APPM 2350
HOMEWORK 06
FALL 2010
Due Thursday, October 7, 2010 at the start of your recitation
1. You know the routine for the first problem.
2. If you have not finished problem 1, go back and finish it.
3. Suppose you have just washed your favorite 100% cotton turtleneck sweater and have placed it in the
dryer. At a particular time
t
0
, the neck of the sweater is 18 inches in circumference, while the height
of the neck is 3 inches. Sadly, you have forgotten that you are supposed to air dry the sweater. At
time
t
0
, the circumference of the neck is shrinking at a rate of 0.2 in/min, while the twisting and
tumbling action of the dryer is causing the neck to lengthen at a rate of 0.1 in/min.
How is the
volume of the space inside the neck changing at time
t
=
t
0
? Is the volume increasing or decreasing?
4. Suppose you have two particles with positions
x
1
(
t
) and
x
2
(
t
) and velocities ˙
x
1
(
t
) and ˙
x
2
(
t
). They
have total kinetic energy
T
=
m
1
2
( ˙
x
1
(
t
))
2
+
m
2
2
( ˙
x
2
(
t
))
2
,
(1)
where
m
j
denotes the mass of the
j
th
particle, which we assume is constant with respect to time. We
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 Fall '07
 ADAMNORRIS
 Energy, Kinetic Energy, Potential Energy, xj, xj dt, mj xj

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