9781118230725.pdf

130 CHAPTER 6 FORCE AND MOTION—II

force, not the full force. From Sample Problem 5.04 (see Fig.
5-15i), we write that balance as

FNmgcosu.

In spite of these changes, we still want to write Newton’s
second law (Fnet,xmax) for the motion along the (now
tilted)xaxis. We have

fk mgsinumax,
mkFN mgsinumax,
and mkmgcosu mgsinumax.

Solving for the acceleration and substituting the given data

now give us

axmkgcosugsinu

(0.10)(9.8 m/s^2 ) cos 5.00(9.8 m/s^2 ) sin 5.00

0.122 m/s^2. (6-13)

Substituting this result into Eq. 6-11 gives us the stopping

distance hown the hill:

xx 0 409 m 400 m, (Answer)

which is about mi! Such icy hills separate people who can

do this calculation (and thus know to stay home) from peo-

ple who cannot (and thus end up in web videos).

1

4



Additional examples, video, and practice available at WileyPLUS

6-2THE DRAG FORCE AND TERMINAL SPEED

After reading this module, you should be able to...
6.04Apply the relationship between the drag force on an
object moving through air and the speed of the object.

6.05Determine the terminal speed of an object falling

through air.

●When there is relative motion between air (or some other
fluid) and a body, the body experiences a drag force that
opposes the relative motion and points in the direction in
which the fluid flows relative to the body. The magnitude of
is related to the relative speed vby an experimentally deter-
mined drag coefficient Caccording to

,

whereris the fluid density (mass per unit volume) and A
is the effective cross-sectional area of the body (the area

D^12 C Av^2

D

:

D

: of a cross section taken perpendicular to the relative

velocity ).

●When a blunt object has fallen far enough through air, the

magnitudes of the drag force and the gravitational force

on the body become equal. The body then falls at a constant

terminal speed vtgiven by

vtA.

2 Fg

CrA

Fg

:

D

:

:v

Learning Objectives

Key Ideas

The Drag Force and Terminal Speed

Afluidis anything that can flow—generally either a gas or a liquid. 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

adrag force that opposes the relative motion and points in the direction in

which the fluid flows relative to the body.

Here we examine only cases in which air is the fluid, 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 upinto swirls) behind the

body. In such cases, the magnitude of the drag force is related to the relative

speedvby an experimentally determined drag coefficientCaccording to

D^12 C Av^2 , (6-14)

D

:

D

: