# Friction Formula

Friction is caused by one surface moving over another. It is a force that can resist the motion of an object. Friction can cause energy of motion to be lost in the form of heat. The amount of force created depends on the materials involved, and every combination is different. The coefficient of friction is used to describe the way two surfaces interact. The coefficient of friction is assigned the Greek letter “mu” (μ), and it is unitless. The force of friction is μ times the normal force on an object. The unit for friction is the Newton (N).

force of friction = (coefficient of friction)(normal force)

Ff = μη

Ff = force of friction

μ = coefficient of friction

η = normal force (Greek letter “eta”)

Friction Formula Questions:

1) A large block of ice is being pulled across a frozen lake. The block of ice has a mass of 250 kg. The coefficient of friction between two ice surfaces is small: μk = 0.05. What is the force of friction that is acting on the block of ice?

Answer: On a flat surface, the normal force on an object is η = mg. Using this, the formula can be used to find the force of friction:

Ff = μη

Ff = μmg

Fk = (0.05)(250 kg)(9.8 m/s2)

Fk = 122.5 kg∙m/s2

Fk = 122.5 N

The force of friction acting in the opposite direction as the motion of the block of ice as it is pulled across the lake is 122.5 N.

2) A man’s boat was stuck on shore when the tide went out. He begins pushing his boat across the mud to get to the water. The coefficient of friction between his wooden boat and the mud is μ = 0.400. If the boat has a mass of 50.0 kg, what is the magnitude of the force of friction acting on the boat?

Answer: On a flat surface, the normal force on an object is η = mg. Using this, the formula can be used to find the force of friction:

Ff = μη

Ff = μ mg

Ff = (0.400)(50.0 kg)(9.80 m/s2)

Ff = 196 kg∙m/s2

Ff = 196 N

The force due to friction acting on the boat is 196 N.