Forces & Motion

The Force of Friction

Frictional Forces

• Frictional forces arise from complex interactions between the surfaces of objects.

• Even very smooth surfaces are actually very rough on the microscopic level.

Friction

• Let’s consider the following situation.• We have a book lying on a table.• Newton’s 1st law tells us that the net external force

acting on the book is zero because it is not moving.

• Newton’s 2nd law tells us that any additional force applied to the book will cause it to accelerate and to remain in motion until another force acts on it again.

Friction

• Experience tells us that this won’t happen if we apply a small enough force to the book.

• Even if we apply a larger force to the book and it does finally move, it will stop almost as soon as we remove the force.

Static Friction

• When we push on the book with a small force, the table the book is on exerts an equal force in the opposite direction.

• The resistive force that keeps the book from moving when we apply a small enough force is called static friction.

• The symbol for static friction is Fs.

Static Friction

• As long as the book doesn’t move, the force of static friction is equal and opposite to the force that is being applied.

• When the applied force reaches the maximum value it can attain without moving the book, the force of friction has reached it maximum value - Fsmax

Kinetic Friction

• When the force on the book exceeds Fsmax, the book begins to move with acceleration in the direction of the force.

• There is still frictional force acting on the book, but it is less than Fsmax.

• The frictional force acting on an object already in motion is called kinetic friction - Fk

Net External Force

• The net external force that is causing the motion of the book can be determined by subtracting the force of kinetic friction from the force acting on the book.

• If we have a 12N force acting on the book and the force of friction was 1 N, we would have a net force of 11 N. (Fapp – Fk)

Coefficient of Friction

• Remember that the surfaces of objects are rarely truly smooth.

• The quantity that expresses how much friction is caused by two surfaces coming into contact with each other is called the coefficient of friction.

Mu

• The coefficient of friction is represented by the symbol μ, the lower case Greek letter mu.

Frictional Force Is Dependent On The Normal Force

• The force of friction is not only dependent on the surfaces of the objects that are sliding against each other but also on the normal force.

• Remember that the normal force is the reaction to the force of gravity.

• We find that the heavier the object, the more the frictional force will be.

Coefficients of Friction

Coefficient of Static Friction

• The coefficient of static friction can be determined by the following formula:

FF

n

s

s

max

Coefficient of Kinetic Friction

• The coefficient of kinetic friction can be determined by the following equation:

FF

n

k

k

Frictional Force

• If the value of mu and the normal force are known, the magnitude of the frictional force can be calculated directly with the following formula:

FF nf