Create assignment, 00223, Homework 4, Sep 15 at 9:06 pm
1
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have
14
questions.
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The due time is Central
time.
Perpendicular Vectors 02
05:01, trigonometry, numeric,
>
1 min, nor
mal.
001
Two vectors of magnitudes 10 N and 20 N act
at right angles to each other.
What is the magnitude of their resultant?
Correct answer: 22
.
3607 N.
Explanation:
The resultant of two vectors acting at right
angles to each other is the hypotenuse of a
right triangle, so
f
=
q
f
2
1
+
f
2
2
=
q
(10 N)
2
+ (20 N)
2
= 22
.
3607 N
Hanging Weight 04
05:07,
trigonometry,
numeric,
>
1
min,
wordingvariable.
002
Consider the 700 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 570 N and
makes an angle of 55
◦
with the ceiling.
The righthand cable makes an angle of 55
◦
with the ceiling and has a tension of 570 N
.
700 N
T
2
570 N
55
◦
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: 401
.
518 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
= 700 N
,
F
1
= 570 N
,
θ
1
= 55
◦
,
and
θ
2
= 90
◦

θ .
Basic Concept:
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)
= (570 N) cos 55
◦
= 326
.
939 N
,
and
F
y
2
=
F
3

F
1
sin
θ
1
(2)
= 700 N

(570 N) sin 55
◦
= 700 N

466
.
917 N
= 233
.
083 N
,
so
F
2
=
q
(
F
x
2
)
2
+ (
F
y
2
)
2
=
q
(326
.
939 N)
2
+ (233
.
083 N)
2
= 401
.
518 N
.
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Create assignment, 00223, Homework 4, Sep 15 at 9:06 pm
2
003
b) What is the angle
θ
2
which the lefthand
cable makes with respect to the ceiling?
Correct answer: 35
.
4861
◦
.
Explanation:
Using Eq. 2, we have
θ
2
= arctan
F
y
1
F
x
1
¶
= arctan
466
.
917 N
326
.
939 N
¶
= 35
.
4861
◦
.
Three Forces
05:07, trigonometry, numeric,
>
1 min, nor
mal.
004
An object in equilibrium has three forces ex
erted on it. A(n) 33 N force acts at 80
◦
, and
a(n) 44 N force acts at 60
◦
.
What is the direction of the third force?
(Consider all angles to be measured counter
clockwise from the positive
x
axis.)
Correct answer: 248
.
557
◦
.
Explanation:
Basic Concepts:
Choose a coordinate system with the pos
itive
x
axis representing 0
◦
and the positive
yaxis representing 90
◦
.
Any force
F
has an
x
component of
F
x
=
F
cos
θ
and a
y
component of
F
y
=
F
sin
θ
where
θ
is measured from the
x
axis.
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