Aim: How do we explain air resistance?

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)

Motion- Graphs with Air Resistance Now draw these graphs for objects falling under the influence of 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 A sky diver of mass 64 kg falls with a terminal speed of 50 m/s with her arms and legs outspread. a) What is the magnitude of the upward drag force Fd on the skydiver? 640 N b) If the drag force is equal to bv2, what is the value of b? mg=bv2 64(10)=b(50)2 b=0.256

Air Resistance Problem 2 A ping pong ball has a mass of 0.023 kg abd a terminal speed of 9m/s. The retarding force is of the form bv2. What is the value of b? 2.79 x 10^-4

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) 24.5m/s

Velocity function for object before it hits terminal velocity Write a differential equation under the influence of drag force bv. In other words, what is the net force on a falling body equal to at any specific time mg – kv = m dv/dt

Solution to Differential Equation v(t) = mg/k (1 – e (-k/m)t ) Test this function for v(0) and v(infinity)