Class 13 - Force and Motion II Chapter 6 - Wednesday September 22nd Friction More on friction (sample problems) Air resistance Reading: pages 99 thru 124 (chapter 6) in HRW Read and understand the sample problems Assigned problems from chapter 6: 8, 18, 20, 28, 30, 32, 40, 50, 52, 68, 84, 102 These will be due on Sunday October 3rd Note: chapter 5 homework deadline THIS SUNDAY! Exams available for pick-up. After Friday class, they will be filed in NPB1100.

Microscopic origin of friction

Static friction In static situations, the static frictional force exactly cancels the component of the applied force parallel to the surface. There is a maximum static frictional force which depends on the normal force between the surface and the object, i.e. where ms is the coefficient of static friction and N is the magnitude of the normal force. ms is a parameter that depends on both surfaces. Once the force component parallel to the surface exceeds fs,max, then the body begins to slide along the surface.

Kinetic friction If a body begins to slide along the surface, the magnitude of the frictional force instantly decreases to a value fk given by where mk is the coefficient of kinetic friction and N is the magnitude of the normal force. Therefore, during the sliding, a kinetic frictional force of magnitude fk opposes the motion. When several agents push in different directions on an object, the frictional force opposes the component of the net force on the object which is parallel to the surface.

A word about resolving forces When does the block slide? Trying to prevent the tendency for the sled to slide downhill, so the frictional force must act uphill and parallel to the slope

Alternative recipe (! ! ! !) method Measure q from the x-axis Then:  Chapter 2 j q

Compare methods (2nd law) + - cosine sine x y

Compare methods (2nd law) j = 90 + q cosj sinj y x

Compare methods (2nd law) y So the methods agree!! cosq q q x -sinq

Drag force and terminal speed Mass v is the velocity of the body. r is the air density (mass unit per volume). A is the effective cross sectional area of the body. C is the drag coefficient (typical values range from 0.4 to 1).

Drag force and terminal speed Mass Newton's 2nd law: Terminal speed when a = 0.

Terminal speeds in air