Adams, Russell – Homework 7 – Due: Oct 27 2006, 11:00 pm – Inst: Opyrchal, H
1
This
printout
should
have
10
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
001
(part 1 of 1) 10 points
A block of mass
m
slides on a horizontal
frictionless table with an initial speed
v
0
.
It
then compresses a spring of force constant
k
and is brought to rest.
The acceleration of gravity is 9
.
8 m
/
s
2
.
v
m
k
m
μ
= 0
How much is the spring compressed
x
from
its natural length?
1.
x
=
v
0
m g
k
2.
x
=
v
0
m
k g
3.
x
=
v
2
0
2
m
4.
x
=
v
0
k
g m
5.
x
=
v
0
r
m g
k
6.
x
=
v
0
r
m
k
correct
7.
x
=
v
2
0
2
g
8.
x
=
v
0
s
k
m g
9.
x
=
v
0
r
k
m
10.
x
=
v
0
m k
g
Explanation:
Total energy is conserved (no friction). The
spring is compressed by a distance
x
from its
natural length, so
1
2
m v
2
0
=
E
i
=
E
f
=
1
2
k x
2
,
or
x
2
=
m
k
v
2
0
,
therefore
x
=
v
0
r
m
k
.
Anyone who checks to see if the units are
correct should get this problem correct.
keywords:
002
(part 1 of 2) 10 points
A bead slides without friction around a loop
theloop. The bead is released from a height
11
.
7 m from the bottom of the looptheloop
which has a radius 4 m.
The acceleration of gravity is 9
.
8 m
/
s
2
.
11
.
7 m
4 m
A
What is its speed at point
A
?
Correct answer: 8
.
51587 m
/
s.
Explanation:
Let :
m
= 4 g
,
R
= 4 m
,
and
h
= 11
.
7 m
.
From conservation of energy, we have
K
i
+
U
i
=
K
f
+
U
f
0 +
m g h
=
m v
2
2
+
m g
(2
R
)
v
2
= 2
g
(
h

2
R
)
.
Therefore
v
=
p
2
g
(
h

2
R
)
=
r
2 (9
.
8 m
/
s
2
)
h
11
.
7 m

2 (4 m)
i
= 8
.
51587 m
/
s
.
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Adams, Russell – Homework 7 – Due: Oct 27 2006, 11:00 pm – Inst: Opyrchal, H
2
003
(part 2 of 2) 10 points
How large is the normal force on it at point
A
if its mass is 4 g?
Correct answer: 0
.
03332 N.
Explanation:
The centripetal force is equal to the normal
force due to the track and gravity,
F
c
=
N
+
m g
, so
N
=
m
v
2
R
¶

m g
= (4 g)(0
.
001 kg
/
g)
×
•
(8
.
51587 m
/
s)
2
4 m

9
.
8 m
/
s
2
‚
= 0
.
03332 N
.
keywords:
004
(part 1 of 1) 10 points
A block starts at rest and slides down a fric
tionless track except for a small rough area on
a horizontal section of the track (as shown in
the figure below).
It leaves the track horizontally, flies through
the air, and subsequently strikes the ground.
The acceleration of gravity is 9
.
81 m
/
s
2
.
μ
=0
.
3
1
.
4 m
462 g
h
2 m
4
.
08 m
9
.
81 m
/
s
2
v
At what height
h
above the ground is the
block released?
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 Spring '08
 moro
 Physics, Energy, Force, Potential Energy, Work, Correct Answer

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