3. Chapter 6 Friction

4. We have used friction to a limited degree up to this point. We will now explore friction and develop mathematical relationships that will allow us to use friction effectively. Friction – A force tangential to a surface, resisting the motion of an object across the surface. Friction as a hindrance: Resistance to motion Fluid resistance Friction as a benefit: Walking Rolling Brakes Belts Types of Friction: Dry– Contact between non-lubricated surfaces of two solids. Most common type. Fluid – Interface between two parcels of a fluid moving at different velocities. Can also be used to discuss the interaction between a fluid and a solid. Depends on the relative velocities and viscosities of the fluids. (This type is beyond the scope of this course.) Internal – Friction inside a solid due to cyclic loading. (This type is beyond the scope of this course.)

5. Dry Friction The most common example of dry friction is an object sliding across a flat surface. Friction is difficult to characterize using a single theory, since there are a large number of variable that can influence it. Friction is typically described in terms of the microscopic interactions between two surfaces that are not perfectly flat (there are always some microscopic variations in surface morphology). From experimental analysis it is possible to determine an “average” measure of the interaction between two surfaces, called the coefficient of friction (  ). This coefficient can be used to relate the frictional force to the normal force. This relationship cannot be used under all conditions, and is different for an object that is moving as compared to it being stationary.

6. To further examine friction we discuss static friction, when the object is stationary, and kinetic friction when the object is moving. The frictional force will be different because the coefficient of friction (  ) is different for the two cases. When stationary the irregularities in the surfaces “settle in” making it more difficult to start moving. Therefore, the frictional force is the greatest just before it begins moving, at impending motion. We can only use the coefficient of static friction (  s ) to determine the friction at impending motion. Prior to impending motion the frictional force is equivalent to the applied force. When an object begins to move it “skips” across the tops of the irregularities and will therefore have the friction reduced. We can use the coefficient of kinetic friction (  k ) to predict the kinetic frictional force over the region where f k is constant (f k actually varies with velocity, which becomes more apparent with larger applied forces).

7. The direction of the resultant is defined by the angle  as shown earlier. If you consider all possible directions of motion you will sweep R in a circle creating a cone, which is called the cone of static (or kinetic) friction. This cone will correspond to specific angles for a constant  s or  k. We can redefine the angles made by R relative to the vertical as  s and  k. This would make the total angle between forward and reverse motion 2  s (or 2  k ). Notice that tan  is equal to the ratio of f to N, which is the same definition of  !