# Friction and Drag

Friction and drag are both forces that results form the motion of an object against its environment. Unlike the other forces we have encountered so far, friction and drag always oppose the motion of an object so as to slow it down and bring it to reset with respect to its environment. These forces are present everywhere, and almost every practical device must account for the presence of friction and drag.

### Friction

As we previously discussed, when a solid object presses against another surface, if feels a normal force pointing perpendicularly away from the surface. If the first object begins moving along the surface, then it will result in a force of friction parallel to the surface acting to oppose the motion of the object. The magnitude of this force is given by the following:

$$F = \mu_k N$$

Where \( N \) is the normal force acting on the object due to the surface, and \( \mu_K \) is a dimensionless constant coefficient characterizing the materials involved. The subscript \( k \) stands for kinetic friction, which denotes the case where two surfaces are moving against each other.

If the solid object is resting against another surface, but is not moving relative to it, then there is a force of friction present known as static friction. This is a force acting on the object due to the surface that opposes any other force acting on the object that tries to move this object. The maximum magnitude of this static friction is:

$$F = \mu_s N$$

Where \( \mu_s \) is the coefficient of static friction, which in general is different from the coefficient of kinetic friction, \( \mu_k \).

The force of static friction is present only when another force is pressing on the object, trying to move it from rest along the surface. The force of static friction force is the maximum force available to oppose any other force attempting to move the object. In contrast, kinetic friction is present as long as the object moves along the surface independently of the other forces acting on the object, as long as it maintains contact with the surface so that the normal force is not zero.

### Drag

Similar to friction, drag always opposes the motion of an object on which it is acting. Unlike friction, drag increases with the velocity of the object in the medium. Drag is always present when objects move in liquids and gases.

There are two main types of drag: linear drag and quadratic drag. The names denote the linear and quadratic dependence on velocity, respectively. Linear drag, which is appropriate at low velocity, is represented by:

$$\vec{F} = - b \vec{v}$$

Where \( \vec{v} \) is the velocity of the object in the medium, and \( b \) is some constant coefficient with the dimensions of \( Ns / m \) characterizing the strength of the drag force.

Quadratic drag is appropriate when an object moves at high velocities in the medium and is given by:

$$F = \frac{1}{2} \rho A C_d v^2$$

Here, \( \rho \) is the mass density of the medium, \( A \) is the reference area, \( v \) is the magnitude of the velocity, and \( C_d \) is a dimensionless constant characterizing the quadratic drag in the medium. The direction of the forces are always opposite to the motion.