a ramp) the normal force acting on that body is still perpendicular to the slope.

Let's add the normal force to our FBD and represent the normal force with the letter N.

## Friction

Related to the normal force is the frictional force. The two are related because they are both due to the fact that the body is in contact with the surface. Whereas the normal force was perpendicular to the surface, the frictional force is parallel. Furthermore, friction opposes motion, and so its vector always points away from the direction of movement.

Friction is divided into two types-static and kinetic. These are represented by $F_f$, with a further subscript '$s$' for static friction, and a subscript '$k$' for kinetic friction, . As its name suggests, static friction occurs when the body is not moving with respect to the surface. It is the force which makes it difficult to start something moving. On the other hand, kinetic friction occurs when the body is sliding over the surface. (Of course rolling objects experience friction as well.) This is the force which causes objects to slow down and eventually stop. Friction is usually approximated as being proportional to the normal force. The proportionality constant is called the coefficient of (static or kinetic) friction. The coefficient is represented as $\mu_s$ for static friction, and $\mu_k$ for kinetic friction; the numerical value of $\mu$ depends on the nature of the surface with which the body is in contact.

We've added (kinetic) friction to our free body diagram.

## Push or Pull

Another force which may act on an object could be any physical push or pull. This could be caused by a person pushing a crate on the floor, a child pulling on a wagon, or in the case of our example, the horse pulling on the carriage.

We will label the applied push (or pull) force with $F$.

### Tension

Tension in an object results if the pulling force acts on its ends, such as in a rope used to pull a boulder.

If we say that our carriage is being pulled by a bar (by the horse) at its front end, then we can add this force to our FBD.

And there we have it: all the forces acting on our carriage have been labelled in this figure. This is the complete FBD for our problem of a carriage being pulled along a road.