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Class 14 - Force and Motion II
Chapter 6 - Friday September 24th
•Review drag force and terminal speed
•Uniform circular motion revisited
•Sample problems
Reading: pages 99 thru 130 (chapter 6) in HRW
Read and understand the sample problems
Assigned problems from chapter 6:
8, 18, 20, 28, 30, 32, 40, 50, 52, 68, 84, 102
These will be due on Sunday October 3rd
Note: chapter 5 homework deadline THIS SUNDAY!
Exams available for pick-up now or in NPB1100.
Drag force and terminal speed
DMA
D  C  Av
1
2
2
• v is the velocity of the body.
Mass
•  is the air density (mass unit
per volume).
•A is the effective cross sectional
area of the body.
•C is the drag coefficient (typical
values range from 0.4 to 1).
g
ME
F
Drag force and terminal speed
D  C  Av
1
2
DMA
2
Newton's 2nd law:
Mass
D  F  C  Av  mg  ma
g
2
1
2
Terminal speed when a = 0.
1
2
g
ME
F
C  Av  mg
2
2mg
or v 
C A
Terminal speeds in air
The mysterious sliding stones the remote Racetrack Playa in Death Valley, California
20 kg, mk = 0.80, A = 0.040 m2, C = 0.80,  = 1.21 kg/m3
Review of uniform circular motion
•Although v does not change, the
direction of the motion does, i.e. the
velocity (a vector) changes.
•Thus, there is an acceleration
associated with the motion.
•We call this a centripetal
acceleration.
2
Acceleration:
v
a
r
2 r
Period: T 
v
•Since v does not change, the acceleration must be
perpendicular to the velocity.
Newton's second law
v
F
mv 2
F  ma 
r
m
Newton's second law
v
m
F
mv 2
F  ma 
r
Newton's second law
m
v
mv 2
F  ma 
r
F
Newton's second law
m
F
v
mv 2
F  ma 
r
Centripetal force always directed
towards the center of the motion
More on Newton's laws
a , F and v are constantly changing
•However, the magnitudes a, F, v and r are constants of the
motion.
•The frame in which the mass is moving is not inertial, i.e. it
is accelerating.
•Therefore, one cannot apply Newton's laws in the moving
frame associated with the mass.
•However, we can only apply Newton's laws from the
stationary lab frame.
•Examples of centripetal forces: gravity on an orbiting
body; the tension in a string when you swirl a mass in around
in a circle; friction between a car's tires and the racetrack
as a racing car makes a tight turn....
•The normal forces between the roller coaster and tracks
•The normal forces between you and the roller coaster
So why do you appear weightless in orbit?
m
ag
So why do you appear weightless in orbit?
vo
m
ag
So why do you appear weightless in orbit?
m
ag
v (t )
So why do you appear weightless in orbit?
m
So why do you appear weightless in orbit?
m
So why do you appear weightless in orbit?
•Gravity still exerts a centripetal force on your body!
•However, this force acts upon each and every atom in your
body, i.e. the centripetal force is distributed evenly over
your entire body.
•There is no normal force, as was the case in the roller
coaster. There, the centripetal force was concentrated at
the part of your body pushing against the roller coaster.
•It is the normal force that gives us the sensation of
weight. In orbit, we experience no normal force, so we feel
weightless.
•We are never massless!
Looping the loop
2
v
a
r
N
v (t )
Fg
v (t )
2
v
a
r
Fg , N