When a single force is applied to an object of mass  m, it will cause an acceleration. This is described by Newton's Second Law, using the relation  F = m · a   With this equation, you can predict the acceleration given to the object by the applied force, or you can find the force if you know the acceleration.
This is the simplest case, and it is not very realistic. In order for this simple calculation using  F = m · a  to work, there must be no other force applied to the object, which means there can be no friction.

Because gravity applies a downward force on the object, and there is always friction between two surfaces, there will be a frictional force. Frictional forces always act in the opposite direction, so friction will reduce the effect of the applied force. This means that the object will have a smaller acceleration than it would have had, if there had been no friction.

Before we do calculations involving applied forces with friction, let's look at the frictional force  Ff, and how it is calculated.

We'll use a mass of 20 kg. The force of gravity pulls this mass directly downwards, but it is prevented from falling by the equal and opposite force of the ground pushing up. The interface between these two surfaces is the cause of friction, and it is different for every pair of surfaces.
The amount of friction depends on the mass of the object and the nature of the surfaces.

1.   A larger mass will result in a larger downward force. This is the normal force, or FN.
2.   The nature of the surfaces will cause friction. This is described by the coefficient of friction.
3.   Friction does not depend on the size of the area in contact.

1.  The normal force   FN is just the weight of the object. It can be calculated using  F = m · g, where  g is the acceleration due to gravity, or 9.8 m/s2 downwards.

For the 20 kg mass shown above:
FN = (20) · (-9.8) = -196 newtons.
We can ignore the negative sign; it just tells us that the force is downwards, which we already know.
The bigger this downward force is, the more frictional force there will be on the object.

2.  The coefficient of friction is a number which measures the friction between the object and the ground. This number depends on what the surfaces are, and their condition. For example, a wooden box on the ground would have a different coefficient than a wooden box on ice, and the coefficients would be different again if the surfaces were wet.

 ... This symbol is used for the coefficient of friction, a number (without units) that increases as the friction gets bigger.

You can calculate the force of friction if you know the normal force and the coefficient.

         Here's the equation:

Sometimes you will be asked to figure out what the coefficient of friction between two surfaces is. In order to do that, you must know the force of friction, and the normal force; then you solve the equation backwards.

3.  The size of the area of contact does not affect the size of the frictional force. This is not intuitively obvious, because in common everyday situations we often increase the normal force as we are increasing the area, maintaining a constant pressure.

Although a larger contact area between two different surfaces would result in a larger source of frictional forces, it also reduces the pressure between the two surfaces, for any given force holding them together. Since pressure equals force divided by area, the increase in friction-causing area is exactly balanced by the decrease in pressure. It is just as hard to move a 1 cm2 object as a 1 m2 object, if they both are pressed to the surface with the same amount of force.

Now let's look at what happens to an applied force when there is friction. Go on to  page two ...

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