Terminal Velocity

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  The direction of drag force is opposite to the velocity.

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

Falling Leaves  The drag coefficient depends on the surface area. Large surfaces – high dragLarge surfaces – high drag –Leaves –Feathers –Papers Small surfaces – low dragSmall surfaces – low drag –Stones –Balls –Bullets

Skydiving  Terminal velocity for a 75-kg skydiver without a parachute is about 120 mph (53. m/s). With a parachute the terminal velocity is 5.1 m/s. What are the drag coefficients? Balance the weight and drag mg = cv 2 c = mg / v 2 Without a parachute: c = 0.25 kg / m c = 0.25 kg / m With a parachute: c = 28. kg / m c = 28. kg / m

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 The coefficient of kinetic friction is 0.052The coefficient of kinetic friction is 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 80 kgAn average skier is about 80 kg  What is the drag coefficient for a skier?

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

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 