Resource Lesson
Air Resistance
Printer Friendly Version
The
air resistance
that an object encounters is proportional to its cross-sectional area and to its velocity. Notice, that like friction, air resistance opposes motion. That is, if the object is rising through the air, air resistance acts downward; if it is falling, air resistance acts upwards. Notice that in the accompanying diagram, that the air resistance vectors vary in length. This signifies that its magnitude changes as the projectile's velocity changes.
Notice that while rising, both air resistance and weight oppose the object's upward motion. This results in the projectile losing speed at a rate greater than 9.8 m/sec
^{2}
and subsequently, rising to a lower apex height. On the way down, air resistance increases as the object gains velocity. But since air resistance and weight oppose each other, the projectile is gaining speed at an ever decreasing rate; that is, its acceleration is decreasing. Eventually, when air resistance and weight become equal, the projectile's downward acceleration ceases and the object reaches a state of dynamic equilibrium called
terminal velocity
. The remainder of its trajectory is traveled at this constant speed. All of these factors lead to a projectile spending more time falling than it does rising when in the presence of air resistance. The symmetry of freefall is lost for a projectile thrown up into the air.
The air resistance, or drag force, is generally expressed as
AR = F
_{drag}
= -kv
^{n}
where
k
and
n
are constants that depend on the geometry of the object and the medium through which it is moving. When terminal speed is reached,
net F = 0
AR + mg = 0
-kv
^{n}
+ mg = 0
-kv
^{n}
= -mg
kv
^{n}
= mg
v = (mg/k)
^{1/n}
Obviously, the larger the values of
k
and
n
, the smaller the object's terminal speed.
Refer to the following information for the next two questions.
Suppose a skydriver having a mass of 80 kg reaches a terminal velocity of 60 m/sec before he releases his parachute to begin his final descent.
What magnitude drag force, or air resistance, is the skydiver experiencing?
If the drag force obeys the formula F
_{drag}
= -kv
^{2}
, what is the value of
k
?
Related Documents
Lab:
Labs -
Coefficient of Friction
Labs -
Conservation of Momentum in Two-Dimensions
Labs -
Falling Coffee Filters
Labs -
Inelastic Collision - Velocity of a Softball
Labs -
Inertial Mass
Labs -
LabPro: Newton's 2nd Law
Labs -
Loop-the-Loop
Labs -
Mass of a Rolling Cart
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Static Equilibrium Lab
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: LabPro Data for Hooke's Law
Labs -
Terminal Velocity
Labs -
Video LAB: A Gravitron
Resource Lesson:
RL -
Advanced Gravitational Forces
RL -
Air Resistance: Terminal Velocity
RL -
Forces Acting at an Angle
RL -
Freebody Diagrams
RL -
Inclined Planes
RL -
Inertial vs Gravitational Mass
RL -
Newton's Laws of Motion
RL -
Non-constant Resistance Forces
RL -
Properties of Friction
RL -
Springs and Blocks
RL -
Springs: Hooke's Law
RL -
Static Equilibrium
RL -
Systems of Bodies
RL -
Tension Cases: Four Special Situations
RL -
The Law of Universal Gravitation
RL -
Universal Gravitation and Satellites
RL -
Universal Gravitation and Weight
RL -
Welcome! What is Mass?
RL -
Work and Energy
Worksheet:
APP -
Big Fist
APP -
Family Reunion
APP -
The Antelope
APP -
The Box Seat
APP -
The Jogger
CP -
Action-Reaction #1
CP -
Action-Reaction #2
CP -
Equilibrium on an Inclined Plane
CP -
Falling and Air Resistance
CP -
Force and Acceleration
CP -
Force and Weight
CP -
Force Vectors and the Parallelogram Rule
CP -
Freebody Diagrams
CP -
Gravitational Interactions
CP -
Incline Places: Force Vector Resultants
CP -
Incline Planes - Force Vector Components
CP -
Inertia
CP -
Mobiles: Rotational Equilibrium
CP -
Net Force
CP -
Newton's Law of Motion: Friction
CP -
Static Equilibrium
CP -
Tensions and Equilibrium
NT -
Acceleration
NT -
Air Resistance #1
NT -
An Apple on a Table
NT -
Apex #1
NT -
Apex #2
NT -
Falling Rock
NT -
Falling Spheres
NT -
Friction
NT -
Frictionless Pulley
NT -
Gravitation #1
NT -
Head-on Collisions #1
NT -
Head-on Collisions #2
NT -
Ice Boat
NT -
Rotating Disk
NT -
Sailboats #1
NT -
Sailboats #2
NT -
Scale Reading
NT -
Settling
NT -
Skidding Distances
NT -
Spiral Tube
NT -
Tensile Strength
NT -
Terminal Velocity
NT -
Tug of War #1
NT -
Tug of War #2
NT -
Two-block Systems
WS -
Advanced Properties of Freely Falling Bodies #1
WS -
Advanced Properties of Freely Falling Bodies #2
WS -
Calculating Force Components
WS -
Combining Kinematics and Dynamics
WS -
Distinguishing 2nd and 3rd Law Forces
WS -
Force vs Displacement Graphs
WS -
Freebody Diagrams #1
WS -
Freebody Diagrams #2
WS -
Freebody Diagrams #3
WS -
Freebody Diagrams #4
WS -
Introduction to Springs
WS -
Kinematics Along With Work/Energy
WS -
net F = ma
WS -
Practice: Vertical Circular Motion
WS -
Ropes and Pulleys in Static Equilibrium
WS -
Standard Model: Particles and Forces
WS -
Static Springs: The Basics
WS -
Vocabulary for Newton's Laws
WS -
Work and Energy Practice: Forces at Angles
TB -
Systems of Bodies (including pulleys)
TB -
Work, Power, Kinetic Energy
PhysicsLAB
Copyright © 1997-2015
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton