billing (cab4763) – hw 11 – opyrchal – (11109)
1
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printout
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have
10
questions.
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before answering.
001 (part 1 of 2) 10.0 points
A string is wound around a uniform disc of
radius 0
.
55 m and mass 2 kg
.
The disc is
released from rest with the string vertical and
its top end tied to a fixed support.
The acceleration of gravity is 9
.
8 m
/
s
2
.
h
0
.
55 m
2 kg
ω
As the disc descends, calculate the tension
in the string.
Correct answer: 6
.
53333 N.
Explanation:
Let :
R
= 0
.
55 m
,
M
= 2 kg
,
and
g
= 9
.
8 m
/
s
2
.
Basic Concepts
summationdisplay
vector
F
=
mvectora
summationdisplay
vector
τ
=
I vectorα
Δ
U
+ Δ
K
rot
+ Δ
K
trans
= 0
Solution
summationdisplay
F
=
T
−
M g
=
−
M a
and
(1)
summationdisplay
τ
=
T R
=
I α
=
1
2
M R
2
parenleftBig
a
R
parenrightBig
.
(2)
Solving for
a
in (2),
a
=
2
T
M
.
(3)
Using
a
from Eq. (3) and solving for
T
in (1),
T
=
M
(
g
−
a
)
=
M
parenleftbigg
g
−
2
T
M
parenrightbigg
=
M g
−
2
T
3
T
=
M g
T
=
M g
3
(4)
=
(2 kg) (9
.
8 m
/
s
2
)
3
= 6
.
53333 N
.
002 (part 2 of 2) 10.0 points
Calculate the speed of the center of mass
when, after starting from rest, the center of
mass has fallen 1
.
7 m.
Correct answer: 4
.
7131 m
/
s.
Explanation:
From conservation of mechanical energy we
have
Δ
U
+ Δ
K
rot
+ Δ
K
trans
= 0
1
2
parenleftbigg
1
2
M R
2
parenrightbigg
ω
2
+
1
2
M v
2
=
M g
Δ
h .
When there is no slipping
v
=
R ω ,
so
1
4
R
2
ω
2
+
1
2
v
2
=
g
Δ
h
1
4
v
2
+
1
2
v
2
=
g
Δ
h
3
4
v
2
=
g
Δ
h
v
=
radicalbigg
4
g
Δ
h
3
=
radicalbigg
4 (9
.
8 m
/
s
2
) (1
.
7 m)
3
=
4
.
7131 m
/
s
.
003
10.0 points
Consider a wheel (solid disk) of radius 1
.
23 m,
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billing (cab4763) – hw 11 – opyrchal – (11109)
2
mass 13 kg and moment of inertia
1
2
M R
2
.
The wheel rolls without slipping in a straight
line in an uphill direction 33
◦
above the hor
izontal.
The wheel starts at angular speed
21
.
2195 rad
/
s but the rotation slows down
as the wheel rolls uphill, and eventually the
wheel comes to a stop and rolls back downhill.
How far does the wheel roll in the uphill
direction before it stops? The acceleration of
gravity is 9
.
8 m
/
s
2
.
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 Spring '10
 gayen
 Physics, Angular Momentum, Mass, Moment Of Inertia, kg

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