Morby, Grant – Homework 14 – Due: Feb 24 2006, noon – Inst: Drummond
1
This printout should have 13 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
be±ore answering.
The due time is Central
time.
001
(part 1 o± 2) 10 points
A 78
.
3 g bullet is fred ±rom a ri²e having a
barrel 0
.
783 m long. Assuming the origin is
placed where the bullet begins to move, the
±orce exerted on the bullet by the expanding
gas is
F
=
a
+
bx

cx
2
, where
a
= 15400 N,
b
= 5720 N
/
m,
c
= 36300 N
/
m
2
, with
x
in
meters.
Determine the work done by the gas on the
bullet as the bullet travels the length o± the
barrel.
Correct answer: 8003
.
05 J.
Explanation:
The work is ±ound by integrating the ±orce
over the distance.
W
=
Z
x
f
x
i
F
·
ds
For the ±orce in this problem we have,
W
=
Z
‘
0
(
a
+
bx

cx
2
)
dx
=
ax
+
1
2
bx
2

1
3
cx
3
f
f
f
‘
0
= (15400 N)(0
.
783 m)
+
1
2
(5720 N
/
m)(0
.
783 m)
2

1
3
(36300 N
/
m
2
)(0
.
783 m)
3
=
8003
.
05 J
.
002
(part 2 o± 2) 10 points
I± the barrel is 0
.
953 m long, how much work
is done?
Correct answer: 6800
.
85 J.
Explanation:
For the barrel o± length
‘
n
= 0
.
953 m m, we
need only change the limits o± integration,
W
=
Z
‘
n
0
(
a
+
bx

cx
2
)
dx
=
ax
+
1
2
bx
2

1
3
cx
3
f
f
f
‘
n
0
= (15400 N)(0
.
953 m)
+
1
2
(5720 N
/
m)(0
.
953 m)
2

1
3
(36300 N
/
m
2
)(0
.
953 m)
3
=
6800
.
85 J
.
003
(part 1 o± 1) 10 points
A block starts at rest and slides down a ±ric
tionless track except ±or a small rough area on
a horizontal section o± the track (as shown in
the fgure below).
Itleavesthetrackhorizontally, ²iesthrough
the air, and subsequently strikes the ground.
The acceleration o± gravity is 9
.
81 m
/
s
2
.
μ
=0
.
3
1
.
4 m
451 g
h
2
.
1m
3
.
53 m
9
81m
/
s
v
At what height
h
above the ground is the
block released?
Correct answer: 4
.
00344 m.
Explanation:
Let :
x
= 3
.
53 m
,
g
= 9
.
81 m
/
s
2
,
m
= 451 g
,
μ
= 0
.
3
,
‘
= 1
.
4 m
,
h
2
=

2
.
1 m
,
h
=
h
1

h
2
,
and
v
x
=
v .
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View Full DocumentMorby, Grant – Homework 14 – Due: Feb 24 2006, noon – Inst: Drummond
2
μ
‘
m
h
1
2
x
g
v
Basic Concepts:
Conservation of Me
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 Spring '09
 KLEINMAN
 Physics, Energy, Force, Kinetic Energy, Mass, Potential Energy, Work, Correct Answer

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