alexander (jra2623) – oldhomework 24 – Turner – (92510)
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001
(part 1 of 2) 10.0 points
An 8 kg watermelon is placed at one end
of a 7
.
4 m, 203 N scaffolding supported by
two cables.
One supporting cable is at the
opposite end of the scaffolding, and the other
is 0
.
55 m from the watermelon.
How much tension is in the cable at the end
of the scaffolding? The acceleration of gravity
is 9
.
8 m
/
s
2
.
Correct answer: 87
.
0555 N.
Explanation:
Let :
m
= 8 kg
W
= 203 N
,
ℓ
= 7
.
4 m
,
x
= 0
.
55 m
,
and
g
= 9
.
8 m
/
s
2
.
Let the fulcrum be at the point of attach
ment of the cable closest to the watermelon.
mg
W
T
1
The watermelon
mg
acts down (CCW) at a
distance
x
from the fulcrum. The weight
W
acts down (CCW) at a distance
ℓ
2

x
from the
fulcrum, and the rightmost tension
T
1
acts up
(CCW) at a distance
ℓ

x
from the fulcrum.
Thus
summationdisplay
τ
=
summationdisplay
τ
CW

summationdisplay
τ
CCW
= 0
W
parenleftbigg
ℓ
2

x
parenrightbigg

m g x

T
1
(
ℓ

x
) = 0
W
(
ℓ

2
x
)

2
m g x
= 2
T
1
(
ℓ

x
)
T
1
=
W
(
ℓ

2
x
)

2
m g x
2 (
ℓ

x
)
=
(203 N) [7
.
4 m

2 (0
.
55 m)]
2 (7
.
4 m

0
.
55 m)

2 (8 kg) (9
.
8 m
/
s
2
) (0
.
55 m)
2 (7
.
4 m

0
.
55 m)
=
87
.
0555 N
.
002
(part 2 of 2) 10.0 points
How much tension is in the cable closest to
the watermelon?
Correct answer: 194
.
345 N.
Explanation:
Let the fulcrum be at the point of attach
ment of the rightmost cable.
mg
W
T
2
The watermelon
m g
acts down (CCW) at
a distance
ℓ
from the fulcrum. The weight
W
acts down (CCW) at a distance
ℓ
2
from the
fulcrum, and the tension
T
2
acts up (CCW)
at a distance
ℓ

x
from the fulcrum. Thus
T
2
(
ℓ

x
)

m g ℓ
 W
parenleftbigg
ℓ
2
parenrightbigg
= 0
.
Multiplying by 2,
2
T
2
(
ℓ

x
) = 2
m g ℓ
+
W
ℓ
T
2
=
2
m g ℓ
+
W
ℓ
2 (
ℓ

x
)
=
2 (8 kg) (9
.
8 m
/
s
2
) (7
.
4 m)
2 (7
.
4 m

0
.
55 m)
+
(203 N) (7
.
4 m)
2 (7
.
4 m

0
.
55 m)
=
194
.
345 N
.
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alexander (jra2623) – oldhomework 24 – Turner – (92510)
2
003
(part 1 of 3) 10.0 points
A 1560 N uniform boom is supported by a
cable as shown. The boom is pivoted at the
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 Summer '08
 Kaplunovsky
 Force, Work, Correct Answer, Alexander

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