1. Aim: How do we explain air resistance?

2. 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)

3. Motion- Graphs with Air Resistance
Now draw these graphs for objects falling under the influence of air resistance.

4. 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?

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

6. 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.

7. Terminal velocity

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

9. 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

10. Air Resistance Problem 2
A ping pong ball has a mass of 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

11. 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

12. 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

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