roofner (bar784) – Homework 14 – Weathers – (17104)
1
This
printout
should
have
10
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0 points
An Atwood machine is constructed using a
hoop with spokes of negligible mass.
The
2
.
3 kg mass of the pulley is concentrated on
its rim, which is a distance 20
.
8 cm from the
axle. The mass on the right is 1
.
12 kg and on
the left is 1
.
53 kg.
2
.
5 m
2
.
3 kg
20
.
8 cm
ω
1
.
53 kg
1
.
12 kg
What is the magnitude of the linear acceler
ation of the hanging masses? The acceleration
of gravity is 9
.
8 m
/
s
2
.
Correct answer: 0
.
811717 m
/
s
2
.
Explanation:
Let :
M
= 2
.
3 kg
,
R
= 20
.
8 cm
,
m
1
= 1
.
12 kg
,
m
2
= 1
.
53 kg
,
h
= 2
.
5 m
,
and
v
=
ω R .
Consider the free body diagrams
1
.
53 kg
1
.
12 kg
T
2
T
1
m
2
g
m
1
g
a
a
The net acceleration
a
=
r α
is in the direc
tion of the heavier mass
m
2
.
For the mass
m
1
,
F
net
=
m
1
a
=
m
1
g

T
1
T
1
=
m
1
g

m
1
a
and for the mass
m
2
,
F
net
=
m
2
a
=
T
2

m
2
g
T
2
=
m
2
a
+
m
2
g .
The pulley’s mass is concentrated on the
rim, so
I
=
M r
2
,
and
τ
net
=
summationdisplay
τ
ccw

summationdisplay
τ
cw
=
I α
T
1
r

T
2
r
= (
m r
2
)
parenleftBig
a
r
parenrightBig
=
m r a
m a
=
T
1

T
2
ma
=
m
1
g

m
1
a

m
2
a

m
2
g
ma
+
m
1
a
+
m
2
a
=
m
1
g

m
2
g
a
=
(
m
1

m
2
)
g
m
+
m
1
+
m
2
=
(1
.
12 kg

1
.
53 kg) (9
.
8 m
/
s
2
)
2
.
3 kg + 1
.
12 kg + 1
.
53 kg
=
0
.
811717 m
/
s
2
.
002
(part 1 of 2) 10.0 points
A block of mass 3 kg and one of mass 7 kg are
connected by a massless string over a pulley
that is in the shape of a disk having a radius
of 0
.
25 m, and a mass of 9 kg. In addition, the
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
roofner (bar784) – Homework 14 – Weathers – (17104)
2
blocks are allowed to move on a fixed block
wedge of angle 47
◦
, as shown. The coefficient
of kinetic friction is 0
.
19 for both blocks.
3 kg
7 kg
47
◦
0
.
25 m
9 kg
What is the acceleration of the two blocks?
The acceleration of gravity is 9
.
8 m
/
s
2
.
As
sume the positive direction is to the right.
Correct answer: 2
.
46177 m
/
s
2
.
Explanation:
Let :
m
1
= 3 kg
,
m
2
= 7 kg
,
M
= 9 kg
,
and
R
= 0
.
25 m
.
m
1
m
2
θ
M
T
1
T
2
Applying Newton’s law to
m
1
,
N
1

m
1
g
=
m
1
a
y
= 0
N
1
=
m
1
g ,
where the force of friction on
m
1
is
f
1
=
μ N
1
=
μ m
1
g
= (0
.
19) (3 kg) (9
.
8 m
/
s
2
)
= 5
.
586 N
and
T
1

f
1
=
m
1
a
T
1
=
m
1
a
+
f
1
.
(1)
For the mass
m
2
, applying Newton’s law
perpendicular to the slanted surface
N
2

m
2
g
cos
θ
=
m
2
a
perp
= 0
N
2
=
m
2
g
cos
θ ,
so the force of friction is
f
2
=
μ N
2
=
μ m
2
g
cos
θ
= (0
.
19) (7 kg) (9
.
8 m
/
s
2
) cos 47
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Weathers
 mechanics, Acceleration, Force, Friction, Mass, kg

Click to edit the document details