Morby, Grant – Quiz 2 – Due: Mar 8 2006, 10:00 pm – Inst: Drummond
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The due time is Central
time.
001
(part 1 of 1) 10 points
A(n) 5
.
53 g bullet is fired into a(n) 1
.
59 kg
ballistic pendulum and becomes embedded in
it.
The acceleration of gravity is 9
.
8 m
/
s
2
.
If the pendulum rises a vertical distance
of 5
.
78 cm, calculate the initial speed of the
bullet.
Correct answer: 307
.
094 m
/
s.
Explanation:
Basic Concepts:
Applying conservation
of mechanical energy from just after the colli
sion until the end of the swing is reached, we
have
1
2
(
M
+
m
)
V
2
= (
M
+
m
)
g h
where M is the mass of the pendulum, m
the mass of the bullet, h the vertical height
through which the pendulum swings, and V
is the velocity of the (pendulum plus bullet)
immediately after the collision. The equation
above reduces to
V
=
p
2
g h .
(1)
Now apply conservation of momentum from
just before to just after the collision. We have
m v
0
= (
M
+
m
)
V ,
(2)
where
v
0
is the velocity of the bullet just prior
to collision. Thus,
m v
0
= (
M
+
m
)
p
2
g h ,
so
v
0
=
(
M
+
m
)
m
p
2
g h
=
(1
.
59 kg) + (0
.
00553 kg)
(0
.
00553 kg)
×
q
2 (9
.
8 m
/
s
2
) (0
.
0578 m)
=
307
.
094 m
/
s
.
002
(part 1 of 4) 10 points
The following figure shows a Ferris wheel that
rotates 3 times each minute and has a diame
ter of 17 m.
The acceleration of gravity is 9
.
8 m
/
s
2
.
What is the centripetal acceleration of a
rider?
Correct answer: 0
.
838916 m
/
s
2
.
Explanation:
The period of the Ferris wheel is
T
=
(60 s)
(3)
= 20 s
.
The speed of the wheel is
v
=
2
π r
T
=
2
π
(8
.
5 m)
20 s
= 2
.
67035 m
/
s
,
so the centripetal acceleration is
a
=
v
2
r
=
(2
.
67035 m
/
s)
2
(8
.
5 m)
=
0
.
838916 m
/
s
2
.
003
(part 2 of 4) 10 points
What force does the seat exert on a 51 kg
rider at the lowest point of the ride?
Correct answer: 542
.
585 N.
Explanation:
The force exerted by the seat balances the
gravity and provides the centripetal force, so
F
l
=
m
[
g
+
a
]
= (51 kg) (9
.
8 m
/
s
2
+ 0
.
838916 m
/
s
2
)
=
542
.
585 N
.
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Morby, Grant – Quiz 2 – Due: Mar 8 2006, 10:00 pm – Inst: Drummond
2
004
(part 3 of 4) 10 points
What force does the seat exert on a 51 kg
rider at the highest point of the ride?
Correct answer: 457
.
015 N.
Explanation:
The gravity is partly balanced by the force
exerted by the seat and this resultant provides
the centripetal force, so
F
l
=
m
[
g

a
]
= (51 kg) [(9
.
8 m
/
s
2
)

(0
.
838916 m
/
s
2
)]
=
457
.
015 N
.
005
(part 4 of 4) 10 points
What force (magnitude) does the seat exert
on a rider when the rider is halfway between
top and bottom?
Correct answer: 501
.
628 N.
Explanation:
In this case, the force exerted by the seat
has two components: the vertical one balanc
ing the gravity and the horizontal one provid
ing the centripetal force. Thus we have
F
m
=
m
p
g
2
+
a
2
= (51 kg)
q
(9
.
8 m
/
s
2
)
2
+ (0
.
838916 m
/
s
2
)
2
=
501
.
628 N
.
006
(part 1 of 1) 10 points
Consider a frictionless roller coaster such as
depicted below.
The acceleration of gravity is 9
.
8 m
/
s
2
.
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 Spring '09
 KLEINMAN
 Physics, Force, Friction, Correct Answer, kg

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