Free Body Diagrams
FREE BODY DIAGRAMS

No doubt you are aware of free body diagrams (otherwise known as FBD's). These are simplified representations of an object (the body) in a problem, and includes force vectors acting on the object. 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.

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


Figure 1 A ship, pulled by a rope, on a sunny day. (Use your imagination.)


Let's take Figure 1 to be a pictoral representation of our problem: a boat on the floor, with a rope pulling it. First we will represent the boat -- the 'body' in our problem -- as a (really) simplified figure, a square (Figure 2).
Figure 2 Simplified diagram of the ship


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. The force, by Newton's Second Law is

    F = m g

where g is the acceleration due to gravity. Let's add this to our diagram (Figure 3). Note that the force vector, labelled Fmg, points downward, as this is the direction in which the gravitation force acts.

Note that this force is commonly called weight. This 'weight' (m g) is different from our everyday use of the word 'weight' (which is known in physics as 'mass').


Figure 3 Ship, with the gravitational force labelled


Normal
The normal force 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 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 constact. For a body on a sloped surface (say a ramp), the normal force acting on that body is still perpendicular to the slope.

In the case of our problem, the ship, we will pretend the ship is being pulled on a floor. (This is because on water there is the complication with another force, buoyancy. For simplicity's sake, we will ignore buoancy by putting the ship on the floor.) Let's add the normal force to our FBD (Figure 4), and represent the normal force with the script 'N', .


Figure 4 Ship, with gravitational and normal forces.


Friction
Related to the normal force is the frictional force. The two are related because they are both due to the surface in contact with the body. 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 categories, static and kinetic. These are represented by the script 'F', with a 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 (i.e. "static"). It is the force which makes it difficult to start something moving. On the other hand, kinetic friction occurs when the body is in motion. 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 constant is represented as for static friction, and for kinetic friction; it depends on the actual surface with which the body is in contact.

To summarize,

    =
    =
We've added (kinetic) friction to our free body diagram, Figure 5.

Figure 5 Ship, with gravitational, normal, and frictional forces


Push and 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 wind pushing on the ship.

We will label the push force caused by the wind with Fpush


Figure 6 Ship, with gravitational, normal, frictional, and push forces


Tension
Tension in an object results if pulling force act on its ends, such as in a rope used to pull a boulder. If no forces are acting on the rope, say, except at its ends, and the rope itself is in equilibrium, then the tension is the same throughout the rope.

We will use the letter T to represent tension in a free body diagram.

If we say that our ship is being pulled by a rope at its front end, then we can add this force to our FBD (Figure 7).


Figure 7 Ship with gravitational, normal, frictional, push, and tension forces

And there we have it: all the forces acting on our ship has been labelled in Figure 7. This is the complete FBD for our problem of a ship being pulled along a floor by a rope.


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