Terminal Velocity

1. Terminal Velocity

2. Drag • Kinetic friction is a constant force. • If 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, Fd = bv • At higher velocity drag goes as velocity squared, Fd = cv2 • The direction of drag force is opposite to the velocity.

3. 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. Fd =cv2 Fg = -mg

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

5. 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 = cv2 • c = mg / v2 Without a parachute: c = 0.25 kg / m With a parachute: c = 28. kg / m

6. 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 m • The coefficient of kinetic friction is 0.052 • The speed gun clocks the skier at a maximum of 130 km/h • An average skier is about 80 kg • What is the drag coefficient for a skier?

7. 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. Fd = -cv2 FN = mg cosq Ffr = -mkFN Fgy = -mg cosq Fg = -mg q

8. Downhill Run • The slope of the downhill course is • sinq = 800 m / 2500 m • q = 19° • Drag force balances the force of gravity and kinetic friction. Fd = -cv2 FN = mg cosq Ffr = -mkFN Fgx = mg sinq q = 19°