louey (cal2859) – Ch3-HW4 – florin – (56930)
1
This
print-out
should
have
28
questions.
Multiple-choice questions may continue on
the next column or page – find all choices
before answering.
001
10.0points
A bullet of mass
m
traveling horizontally at
a very high speed
v
embeds itself in a block
of mass
M
that is sitting at rest on a nearly
frictionless surface.
What is the final speed
v
f
of the block-bullet system after the bullet
embeds itself in the block?
1.
v
f
=
parenleftbigg
m
2
m
+
M
parenrightbigg
v
2.
v
f
=
parenleftbigg
M
m
parenrightbigg
v
3.
v
f
=
parenleftBig
m
M
parenrightBig
v
4.
v
f
=
parenleftbigg
M
m
+
M
parenrightbigg
v
5.
v
f
=
parenleftbigg
m
m
+
M
parenrightbigg
v
correct
Explanation:
Assume the bullet travels in the +
x
direc-
tion, so that
v
bullet
,
i
=
(
v,
0
,
0
)
m
/
s
.
Define the system to be the bullet and the
block.
Assume that the net external force
on the system is zero. Apply the momentum
principle with the initial momentum being
before the collision and the final momentum
being after the collision.
vectorp
bullet
,
i
+
vectorp
block
,
i
=
vectorp
bullet
,
f
+
vectorp
block
,
f
mvectorv
bullet
,
i
+ 0 =
mvectorv
f
+
Mvectorv
f
mvectorv
bullet
,
i
+ 0 = (
m
+
M
)
vectorv
f
⇒
vectorv
f
=
parenleftbigg
m
m
+
M
parenrightbigg
vectorv
bullet
,
i
⇒
vextendsingle
vextendsingle
vectorv
f
vextendsingle
vextendsingle
=
parenleftbigg
m
m
+
M
parenrightbigg
vextendsingle
vextendsingle
vectorv
bullet
,
i
vextendsingle
vextendsingle
=
parenleftbigg
m
m
+
M
parenrightbigg
v.
002(part1of2)10.0points
A car of mass 2800 kg collides with a truck of
mass 4300 kg, and just after the collision the
car and truck slide along, stuck together. The
car’s velocity just before the collision was
vectorv
car
,
i
=
(
40
,
0
,
0
)
m
/
s
,
and the truck’s velocity just before the colli-
sion was
vectorv
truck
,
i
=
(−
13
,
0
,
31
)
m
/
s
.
The velocity of the stuck together car and
truck just after the collision will be of the form
vectorv
sys
,
f
=
(
v
sys
,
f
,x
,
0
,v
sys
,
f
,z
)
m
/
s
.
Find the
x
component,
v
sys
,
f
,x
.
Correct answer: 7
.
90141 m
/
s.
Explanation:
We can use the momentum principle.
We
know that the momenta before and after the
collision will be given by
vectorp
sys
,
i
=
m
car
vectorv
car
,
i
+
m
truck
vectorv
truck
,
i
vectorp
sys
,
f
= (
m
car
+
m
truck
)
vectorv
sys
,
f
The
momentum
principle
predicts
that
vectorp
sys
,
i
=
vectorp
sys
,
f
, so we can use this to solve
for
vectorv
sys
,
f
.
vectorp
sys
,
f
= (
m
car
+
m
truck
)
vectorv
sys
,
f
⇒
vectorv
sys
,
f
=
vectorp
sys
,
i
m
car
+
m
truck
=
m
car
vectorv
car
,
i
+
m
truck
vectorv
truck
,
i
m
car
+
m
truck
=
(
7
.
90141
,
0
,
18
.
7746
)
m
/
s
.
003(part2of2)10.0points
Find the
z
component,
v
sys
,
f
,z
.
Correct answer: 18
.
7746 m
/
s.
Explanation:
See the explanation for part 1.