schneiter (tcs639) – HW07 – Ross – (89152)
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001
(part 1 of 2) 10.0 points
Consider the 693 N weight held by two cables
shown below. The lefthand cable had tension
T
2
and makes an angle of
θ
2
with the ceiling.
The righthand cable had tension 540 N and
makes an angle of 42
◦
with the ceiling.
The righthand cable makes an angle of 42
◦
with the ceiling and has a tension of 540 N
.
693 N
T
2
540 N
42
◦
θ
2
a) What is the tension
T
2
in the lefthand
cable slanted at an angle of
θ
2
with respect to
the wall?
Correct answer: 520
.
62 N.
Explanation:
Observe the freebody diagram below.
F
2
F
1
θ
1
θ
2
W
g
Note:
The sum of the
x
 and
y
components of
F
1
, F
2
,
and
W
g
are equal to zero.
Given :
W
g
= 693 N
,
F
1
= 540 N
,
θ
1
= 42
◦
,
and
θ
2
= 90
◦

θ .
BasicConcept:
Vertically and Horizontally,
we have
F
x
net
=
F
x
1

F
x
2
= 0
=
F
1
cos
θ
1

F
2
cos
θ
2
= 0
(1)
F
y
net
=
F
y
1
+
F
y
2
 W
g
= 0
=
F
1
sin
θ
1
+
F
2
sin
θ
2
 W
g
= 0 (2)
Solution:
Using Eqs. 1 and 2, we have
F
x
2
=
F
1
cos
θ
1
(1)
= (540 N) cos 42
◦
= 401
.
298 N
,
and
F
y
2
=
F
3

F
1
sin
θ
1
(2)
= 693 N

(540 N) sin 42
◦
= 693 N

361
.
331 N
= 331
.
669 N
,
so
F
2
=
radicalBig
(
F
x
2
)
2
+ (
F
y
2
)
2
=
radicalBig
(401
.
298 N)
2
+ (331
.
669 N)
2
= 520
.
62 N
.
002
(part 2 of 2) 10.0 points
b) What is the angle
θ
2
which the lefthand
cable makes with respect to the ceiling?
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 Spring '08
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 mechanics, Force, Mass, kg

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