1. Kinetic Friction

2. Sliding  Sliding objects also have a frictional force exerted on them.  This frictional force is kinetic friction.  An approximate formula:  k is the coefficient of kinetic friction

3. Continuing Motion  F fr =  k F N =  k mg cos   Compare to the downslope component of gravity F gx = mg sin . Block increases or decreases speed depending on which is greater.  If equal there is constant velocity. m 

4. Static vs. Kinetic  Static and kinetic friction are similar. Force in opposite direction to motionForce in opposite direction to motion Proportional to normal forceProportional to normal force Coefficient of friction depends on materialsCoefficient of friction depends on materials  Static and kinetic friction are different. Static friction is an inequality up to a maximum Coefficient of friction is typically greater for static friction at the same surface Wood on wood (0.4 vs. 0.2)

5. Drag  Kinetic friction is a constant force. If there is a net force an object would accelerate foreverIf there is a net force an object would accelerate forever  Air resistance causes a friction called drag. At low velocity drag is proportional to velocity, F d = -bvAt low velocity drag is proportional to velocity, F d = -bv At higher velocity drag goes as velocity squared, F d = -cv 2At higher velocity drag goes as velocity squared, F d = -cv 2  Because it depends on velocity the force increases as an object speeds up.

6. Terminal Velocity  An object may fall through the air at constant velocity.  By the law of inertia the net force is zero.  The force of drag must balance the force of gravity.  This velocity is called the terminal velocity. F g =  mg F d = cv 2

7. Downhill Skiing  CBS Sports has invited you to be the special science commentator for the Winter Olympics downhill ski race.  You observe the following: The downhill course is 2.5 km long with a drop of 800 mThe downhill course is 2.5 km long with a drop of 800 m A downhill skier needs at least 3° of slope to move forwardA downhill skier needs at least 3° of slope to move forward The speed gun clocks the skier at a maximum of 130 km/hThe speed gun clocks the skier at a maximum of 130 km/h An average skier is about 90 kgAn average skier is about 90 kg  What is the coefficient of kinetic friction and drag coefficient for a skier?

8. Force Diagram  At constant velocity the forces must all balance.  Friction doesn’t act in the direction of the normal force.  The normal force cancels the component of gravity.  F g = -mg F gy = -mg cos  F N = mg cos  F d = -cv 2 F fr = -  k F N

9. Minimum Sliding  When the skier is sliding to a halt we can neglect drag.  Kinetic friction balances the component of gravity pulling forward.  ° F gx = mg sin  F N = mg cos  F fr = -  k F N

10. Downhill Run  The slope of the downhill course is sin  = 800 m / 2500 m  = 19°  Drag force balances the force of gravity and kinetic friction.  ° F N = mg cos  F d = -cv 2 F fr = -  k F N F gx = mg sin 