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Homework 5 help
1)
A bullet is shot through two cardboard disks attached a distance D apart to a shaft
turning with a rotational period T.
The speed of bullet is
2
D
V
T
π
θ
=
7.24.
Model:
Model the child on the merrygoround as a particle in nonuniform circular motion.
Visualize:
Solve:
(a)
The speed of the child is
v
0
=
r
ω
=
(2.5 m)(1.57 rad/s)
=
3.93 m/s.
(b)
The merrygoround slows from 1.57 rad/s to 0 in 20 s. Thus
2
0
10
1
1
(2.5 m)(1.57 rad/s)
0
–0.1965 m/s
20 s
t
t
ar
ta
rt
ωω
== +
⇒ =
−
=
−
=
During these 20 s, the wheel turns through angle
2
22
10 0
1
1
0.1965 m/s
0
(1.57 rad/s) (20 s)
(20 s)
15.7 rad
(
2
.
5
m
)
t
a
tt
r
θθ
=+
+
−
=
In terms of revolutions,
1
=
(15.7 rad)(1 rev/2
rad)
=
2.50 rev.
7.47.
Model:
Model a passenger as a particle rotating in a vertical circle.
Visualize:
Solve:
(a)
Netwon’s second law at the top is
2
T
rr
mv
Fnwm
a
r
=+= =
∑
2
T
mv
nm
g
r
=
⇒+
The speed is
( )
28
m
2
11.17 m/s
4.5 s
r
v
T
==
=
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2
2
2
11.17 m/s
55 kg
9.8 m/s
8 m
T
v
nm
g
r
⇒=
−=
−
=
319 N
That is, the ring pushes on the passenger with a force of 319 N at the top of the ride. Newton’s second law at the
bottom:
22
2
BB
2
2
11.17 m/s
55 kg
9.8 m/s
1397 N
8 m
rr
mv
mv
v
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 Spring '10
 ZHOU

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