Morby, Grant – Homework 17 – Due: Mar 3 2006, noon – Inst: Drummond
1
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printout
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8
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before answering.
The due time is Central
time.
001
(part 1 of 2) 10 points
A bead slides without friction around a loop
theloop. The bead is released from a height
h
from the bottom of the looptheloop which
has a radius
r
.
h
r
Which of the following diagrams best rep
resents the kinetic energy of the bead versus
time?
1.
t
K
2.
t
K
3.
t
K
4.
t
K
5.
t
K
6.
t
K
correct
Explanation:
The bead reaches a maximum kinetic en
ergy each time it reaches the bottom of the
loop. Consequently, the only curve which fits
this criteria is one which has two equally high
maxima.
Also, the kinetic energy must be
zero at
t
= 0.
002
(part 2 of 2) 10 points
Which of the following could represent the
gravitational potential energy of the bead ver
sus time?
1.
t
U
correct
2.
t
U
3.
t
U
4.
t
U
5.
t
U
6.
t
U
Explanation:
Since the kinetic energy plus potential en
ergy is constant, this curve must be the inverse
of the curve in Part 1.
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Morby, Grant – Homework 17 – Due: Mar 3 2006, noon – Inst: Drummond
2
003
(part 1 of 1) 10 points
A particle of mass 9
.
03 kg is attached to two
identical springs on a horizontal frictionless
tabletop as shown.
The springs have spring constant 38
.
9 N
/
m
and equilibrium length
L
= 1
.
74 m.
L
L
x
x
k
k
m
Top View
If the mass is pulled 0
.
665 m to the right
and then released, what is its speed when it
reaches the equilibrium point
x
= 0?
Correct answer: 0
.
360294 m
/
s.
Explanation:
First calculate the potential energy of the
springs. When the mass moves a distance
x
,
the length of each spring changes from
L
to
p
L
2
+
x
2
, so each exerts a force
F
=
k
‡
p
L
2
+
x
2

L
·
toward its fixed end. The
y
components can
cel out and the
x
components add to
F
x
=
2
F x
√
L
2
+
x
2
=

2
k x
+
2
k L x
√
L
2
+
x
2
.
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 Spring '09
 KLEINMAN
 Physics, Conservation Of Energy, Energy, Force, Friction, Potential Energy, Work

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