Busto, Anthony – Homework 10 – Due: Nov 17 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 cylindrical pulley with a mass of
M
= 4
.
7 kg
and a radius of
r
= 0
.
562 m is used to lower
a bucket with a mass of
m
= 2 kg into a well.
The bucket starts from rest and falls for 2
.
7 s.
The acceleration of gravity is 9
.
8 m
/
s
2
.
r
M
m
What is the linear acceleration of the falling
bucket?
Correct answer: 4
.
50575 m
/
s
2
.
Explanation:
The
disk
has
moment
of
inertia,
I
=
1
2
M r
2
.
Let
T
be the tension in the cord
and let
α
be the angular acceleration of the
wheel. Newton’s equation for the disk is
T r
=
I α .
(1)
Newton’s equation for the mass
m
is
m g

T
=
m a .
(2)
The linear acceleration
a
of the mass is related
to the angular acceleration
α
of the wheel by
the formula,
a
=
α r
. From Eq. (2) the tension
is
T
=
m
(
g

a
).
Putting this into Eq. (1)
and solving for
a
gives
(
m g

m a
)
r
=
1
2
M r
2
‡
a
r
·
2
m g

2
m a
=
M a
2
m g
= (
M
+ 2
m
)
a
a
=
2
m g
M
+ 2
m
.
Or
a
=
g
1
1 +
M
2
m
=
(
9
.
8 m
/
s
2
)
1
1 +
(4
.
7 kg)
2 (2 kg)
= 4
.
50575 m
/
s
2
.
keywords:
002
(part 1 of 1) 10 points
Given:
g
= 9
.
8 m
/
s
2
.
Consider a thin rod of mass
m
= 1
.
7 kg,
length
‘
= 5
.
8 m and uniform density.
The
rod is pivoted at one end on a frictionless
horizontal pin.
5
.
8 m
1
.
7 kg
O
63
◦
The rod is initially held in horizontal po
sition but eventually allowed to swing down.
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 Spring '08
 moro
 Physics, Force, Work, Angular Acceleration, Correct Answer, kg, Busto

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