Forces & Motion

1. Forces & Motion The Force of Friction

2. 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.

3. 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.

4. 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.

5. 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 isFs.

6. 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

7. 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

8. 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)

9. 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.

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

11. 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.

12. Coefficients of Friction

13. Coefficient of Static Friction • The coefficient of static friction can be determined by the following formula:

14. Coefficient of Kinetic Friction • The coefficient of kinetic friction can be determined by the following equation:

15. 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: