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001
10.0 points
Find the magnitude of the torque produced
by a 4.8 N force applied to a door at a per
pendicular distance of 0.21 m from the hinge.
Correct answer: 1
.
008 N
·
m.
Explanation:
Let :
F
= 4
.
8 N
,
d
= 0
.
21 m
,
and
θ
= 90
.
0
◦
.
τ
=
F d
sin
θ
= (4
.
8 N) (0
.
21 m) sin 90
.
0
◦
=
1
.
008 N
·
m
.
002
10.0 points
An Atwood machine is constructed using a
disk of mass 2
.
3 kg and radius 23
.
7 cm.
3
.
7 m
23
.
7 cm
2
.
3 kg
ω
1
.
78 kg
1
.
12 kg
What is the acceleration of the system?
The acceleration of gravity is 9
.
8 m
/
s
2
.
Correct answer: 1
.
59704 m
/
s
2
.
Explanation:
Let :
m
= 2
.
3 kg
,
R
= 23
.
7 cm = 0
.
237 m
,
m
1
= 1
.
12 kg
,
m
2
= 1
.
78 kg
,
and
h
= 3
.
7 m
.
Consider the free body diagrams
1
.
78 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 di
rection of the heavier mass
m
1
. 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 is a solid disk, so
I
=
1
2
m r
2
and
τ
net
=
τ
ccw

τ
cw
=
I
α
T
1
r

T
2
r
=
1
2
m r
2
a
r
=
1
2
m r a
Multiplying by
2
r
gives
m a
= 2
T
1

2
T
2
= 2 (
m
1

m
2
)
g

2 (
m
1
+
m
2
)
a
a
=
2 (
m
1

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

1
.
78 kg) (9
.
8 m
/
s
2
)
2
.
3 kg + 2 (1
.
12 kg) + 2 (1
.
78 kg)
=
1
.
59704 m
/
s
2
.
003
10.0 points
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A 308 kg merrygoround in the shape of a
horizontal disk with a radius of 1
.
3 m is set in
motion by wrapping a rope about the rim of
the disk and pulling on the rope.
How large a torque would have to be ex
erted to bring the merrygoround from rest
to an angular speed of 3
.
4 rad
/
s in 2
.
2 s?
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 Spring '08
 Jones,S
 Physics, Angular Momentum, Force, 1 m, τ, Fnet

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