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Chapter 6
159
Q6.17
From the proportionality of the drag force to the speed squared and from Newton’s second law, we
derive the equation that describes the motion of the skydiver:
m
dv
dt
mg
DA
v
y
y
=−
ρ
2
2
where
D
is the coefficient of drag of the parachutist, and
A
is the projected area of the parachutist’s
body. At terminal speed,
a
dv
dt
y
y
==
0 and
V
mg
T
2
12
F
H
G
I
K
J
.
When the parachute opens, the coefficient of drag
D
and the effective area
A
both increase, thus
reducing the speed of the skydiver.
Modern parachutes also add a third term, lift, to change the equation to
m
dv
dt
mg
v
LA
v
y
yx
−
ρρ
22
where
v
y
is the vertical velocity, and
v
x
is the horizontal velocity. The effect of lift is clearly seen in
the “paraplane,” an ultralight airplane made from a fan, a chair, and a parachute.
Q6.18
The larger drop has higher terminal speed. In the case of spheres, the text demonstrates that
terminal speed is proportional to the square root of radius. When moving with terminal speed, an
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics, Force

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