alexander (jra2623) – homework 23 – Turner – (92510)
1
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001
(part 1 of 3) 10.0 points
A mobile consists of four weights hanging
on three horizontal rods of negligible mass.
20 N
W
1
W
2
W
3
4 m
9 m
6 m
5 m
5 m
4 m
Find the unknown weight on the lower rod.
Correct answer: 8
.
88889 N.
Explanation:
Let :
W
= 20 N
,
ℓ
r
1
= 9 m
,
and
ℓ
l
1
= 4 m
.
Applying rotational equilibrium about an
axis through the point of suspension of the
lowest rod in the mobile,
summationdisplay
vector
τ
=
ℓ
l
1
W 
ℓ
r
1
W
1
= 0
W
1
=
ℓ
l
1
W
ℓ
r
1
=
(4 m) (20 N)
9 m
=
8
.
88889 N
.
002
(part 2 of 3) 10.0 points
Find the unknown weight on the middle rod.
Correct answer: 24
.
0741 N.
Explanation:
Let :
ℓ
r
2
= 5 m
and
ℓ
l
2
= 6 m
.
Applying rotational equilibrium about an
axis through the point of suspension of the
middle rod in the mobile,
summationdisplay
vector
τ
=
ℓ
l
w
W
2

ℓ
r
2
(
W
+
W
1
) = 0
W
2
=
ℓ
r
2
(
W
+
W
1
)
ℓ
l
w
=
(5 m) (20 N + 8
.
88889 N)
6 m
=
24
.
0741 N
.
003
(part 3 of 3) 10.0 points
Find the unknown weight on the upper rod.
Correct answer: 66
.
2037 N.
Explanation:
Let :
ℓ
r
3
= 4 m
and
ℓ
l
3
= 5 m
.
Applying rotational equilibrium about an axis
through the point of suspension of the top rod
in the mobile,
summationdisplay
vector
τ
=
ℓ
l
e
(
W
+
W
1
+
W
2
)

ℓ
r
3
W
3
= 0
W
3
=
ℓ
l
3
(
W
+
W
1
+
W
2
)
ℓ
r
3
=
5 m
4 m
(20 N + 8
.
88889 N
+24
.
0741 N)
=
66
.
2037 N
.
004
10.0 points
The angle of the inclination is 36
.
6
◦
, the outer
part of the large pulley has a radius of 3
r
and
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alexander (jra2623) – homework 23 – Turner – (92510)
2
the inner part of the large pulley has a radius
of
r
.
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 Summer '08
 Kaplunovsky
 Force, Mass, Work, Correct Answer, Alexander

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