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Terminal Velocity. 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, F d = bv

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Terminal Velocity


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slide2
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.
terminal velocity3
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

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

downhill skiing
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?
force diagram
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

downhill run
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°