Physics Study Guide/Normal force and friction

The Normal Force

Why is it that we stay steady in our chairs when we sit down? According to the first law of motion, if an object is translationally in equilibrium (velocity is constant), the sum of all the forces acting on the object must be equal to zero. For a person sitting on a chair, it can thus be postulated that a normal force is present balancing the gravitational force that pulls the sitting person down. However, it should be noted that only some of the normal force can cancel the other forces to zero like in the case of a sitting person. In Physics, the term normal as a modifier of the force implies that this force is acting perpendicular to the surface at the point of contact of the two objects in question. Imagine a person leaning on a vertical wall. Since the person does not stumble or fall, he/she must be in equilibrium. Thus, the component of his/her weight along the horizontal is balanced or countered (opposite direction) by an equal amount of force -- this force is the normal force on the wall. So, on a slope, the normal force would not point upwards as on a horizontal surface but rather perpendicular to the slope surface.

The normal force can be provided by any one of the four fundamental forces, but is typically provided by electromagnetism since microscopically, it is the repulsion of electrons that enables interaction between surfaces of matter. There is no easy way to calculate the normal force, other than by assuming first that there is a normal force acting on a body in contact with a surface (direction perpendicular to the surface). If the object is not accelerating (for the case of uniform circular motion, the object is accelerating) then somehow, the magnitude of the normal force can be solved. In most cases, the magnitude of the normal force can be solved together with other unknowns in a given problem.

Sometimes, the problem does not warrant the knowledge of the normal force(s). It is in this regard that other formalisms (e.g. Lagrange method of undertermined coefficients) can be used to eventually solve the physical problem.

Friction

When there is relative motion between two surfaces, there is a resistance to the motion. This force is called friction. Friction is the reason why people could not accept Newton's first law of Motion, that an object tends to keep its state of motion. Friction acts opposite to the direction of the original force. The frictional force is equal to the frictional coefficient times the normal force.

Friction is caused due to attractive forces between the molecules near the surfaces of the objects. If two steel plates are made really flat and polished and cleaned and made to touch in a vacuum, it bonds together. It would look as if the steel was just one piece. The bonds are formed as in a normal steel piece. This is called cold welding. And this is the main cause of friction.

The above equation is an empirical one--in general, the frictional coefficient is not constant. However, for a large variety of contact surfaces, there is a well characterized value. This kind of friction is called Coulomb friction. There is a separate coefficient for both static and kinetic friction. This is because once an object is pushed on, it will suddenly jerk once you apply enough force and it begins to move.

Also, the frictional coefficient varies greatly depending on what two substances are in contact, and the temperature and smoothness of the two substances. For example, the frictional coefficients of glass on glass are very high. When you have similar materials, in most cases you don't have Coulomb friction.

For static friction, the force of friction actually increases proportionally to the force applied, keeping the body immobile. Once, however, the force exceeds the maximum frictional force, the body will begin to move. The maximum frictional force is calculated as follows:

$\left|{\vec {F}}_{f}\right|\leq \mu _{s}\left|{\vec {N}}\right|$

The static frictional force is less than or equal to the coefficient of static friction times the normal force. Once the frictional force equals the coefficient of static friction times the normal force, the object will break away and begin to move.

Once it is moving, the frictional force then obeys:

$\left|{\vec {F}}_{f}\right|=\mu _{k}\left|{\vec {N}}\right|$

The kinetic frictional force is equal to the coefficient of kinetic friction times the normal force. As stated before, this always opposes the direction of motion.

Variables

Symbol	Units	Definition
${\vec {F}}_{f}$	$\mathrm {N} \$	Force of friction
$\mu \$	none	Coefficient of friction

Definition of Terms

Normal force (N): The force on an object perpendicular to the surface it rests on utilized in order to account for the body's lack of movement. Units: newtons (N) Force of friction (Ff): The force placed on a moving object opposite its direction of motion due to the inherent roughness of all surfaces. Units: newtons (N) Coefficient of friction (μ): The coefficient that determines the amount of friction. This varies tremendously based on the surfaces in contact. There are no units for the coefficient of either static or kinetic friction

It's important to note, that in real life we often have to deal with viscose and turbulent friction - they appear when you move the body through the matter.

Viscose friction is proportional to velocity and takes place at approximately low speeds. Turbulent friction is proportional to $V^{2}$ and takes place at higher velocities.