fryer (vdf96) – Conservation of Momentum – graves – (6)
1
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17
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before answering.
001(part1of3)10.0points
Assume:
The bullet penetrates into the block
and stops due to its friction with the block.
The compound system of the block plus the
bullet rises to a height of 18 cm along a circu
lar arc with a 32 cm radius.
Assume:
The entire track is frictionless.
A bullet with a
m
1
= 30 g mass is fired
horizontally into a block of wood with
m
2
=
4
.
78 kg mass.
The acceleration of gravity is 9
.
8 m
/
s
2
.
32 cm
4
.
78 kg
30 g
v
bullet
18 cm
Calculate the total energy of the composite
system at any time after the collision.
Correct answer: 8
.
48484 J.
Explanation:
Let :
r
= 32 cm = 0
.
32 m
,
h
= 18 cm = 0
.
18 m
,
m
block
= 4
.
78 kg
,
and
m
bullet
= 30 g = 0
.
03 kg
.
The mechanical energy is conserved after
collision. Choose the position when the sys
tem stops at height
h
, where the kinetic en
ergy is 0 and the potential energy is given
by
(
m
bullet
+
m
block
)
g h
= 8
.
48484 J
,
which is the total energy after collision.
002(part2of3)10.0points
Taking the same parameter values as those in
Part 1, determine the initial velocity of the
bullet.
Correct answer: 301
.
154 m
/
s.
Explanation:
During the rising process the total energy
is conserved
E
i
=
1
2
(
m
bullet
+
m
block
)
v
2
f
and
E
f
= (
m
bullet
+
m
block
)
g h ,
so
v
f
=
radicalbig
2
g h
=
radicalBig
2 (9
.
8 m
/
s
2
) (0
.
18 m)
= 1
.
8783 m
/
s
.
The linear momentum is conserved in a colli
sion.
p
i
=
m
bullet
v
i
p
f
= (
m
bullet
+
m
block
)
v
f
.
Therefore
v
i
=
m
bullet
+
m
block
m
bullet
v
f
=
(0
.
03 kg) + (4
.
78 kg)
(0
.
03 kg)
×
(1
.
8783 m
/
s)
= 301
.
154 m
/
s
.
003(part3of3)10.0points
Denote
v
bullet
to be the initial velocity, find
the momentum of the compound system im
mediately after the collision.
1.
p
f
=
m
block
v
bullet
2.
p
f
=
√
m
bullet
+
m
block
v
bullet
3.
p
f
= (
m
bullet
+
m
block
)
radicalbig
g h
4.
p
f
=
√
m
bullet
+
m
block
g h
5.
p
f
=
m
block
radicalbig
g h
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fryer(vdf96)–ConservationofMomentum–graves–(6)
2
6.
p
f
=
1
2
(
m
bullet
+
m
block
)
v
bullet
7.
p
f
=
1
2
(
m
bullet
+
m
block
)
radicalbig
g h
8.
p
f
=
m
bullet
radicalbig
g h
9.
p
f
=
m
bullet
v
bullet
correct
10.
p
f
= (
m
bullet
+
m
block
)
v
bullet
Explanation:
As in part 2, due to conservation of linear
momentum,
p
f
=
p
i
=
m
bullet
v
bullet
.
004(part1of2)10.0points
A student performs a ballistic pendulum
experiment using an apparatus similar to that
shown in the figure.
Initially the bullet is fired at the block while
the block is at rest (at its lowest swing point).
After the bullet hits the block, the block rises
to its highest position, see dashed block in the
figure, and continues swinging back and forth.
The following data is obtained:
the maximum height the pendulum rises is
3
.
8 cm,
the mass of the bullet is 88 g, and
the mass of the pendulum bob is 901 kg.
The acceleration of gravity is 9
.
8 m
/
s
2
.
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 Fall '10
 Graves
 Physics, Energy, Kinetic Energy, Mass, Momentum, Correct Answer, fryer

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