1. Terminal Velocity, Weight & Area

2. As v increases, so does air friction…

3. …until F = W-f =0. Now a=0, and the maximum or “terminal” velocity is achieved

4. Curveballs

5. Lab: Coffee Filter, Air Drag & Terminal Velocity with Motion Detector

7. Ailerons

8. Motion in the presence of resistive forces
Motion in viscous media.

9. Objects interact with the medium through which they are moving.
Air
Water, oil, liquids.
The resistive forces depend on the speed of the object.
F ~ v: Objects falling in liquid, tiny objects falling in air.
F ~ v2: Large objects moving in air.

10. Terminal velocity.
When the resistive force of the falling object is equal to the gravitational force on the object.
Examples:
- skydivers
soap bubbles falling in air
small spheres dropping in liquid.

11. Air drag at high speeds.
For objects moving at high speeds through air:
Resistive force:
Where:
D… Drag coefficient of object (depends on shape)
r…density of air
A… cross-sectional area of object
v… velocity of object

12. Example
CC Sabathia fires a baseball (m = kg) past you at 100 miles/hr (45 m/s).
Calculate the resistive force acting on the ball at that speed.
D… Drag coefficient = 0.284
r…density of air = 1.29 kg/m3
r… radius of baseball = m
v… velocity of object

13. Air Drag a.k.a. Fluid Drag Fluid friction = ½ CAv2 @ V terminal,
F = W – f = 0
Solve for v:
mg - ½ CAv2 = 0
V terminal = (2mg/ CA)½

14. ©2008 by W.H. Freeman and Company
Drag Forces
This chute is called a drag chute, but not directly for same reason as car is called drag racer.
©2008 by W.H. Freeman and Company

15. What factors influence drag?
Shape of the object.
Cars and planes are given aerodynamic shape to reduce drag.
Properties of the fluid.
Denser fluids increase drag.
Speed of the object relative to the fluid.

16. Terminal Velocity
Because the drag force increases with increasing velocity, an object in free fall will reach a speed where the drag force balances the force of gravity.
This speed is called terminal velocity.

17. Terminal Velocity
At terminal velocity

18. Getting to Terminal Velocity
Because the drag force depends on velocity, at first the drag force is small and the motion is like free fall.
At terminal velocity the velocity is constant.
The graph is exponential growth.

19. Getting to Terminal Velocity