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06__Chapter_6__Force_and_Motion_2_Friction_Drag_Circular_Motion.pdf
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06  Chapter 6  Force and Motion 2 Friction Drag ...
06__Chapter_6__Force_and_Motion_2_Friction_Drag_Circular_Motion.pdfChapter 6 Force and MotionII (Friction,
06  Chapter 6  Force and Motion 2...
06__Chapter_6__Force_and_Motion_2_Friction_Drag_Circular_Motion.pdfChapter 6 Force and MotionII (Friction,
Page 6
Sample Problem
Assume that the constant acceleration
a was due only to a
kinetic frictional
force on the car from the road, directed
opposite the direction of the car’s motion. This results in:
where
m is the car’s mass. The minus sign indicates the
direction
of the kinetic frictional force.
Calculations:
The frictional force has the magnitude
f
k
=
μ
k
F
N
,
where F
N
is the magnitude of the normal
force on the car
from the road. Because the car is not accelerating vertically,
F
N
=
mg.
Thus,
f
k
=μ
k
F
N
= μ
k
mg
a =
−
f
k
/m =
−
μ
k
mg/m =
−
μ
k
g,
where the minus sign indicates that the acceleration is in
the negative direction. Use
where (
x

x
0
) = 290 m, and the final speed is 0.
Solving for v
o
,
We assumed that
v = 0 at the far end of the skid marks.
Actually, the marks ended only because the Jaguar left
the road after 290 m. So
v
0
was at least 210 km/h.
Page 7
Sample Problem: Friction applied at an angle
Page 8
Sample Problem: Friction applied at an angle
Page 9
6.4 The Drag Force and Terminal Speed
When there is a relative velocity between a fluid and a body (either because the body
moves through the fluid or because the fluid moves past the body), the body
experiences a
drag force,
D
,
that opposes the relative motion and points in the direction
in which the fluid flows relative to the body.
Page 10
6.4 The Drag Force and Terminal Speed
For cases in which air is the fluid,
and the body is blunt (like a
baseball) rather than slender (like a
javelin), and the relative motion is
fast enough so that the air becomes
turbulent (breaks up into swirls)
behind the body,
where
ρ
is the air density (mass per
volume),
A
is the
effective cross
sectional
area of the body (the area
of a cross section taken
perpendicular to the velocity), and C
is the drag coefficient
.
When a blunt body falls from rest through air, the
drag force is directed upward; its magnitude
gradually increases from zero as the speed of the
body increases. From Newton’s second law along
y
axis
where m is the mass of the body. Eventually,
a
= 0,
and the body then falls at a constant speed, called
the
terminal speed
v
t
.
Page 11
Some typical values of terminal speed
6.4 The Drag Force and Terminal Speed