Transcript Air Drag Fluid Drag - AdvancedPlacementPhysicsC

Terminal Velocity, Weight &
Area
As v increases, so does air friction…
…until F = W-f =0.
Now a=0, and the maximum or
“terminal” velocity is achieved
Curveballs
Lab: Coffee Filter, Air Drag & Terminal
Velocity with Motion Detector
Ailerons
Motion in the presence of resistive forces
Motion in viscous media.
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.
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.
Air drag at high speeds.
For objects moving at high speeds through air:
Resistive force:
1
2
R  D    Av
2
Where:
D… Drag coefficient of object (depends on shape)
…density of air
A… cross-sectional area of object
v… velocity of object
Example
CC Sabathia fires a baseball (m
= 0.145 kg) past you at 100
miles/hr (45 m/s).
(a) Calculate the resistive force
acting on the ball at that
speed.
D… Drag coefficient = 0.284
…density of air = 1.29 kg/m3
r… radius of baseball = 0.037 m
v… velocity of object
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
Drag Forces
©2008 by W.H. Freeman and
Company
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.
Fd  bv
n
n  1 at low speeds.
n  2 at higher speeds.
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.
Terminal Velocity
Fd  mg  ma y
•
bv  mg  ma y
n
• At terminal velocity
bvTn  mg  0
mg
v 
b
n
T
 mg 
vT  

 b 
1
n
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.
v  A(1  e
 Bt
)
Getting to Terminal Velocity
Fd  mg  may
bv  mg  may
n
•
Assume n  1.
dv
bv  mg  m
dt
dv b
 vg
dt m
v  A(1  e
 Bt
)

v  vT 1  e



g
t
vT



