# Friction: Static and kinetic

### Friction: Static and kinetic

#### Lessons

In this lesson, we will learn:
• Meaning of static and kinetic friction
• When to apply static and kinetic friction to physics problems
• Solving friction problems

Notes:

• Friction is the force that resists the motion of an object sliding (or trying to slide) over a surface.
• Kinetic friction is the friction that acts when an object slides across a surface.
• It is experimentally observed that kinetic friction is proportional to the force of the object pressing into the surface it slides across. Kinetic friction also depends on how well the two surfaces in contact grip each other.
• This is expressed with the equation $\vec{F}_{k} = \mu_{k}\vec{F}_{N}$. We can see in this equation that if the normal force acting on the object increases (due to the object pushing harder on the surface it slides on), friction force also increases proportionally.
• $\mu_{k}$ is the coefficient of kinetic friction, which tells us about the relationship between normal force and kinetic friction for two surfaces sliding past each other.
• Coefficients of friction are dimensionless: they do not have a unit.
• The larger the coefficient of kinetic friction, the stronger the friction between the two surfaces. A typical range for coefficient of friction values is between 0 and 1.
• A "frictionless" surface has a coefficient of friction of 0, but in real life all surfaces have some amount of friction. Teflon, the coating of non-stick pans and one of the lowest-friction materials known, has a coefficient of friction of ~0.04.
• Coefficients of friction greater than 1 are possible. They indicate the force of friction is greater than the normal force acting on the object. For example, some rubbers used for high-friction purposes (like rain boot soles) can have a coefficient of friction of greater than 1 with the ground.
• Static friction is the friction that acts when a force is applied to an object, but the applied force isn't large enough to overcome the friction between the object and surface it is on.
• Like kinetic friction, the maximum static friction is proportional to the normal force acting on the object. However, static friction only acts on an object in response to an applied force, and balances the applied force so the object does not move.
• If applied force on an object exceeds the maximum static friction, it begins to move. Once the object is moving, the friction acting on it is kinetic friction.
• For an object in contact with a surface, the coefficient of static friction ($\mu_{s}$) is in almost all cases larger than the coefficient of kinetic friction. As a result, the force required to get an object moving is somewhat larger than the force required to keep it in motion.
Kinetic friction

$\vec{F}_{k} = \mu_{k} \vec{F}_{N}$

$\vec{F}_{k}$: Kinetic force of friction, in newtons (N)

$\mu_{k}:$ Coefficient of kinetic friction

$\vec{F}_{N}:$ Normal force, in newtons (N)

Static friction

$\vec{F}_{s} \leq \mu_{s}\vec{F}_{N}$

$\vec{F}_{s (max)} = \mu_{s}\vec{F}_{N}$

$\vec{F}_{s}:$ Static force of friction, in newtons (N)

$\mu_{s}:$ Coefficient of static friction

$\vec{F}_{s (max)}:$ Maximum static force of friction, in newtons (N)

• Introduction
Introduction to friction
1. What causes friction?
2. What is kinetic friction?
3. What is static friction?

• 1.
Understanding kinetic vs. static friction

Joe wants to pull his 136 kg fridge away from the wall to clean behind it. When he pulls on the fridge with a horizontal force of 155 N, it doesn't move.

i. What is the force of friction that acts on the fridge? What type of friction is this?

ii. If the coefficient of friction between the fridge and floor is 0.200, what is the maximum amount of static friction that can act on the fridge?

iii. Joe gets Samantha to pull with an additional 155 N and the fridge begins to accelerate at 0.400 $m/s^{2}$. What is the coefficient of friction between the fridge and the ground? What type of friction is this?

• 2.
Solving friction problems
a)
A crate is pushed across the floor. The coefficient of friction between the crate and the floor is 0.240. If 167 N of applied force is required to keep the crate moving forwards at a constant velocity, find the mass of the crate.

b)

A physics student presses a 0.700 kg textbook against a wall with a force of 30.0 N perpendicular to the wall, and the book does not slide down the wall.

i. What is the force of friction acting on the book? What kind of friction is this?

ii. The student slowly reduces their push. If the book begins to slide when the student pushes with 20.0 N, what is the coefficient of friction?