7.9
Main Rotor:
(
)
2
rad
rev
1 min
3.80 m
450
min
1 rev
60 s
v
r
π
ω
⎛
⎞
⎛
⎞
⎛
⎞
=
⎟
⎠
=
=
⎜
⎟
⎜
⎜
⎟
⎝
⎠
⎝
⎝
⎠
179 m s
m
= 179
=
s
343 m s
sound
v
v
⎛
⎞
⎛
⎞
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
0.522
sound
v
Tail Rotor:
(
)
2
rad
rev
1 min
0.510 m
4138
min
1 rev
60 s
v
r
π
ω
⎛
⎞
⎛
⎞
⎛
⎞
=
⎟
⎠
=
=
⎜
⎟
⎜
⎜
⎟
⎝
⎠
⎝
⎝
⎠
221 m s
m
= 221
=
s
343 m s
sound
v
v
⎛
⎞
⎛
⎞
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
0.644
sound
v
7.21
Friction must supply the needed centripetal force. Hence, it is necessary that
(
)
c
s
max
F
f
≤
, or
(
)
2
t
s
v
m
m
r
µ
≤
g
and the maximum safe speed is
(
)
(
)(
)
(
)
2
0.70
20 m
9.80 m s
t
s
max
v
r g
µ
=
=
=
12 m s
.
7.23
(a)
(
)
(
)
2
2
2.00 m
3.00 rad s
c
a
r
ω
=
=
=
2
18.0 m s
(b)
(
)
(
)
2
50.0 kg
18.0 m s
c
c
F
m a
=
=
=
900 N
(c)
We know the centripetal acceleration is produced by the force of friction. Therefore,
the needed static friction force is
900 N
s
f
=
. Also, the normal force is
. Thus, the minimum coefficient of friction required is
490 N
n
mg
=
=
(
)
900 N
=
490 N
s
max
s
f
n
µ
=
=
1.84 .
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 Fall '08
 VANDENBERG
 Physics, Force, Friction, µs

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