# 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 undetermined 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 may have trouble accepting 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**

In order to set a body into a state of motion, the forward force or the
thrust force exerted upon the body must be greater in magnitude than the
maximum frictional value encountered upon the surface with which the
body is in contact with. If the thrust force does not exceed in
magnitude over the maximum frictional value or limiting value of motion
then the body shall not be set into motion.

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:

**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:

**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

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Definition of Terms

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**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 (F~f~):** 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\

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

Viscous 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.

