morris (gmm643) – HW 7 – Coker – (56625)
1
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printout
should
have
18
questions.
Multiplechoice questions may continue on
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before answering.
This assignment covers the general defini
tion of potential energy for a conservative
force, general types of conservation of energy
examples (with 2 or more forces doing work),
potential energy diagrams, and the concept of
binding energy.
001
10.0 points
A
synthetic
rubber
band
resists
being
stretched a distance
x
from equilibrium with
a force
vector
F
b
(
x
) =
−
ˆ
ı b x
2
,
where
b
is a constant.
What is the potential energy
U
b
(
x
) associ
ated with this elastic band?
1.
−
b x
3
3
2.
−
2
b x
3.
+
b x
2
2
4.
+
b x
3
3
correct
5.
−
b x
2
2
6.
+2
b x
7.
zero
Explanation:
By definition
Δ
U
=
W .
The work we would have to do
against
the
force
vector
F
b
to stretch the band is
integraldisplay
b x
2
dx
=
b x
3
3
.
002
10.0 points
In a certain region of space, a particle expe
riences a potential energy
U
(
x
) =
A
x
2
+
B
,
where
A
and
B
are constants.
What force
F
gives rise to this potential
energy?
1.
−
ˆ
i
parenleftbigg
A
x
2
parenrightbigg
2.
ˆ
i
parenleftbigg
A
x
2
parenrightbigg
3.
ˆ
i
parenleftbigg
A
x
+
B x
parenrightbigg
4.
There is no force, since the slope of the
line is the constant
B
A
.
5.
−
ˆ
i
parenleftbigg
A
x
+
B x
parenrightbigg
6.
ˆ
i
parenleftbigg
A
x
parenrightbigg
7.
ˆ
i
parenleftbigg
2
A
x
3
parenrightbigg
correct
8.
−
ˆ
i
parenleftbigg
A
x
parenrightbigg
9.
−
ˆ
i
parenleftbigg
2
A
x
3
parenrightbigg
Explanation:
The force is
F
=
−
d U
dx
ˆ
i
=
ˆ
i
parenleftbigg
2
A
x
3
parenrightbigg
.
003
10.0 points
A block of mass
m
1
is attached to a horizon
tal spring of force constant
k
and to a spring of
negligible mass. The string runs over a mass
less, frictionless pulley to a hanging block of
mass
m
2
. Initially, the entire system is at rest
and the spring is unstretched.
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morris (gmm643) – HW 7 – Coker – (56625)
2
m
1
m
2
k
m
1
m
2
ℓ
ℓ
If mass
m
1
slides on a horizontal frictionless
surface, what is the speed
v
of the mass
m
2
when it has fallen a distance
ℓ
downward from
its rest position?
1.
Zero, since the spring will stop it from
falling.
2.
radicalBigg
2
m
2
g ℓ
−
k ℓ
2
m
1
+
m
2
correct
3.
radicaltp
radicalvertex
radicalvertex
radicalbt
m
2
g ℓ
−
1
2
k ℓ
2
m
1
+
m
2
4.
radicalBigg
2
m
2
g ℓ
−
k ℓ
2
m
1
−
m
2
5.
radicaltp
radicalvertex
radicalvertex
radicalbt
m
2
g ℓ
−
1
2
k ℓ
2
2 (
m
1
+
m
2
)
6.
radicalBigg
2
m
2
g ℓ
+
k ℓ
2
m
1
−
m
2
7.
radicalBigg
2
m
2
g ℓ
+
k ℓ
2
m
1
+
m
2
Explanation:
Let the gravitational potential energy have
a value of 0 at the end state when the system
has moved a distance
ℓ
.
Applying conserva
tion of energy,
E
0
=
E
f
U
0
+
K
0
=
U
f
+
K
1
,f
+
K
2
,f
m
2
g ℓ
+ 0 =
1
2
k ℓ
2
+
1
2
m
1
v
2
+
1
2
m
2
v
2
2
m
2
g ℓ
=
k ℓ
2
+ (
m
1
+
m
2
)
v
2
2
m
2
g ℓ
−
k ℓ
2
= (
m
1
+
m
2
)
v
2
v
2
=
2
m
2
g ℓ
−
k ℓ
2
m
1
+
m
2
v
=
radicalBigg
2
m
2
g ℓ
−
k ℓ
2
m
1
+
m
2
.
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 Spring '10
 COKER
 Energy, Potential Energy, Coker

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