Friction Forces

Friction Forces

Why does a box sliding on a surface eventually come to a stop? The answer is friction. Friction arises where two surfaces are in contact and moving relative to each other.

For an everyday example, press your hands together and move one backwards and forwards, we have two surfaces in contact with one moving relative to the other. Your hands get warm, you will have experienced this before and probably rub your hands together in winter to warm them up. The heat is generated through friction.

Friction arises because the surfaces interact with each other. Think about sandpaper with lots of bumps on the surface. If you rub sandpaper the bumps will slot into any groove .

When the surface of one object slides over the surface of another, each body exerts a frictional force on the other. For example if a book slides across a table, the table exerts a frictional force onto the book and the book exerts a frictional force onto the table. Frictional forces act parallel to surfaces.

The magnitude of the frictional force depends on the surface and the magnitude of the normal force. Different surfaces will give rise to different frictional forces, even if the normal force is the same. Frictional forces are proportional to the magnitude of the normal force. \[F_{\text{friction}} \propto N\]

For every surface we can determine a constant factor, the coefficient of friction, that allows us to calculate what the frictional force would be if we know the magnitude of the normal force. We know that static friction and kinetic friction have different magnitudes so we have different coefficients for the two types of friction:

• \(\mu_s\) is the coefficient of static friction
• \(\mu_k\) is the coefficient of kinetic friction

A force is not always large enough to make an object move, for example a small applied force might not be able to move a heavy crate. The frictional force opposing the motion of the crate is equal to the applied force but acting in the opposite direction. This frictional force is called static friction. When we increase the applied force (push harder), the frictional force will also increase until it reaches a maximum value. When the applied force is larger than the maximum force of static friction the object will move. The static frictional force can vary from zero (when no other forces are present and the object is stationary) to a maximum that depends on the surfaces.

For static friction the force can vary up to some maximum value after which friction has been overcome and the object starts to move. So we define a maximum value for the static friction: \(f_s^{max} = \mu_sN\).

When the applied force is greater than the maximum, static frictional force, the object moves but still experiences friction. This is called kinetic friction.For kinetic friction the value remains the same regardless of the magnitude of the applied force. The magnitude of the kinetic friction is: \(f_k = \mu_kN\).

Remember that static friction is present when the object is not moving and kinetic friction while the object is moving. For example when you drive at constant velocity in a car on a tar road you have to keep the accelerator pushed in slightly to overcome the friction between the tar road and the wheels of the car. However, while moving at a constant velocity the wheels of the car are rolling, so this is not a case of two surfaces “rubbing” against each other and we are in fact looking at static friction. If you should break hard, causing the car to skid to a halt, we would be dealing with two surfaces rubbing against each other and hence kinetic friction. The higher the value for the coefficient of friction, the more 'sticky' the surface is and the lower the value, the more 'slippery' the surface is.

Friction is very useful. If there was no friction and you tried to prop a ladder up against a wall, it would simply slide to the ground. Rock climbers use friction to maintain their grip on cliffs. The brakes of cars would be useless if it wasn't for friction!