Chapt. 8 Potential Energy and Mechanical Energy 87
HINT:
A diagram might help.
b) Find a formula for the force the groove exerts on the boll weevil as a function of
θ
. Take
the radial inward direction as positive. Show all
θ
dependences
EXPLICITLY
. Simplify
the formula as much as reasonably possible. The force could be called the groovy force.
c) Find a 1st order di±erential equation for angular position
θ
with all
θ
’s and
θ
derivatives
shown
EXPLICITLY
. Don’t try to solve it,
JUST
²nd it. Is the di±erential equation
linear? Explain why it is linear or not.
HINT:
Start from the part (a) answer.
d) An
APPROXIMATE SOLUTION
for the di±erential equation found in the part (c)
answer is
t
=
1
r
g/R
ln
b
θ
R
(
g/R
)
ω
2
0
+
R
(
g/R
)
ω
2
0
θ
2
+ 1
B
,
where
θ
is in
RADIANS
and
ω
0
=
v
0
/R
.
Note it turned out to be easier to get
the slidedown time
t
as a function of
θ
than vice versa. Given that
R
= 2
.
0 m and
ω
0
=
v
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 Fall '06
 Buchler
 Physics, Energy, Force, Potential Energy, Normal Force, 10 m, 2.0 m, 1.0 rad

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