Morby, Grant – Homework 16 – Due: Mar 1 2006, noon – Inst: Drummond
1
This printout should have 11 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
The due time is Central
time.
001
(part 1 oF 1) 10 points
A 1 kg mass slides to the right on a surFace
having a coe±cient oF Friction 0
.
22 as shown
in the fgure. The mass has a speed oF 3 m
/
s
when contact is made with a spring that has
a spring constant 65 N
2
. The mass comes to
rest aFter the spring has been compressed a
distance
d
. The mass is then Forced toward
the leFt by the spring and continues to move
in that direction beyond the unstretched posi
tion. ²inally the mass comes to rest a distance
D
to the leFt oF the unstretched spring.
The acceleration oF gravity is 9
.
8 m
/
s
2
.
m
k
v
v
v
= 0
v
= 0
D
d
i
f
²ind the compressed distance
d
.
Correct answer: 0
.
34041 m.
Explanation:
The principle we are going to use to solve
this problem is that the change in the total
energy oF the system is equal to the work done
by the nonconservative Forces
W
nc
= Δ
K
+ Δ
U .
In our case, the nonconservative Force is the
Frictional Force. ThereFore
W
nc
=

f d
=

(2
.
156 N)
d,
where the Frictional Force is
f
=
μmg
= 0
.
22(1 kg)(9
.
8 m
/
s
2
)
= 2
.
156 N
.
The change in kinetic energy is
Δ
K
= 0

1
2
mv
2
i
=

1
2
(1 kg)(3 m
/
s)
2
=

4
.
5 J
,
and the change in potential energy is
Δ
U
=
1
2
k d
2
=
1
2
(65 N
2
)
d
2
= (32
.
5 N
/
m)
d
2
,
so
W
nc
= Δ
K
+ Δ
U

(2
.
156 N)
d
=

4
.
5 J + (32
.
5 N
/
m)
d
2
.
(32
.
5 N
/
m)
d
2
+ (2
.
156 N)
d
+ (

4
.
5 J) = 0
.
This is a quadratic equation, and since
b
2

4
ac
= (2
.
156 N)
2

4(32
.
5 N
/
m)(

4
.
5 J)
= 589
.
648 N
2
,
the positive solution is
d
=

(2
.
156 N) +
√
589
.
648 N
2
2(32
.
5 N
/
m)
= 0
.
34041 m
.
002
(part 1 oF 3) 10 points
A single conservative Force
F
(
x
) =
bx
+
a
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View Full DocumentMorby, Grant – Homework 16 – Due: Mar 1 2006, noon – Inst: Drummond
2
acts on a 5
.
14 kg particle, where
x
is in meters,
b
= 6
.
52 N
/
m and
a
= 3
.
13 N.
As the particle moves along the
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 Spring '09
 KLEINMAN
 Physics, Energy, Force, Kinetic Energy, Mass, Potential Energy, Work, Wnc

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