Sample Problem 2/4Forces F₁ and F₂ act on the bracket as shown. Determine the projection F,of their resultant R onto the b-axis.Solution. The parallelogram addition of F, and F, is shown in the figure.Using the law of cosines gives usR² = (80)² + (100)² - 2(80)(100) cos 130° R = 163.4 NThe figure also shows the orthogonal projection F, of R onto the b-axis. Itslength isF₁ = 80 + 100 cos 50º = 144.3 NNote that the components of a vector are in general not equal to the projec-tions of the vector onto the same axes. If the a-axis had been perpendicular tothe b-axis, then the projections and components of R would have been equal.32 Chapter 2 Force SystemsPROBLEMSIntroductory Problems2/1 The force F has a magnitude of 800 N. Express F as avector in terms of the unit vectors i and j. Identify thex and y scalar components of F.F = 800 NF = 7kN2/2 The force F has a magnitude of 7 kN and acts at thelocation indicated. Express F as a vector in terms ofthe unit vectors i and j. Next, determine the x and yscalar components of F.25°35° iA (-4,-5)Problem 2/1y, m1Ix, mProblem 2/22/3 The slope of the 6.5-kN force F is specified as shownin the figure. Express F as a vector in terms of theunit vectors i and j.Ans.F₂ = 425 lb2/6 Two forces are applied to the construction bracket asshown. Determine the angle which makes the resul-tant of the two forces vertical. Determine the magni-tude R of the resultant.F₁ = 800 lbA(-3,7)100 N50F₁100 NF = 6.5 kNProblem 2/5F₂ = 80 NF.80 NF₂30-1030⁰Problem 2/32/4 The force F has a magnitude of 1250 lb and has theindicated line of action. Write the unit vector n as-sociated with F and use n to determine the x and yscalar components of F.y, ftR50⁰50 / 535x, ftF=1250 lbProblem 2/42/5 The control rod AP exerts a force F on the sector asshown. Determine both the x-y and the n-t componentsof the force.B (10,-8)2--9Article 2/3 Problems 33...

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Answered: 2/1 The force F has a magnitude of 800…

2/1 The force F has a magnitude of 800 N. Express F as a vector in terms of the unit vectors i and j. Identify the x and y scalar components of F. F = 800 N 35° Problem 2/1

Elements Of Electromagnetics

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Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Question

Sample Problem 2/4
Forces F₁ and F₂ act on the bracket as shown. Determine the projection F,
of their resultant R onto the b-axis.
Solution. The parallelogram addition of F, and F, is shown in the figure.
Using the law of cosines gives us
R² = (80)² + (100)² - 2(80)(100) cos 130° R = 163.4 N
The figure also shows the orthogonal projection F, of R onto the b-axis. Its
length is
F₁ = 80 + 100 cos 50º = 144.3 N
Note that the components of a vector are in general not equal to the projec-
tions of the vector onto the same axes. If the a-axis had been perpendicular to
the b-axis, then the projections and components of R would have been equal.
32 Chapter 2 Force Systems
PROBLEMS
Introductory Problems
2/1 The force F has a magnitude of 800 N. Express F as a
vector in terms of the unit vectors i and j. Identify the
x and y scalar components of F.
F = 800 N
F = 7kN
2/2 The force F has a magnitude of 7 kN and acts at the
location indicated. Express F as a vector in terms of
the unit vectors i and j. Next, determine the x and y
scalar components of F.
25°
35° i
A (-4,-5)
Problem 2/1
y, m
1
I
x, m
Problem 2/2
2/3 The slope of the 6.5-kN force F is specified as shown
in the figure. Express F as a vector in terms of the
unit vectors i and j.
Ans.
F₂ = 425 lb
2/6 Two forces are applied to the construction bracket as
shown. Determine the angle which makes the resul-
tant of the two forces vertical. Determine the magni-
tude R of the resultant.
F₁ = 800 lb
A(-3,7)
100 N
50
F₁100 N
F = 6.5 kN
Problem 2/5
F₂ = 80 N
F.
80 N
F₂
30-10
30⁰
Problem 2/3
2/4 The force F has a magnitude of 1250 lb and has the
indicated line of action. Write the unit vector n as-
sociated with F and use n to determine the x and y
scalar components of F.
y, ft
R
50⁰
50 / 535
x, ft
F=1250 lb
Problem 2/4
2/5 The control rod AP exerts a force F on the sector as
shown. Determine both the x-y and the n-t components
of the force.
B (10,-8)
2--9
Article 2/3 Problems 33
...

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