Terminal Velocity

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Terminal Velocity - PowerPoint PPT Presentation

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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PowerPoint Slideshow about 'Terminal Velocity' - miach

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Presentation Transcript

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, Fd = bv
• At higher velocity drag goes as velocity squared, Fd = cv2
• 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.

Fd =cv2

Fg = -mg

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
• 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
• 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
• 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
• 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°