PHYS 2210
UNIVERSITY OF COLORADO AT BOULDER
CLASSICAL MECHANICS AND MATH METHODS, SPRING, 2011
Homework 4
(Due Date: Start of class on Thurs. Feb 3 )
NOTE:
Be sure to show your work and explain what you are doing. (Correct answers, for which we cannot
follow the work, are worth no credit).
1.
Consider a sports car which is braking hard. There are two significant resistive forces acting on it, a quadratic
(
cv
2
) air drag, and a constant (
μmg
) frictional force. When you write Newton’s law, if you are interested in
finding v(x) (rather than v(t)), there is a nice trick, known as the “v dv/dx rule”, which uses the chain rule
to rewrite ˙
v
=
dv
dt
=
dv
dx
dx
dt
=
v
dv
dx
.
(a) Write down the equation of motion for ˙
v
=
f
(
v
) and use the “v dv/dx” rule to solve the equation of
motion directly for v(x), and show that the distance the car needs for a full stop is:
x
max
=
A
2
2
μg
ln
A
2
+
v
2
0
A
2
(1)
here
μ
is the friction coe
ﬃ
cient. What is the constant
A
in this case ( in terms of given parameters in
the di
ff
erential equation?)
(b) The SSC Ultimate Aero TT, one of the world’s fastest production cars (at a cool $600,000+), has a
maximum speed of 412 Km per hour. The engine provides maximum forward force of 11260 N on the
1200 kg car. For this car,
c
=0.86 kg/m. On a race track, the car exits a turn with a speed of
v
0
= 300
km/hr.
As soon as the driver enters the straight track after the turn, she realizes there is another
car blocking the track 2 km away.
The driver slams on the brakes.
Assuming a friction coe
ﬃ
cient
μ
= 0
.
7, use your above result to compute the distance required for the Aero TT to stop. Compare
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 Spring '11
 STEVEPOLLOCK
 mechanics, Force, Work, The Land, Taylor series expansion, air drag, SSC Aero, quadratic drag, Aero TT

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