74
Chapt. 6
Newton’s Laws and Dynamics II
c) The second law with the forces written explicitly is a differential equation for velocity as
function of variable time.
A differential equation being an equation for a function that
contains derivatives of various orders of the function. To solve a differential equation is to
find the function as an explicit function of the variable.
Many, many physical problems
come down to solving differential equations. In this case, verify that
v
=
v
0
e
−
Ct
+
F
loco
Cm
(1
−
e
−
Ct
)
is the explicit solution of the differential equation:
v
0
is an initial velocity at time zero.
What is the differential equation and solution if
F
loco
= 0?
006 qfull 00740 3 3 0 tough math: quadratic drag force
12. The quadratic drag force magnitude on a body is
F
drag
=
bv
2
=
1
2
CρAv
2
,
where
C
is the dimensionless drag coefficient (which is typically in the range 0.4 to 1 [HRW104]
and is set by all kinds of things like shape and texture of the body),
ρ
is fluid density,
A
is the
area of body perpendicular to the flow (i.e., the cross sectional area), and
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 Fall '06
 Buchler
 Physics, Force, quadratic drag force, Floco

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