Aim: How do we explain air resistance?

Do Now: Motion graphs for object in free fall Draw position-time, velocity-time, and acceleration-time graphs for an object in free fall. (Neglect air resistance)

Drag Forces When an object moves through a fluid it exerts a drag force that opposes the motion of the object. What does the drag force depend on?

Fdrag Fdrag=bvn b is a viscosity constant n=number v= velocity

Terminal velocity When a falling object reaches a certain speed, the drag force is equal to the weight of a falling object, the object stops accelerating. This speed is called the terminal velocity.

Terminal velocity

Deriving Terminal Velocity Fdrag = Fg bvn = mg vterminal= (mg/b)1/n F= 628 N, b=.251

Calculating terminal velocity-Problem 1 A sky diver of mass 64 kg falls with a terminal speed of 50 m/s with her arms and legs outspread. What is the magnitude of the upward drag force Fd on the skydiver? Fg=mg=64(10)=640 N Fg=Fd so Fd=640 N b) If the drag force is equal to bv2, what is the value of b? Fd=bv2 640=b(50)2 b=0.256

Air Resistance Problem 2 A ping pong ball has a mass of 0.023 kg and a terminal speed of 9m/s. The retarding force is of the form bv2. What is the value of b? Fg=mg=Fd=bv2 .023(10)=b(9)2 b=0.0028

Air Resistance Problem 3 An 800 kg car rolls down a very long 6 degree grade. The drag force for motion of the car has the form Fd = 100N + (1.2N s2/m2)v2. What is the terminal velocity for the car rolling down the grade? (We neglect rolling friction) Mgsinθ=100+1.2v2 800(10)sin6°=100+1.2v2 v=24.5 m/s 24.5m/s

TURN AND TALK When an object is thrown upwards, how does its motion as it rises differ from its motion as it falls when air resistance is taken into account? Does it take longer to rise than to fall? It takes longer to fall than to rise Does it take an equal amount of time to rise and fall? Does it take less time to rise than to fall?

Reading Passage-Terminal Velocity As an object falls, the force of gravity initially causes it to continuously speed up as predicted by Isaac Newton. As it gets faster and faster, the air drag force increases until eventually, the air drag force is exactly equal to the force of gravity, and there is no net force acting on the object. If these two forces are exactly balanced, the object will no longer speed up or slow down but will continue falling at a constant velocity, called the terminal velocity. Since the air drag force depends heavily on the size and shape of the object, objects with a large surface area (like a parachute) will have a much lower terminal velocity than objects with a smaller surface area (like a person falling from a plane). The weight of the object does affect the air drag force on the object and, therefore, its terminal velocity. Underline any sentences of confusion. Write a few sentences explaining what factors affect the terminal velocity besides weight.