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Overton, Mays – Homework 15 – Due: Feb 28 2005, 4:00 am – Inst: Turner
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± 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
422 g
h
1
.
9m
4
.
16 m
9
81m
/
s
2
v
At what height
h
above the ground is the
block released?
Correct answer: 4
.
59705 m.
Explanation:
Let :
g
= 9
.
81 m
/
s
2
,
m
= 422 g
,
μ
= 0
.
3
,
‘
= 1
.
4 m
,
h
=
h
1
+
h
2
,
h
2
= 1
.
9 m
,
and
v
x
=
v .
μ
=0
.
3
‘
m
4
6m
x
g
6
.
68 m
/
s
Basic Concepts:
Conservation o± Me
chanical Energy
U
i
=
U
f
+
K
f
+
W .
(1)
since
v
i
= 0 m/s.
K
=
1
2
mv
2
(2)
U
g
=
mg h
(3)
W
=
μmg ‘.
(4)
Choosing the point where the block leaves the
track as the origin o± the coordinate system,
Δ
x
=
v
x
Δ
t
(5)
h
2
=
1
2
g
Δ
t
2
(6)
since
a
x
i
= 0 m/s
2
and
v
y
i
= 0 m/s.
Solution:
From energy conservation Eqs. 1,
2, 3, and 4, we have
1
2
mv
2
x
=
mg
(
h

h
2
)

μmg ‘
h
1
=
v
2
x
2
g
+
μ‘
(7)
h
2
=
1
2
g t
2
(6)
x
=
v
x
t.
(5)
Using Eq. 6 and substituting
t
=
x
v
x
±rom
Eq. 5, we have
h
2
=
1
2
g
µ
x
v
x
¶
2
,
so
v
2
x
=
g x
2
2
h
2
.
(8)
Using Eq. 6 and substituting
v
2
x
±rom Eq. 8,
we have
h
=
h
2
+
h
1
=
h
2
+
g x
2
2
h
2
2
g
+
μ‘
=
h
2
+
x
2
4
h
2
+
μ‘
(9)
= 1
.
9 m +
(4
.
16 m)
2
4(1
.
9 m)
+ (0
.
3)(1
.
4 m)
= 4
.
59705 m
.
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View Full DocumentOverton, Mays – Homework 15 – Due: Feb 28 2005, 4:00 am – Inst: Turner
2
002
(part 1 of 3) 10 points
A block is pushed against the spring with
spring constant
k
(located on the lefthand
side of the track) and compresses the spring a
distance 5
.
3 cm from its equilibrium position
(as shown in the ±gure below).
The block starts at rest, is accelerated by
the compressed spring, and slides across a
frictionless track except for a small rough area
on a horizontal section of the track (as shown
in the ±gure below).
Itleavesthetrackhorizontally, ²iesthrough
the air, and subsequently strikes the ground.
The acceleration of gravity is 9
.
81 m
/
s
2
.
μ
=0
.
2
1
.
3 m
512 g
2
.
3m
4
.
29 m
9
81m
/
s
v
k
5
.
3 cm
What is the spring constant
k
?
Correct answer: 8083
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 Spring '08
 Turner
 Physics, Work

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