1. Friction

2. Static Friction f s - The force on an object that keeps it from slipping f s - The force on an object that keeps it from slipping f s = F push f s = F push

3. Static Friction There is a limit to how big static friction can get – f smax There is a limit to how big static friction can get – f smax f smax is proportional to the magnitude of the normal force between the surface and the object. f smax is proportional to the magnitude of the normal force between the surface and the object. F smax = ų s n where ų s is called the coefficient of static friction. F smax = ų s n where ų s is called the coefficient of static friction. The coefficient is a number that depends on the materials of the object and the surface The coefficient is a number that depends on the materials of the object and the surface The higher the number, the greater the “stickiness” between the object and the surface The higher the number, the greater the “stickiness” between the object and the surface

5. Rules for Static Friction The direction of static friction is such as to oppose motion. The direction of static friction is such as to oppose motion. The magnitude f s of static friction adjusts itself so that the net force is zero and the object doesn’t move. The magnitude f s of static friction adjusts itself so that the net force is zero and the object doesn’t move. The magnitude of static friction cannot exceed the maximum value f smax. If the friction force needed to keep the object stationary is larger than f smax, the object slips and starts to move. The magnitude of static friction cannot exceed the maximum value f smax. If the friction force needed to keep the object stationary is larger than f smax, the object slips and starts to move.

6. Kinetic Friction Once the box starts to slide, the static friction force is replaced by the kinetic friction force. Once the box starts to slide, the static friction force is replaced by the kinetic friction force. The direction of f k is always opposite the direction of motion. The direction of f k is always opposite the direction of motion. Kinetic friction has a nearly constant magnitude. Kinetic friction has a nearly constant magnitude. F k = ų k n where ų k is called the coefficient of kinetic friction. F k = ų k n where ų k is called the coefficient of kinetic friction.

7. Kinetic Friction

8. Ų k < ų s This explains why it is easier to keep a box moving than it was to start moving

9. Rolling Friction A wheel rolling on a surface experiences rolling friction A wheel rolling on a surface experiences rolling friction The portion of the wheel that contacts the surface is stationary with respect to the surface, not sliding. The portion of the wheel that contacts the surface is stationary with respect to the surface, not sliding. A wheel is not perfectly round. A wheel is not perfectly round. Weight causes the bottom of the wheel to flatten where it touches the surface. Weight causes the bottom of the wheel to flatten where it touches the surface. The leading part of the tire becomes deformed. The leading part of the tire becomes deformed. This requires the road push backward on the tire. This requires the road push backward on the tire. The road causes a backward force The road causes a backward force

10. Rolling Friction F r = ų r n F r = ų r n Ų r is the coefficient of rolling friction. Ų r is the coefficient of rolling friction. The direction of the force opposes the direction of motion The direction of the force opposes the direction of motion Rolling friction acts similar to kinetic friction but ų r < ų k Rolling friction acts similar to kinetic friction but ų r < ų k This is why it is easier to roll an object on wheels than to slide it. This is why it is easier to roll an object on wheels than to slide it.

12. Friction Equations Friction Equations are models not laws. Friction Equations are models not laws. We ignore surface area. It has little effect. We ignore surface area. It has little effect. The model assumes kinetic friction force is independent of the object’s speed. The model assumes kinetic friction force is independent of the object’s speed.

13. Causes of Friction Surfaces are rough on the microscopic level. Surfaces are rough on the microscopic level. High points of one surface become jammed against the high points of the other surface. High points of one surface become jammed against the high points of the other surface. A very small fraction (10 -4 ) of the surface area is in actual contact. A very small fraction (10 -4 ) of the surface area is in actual contact. The amount of contact depends on how hard the surfaces are pushed together, which is why friction forces are proportional to n. The amount of contact depends on how hard the surfaces are pushed together, which is why friction forces are proportional to n.