2.6.1 To find the resultant of multiple forces using Cartesian components and to determine the direction of this resultant from its components. As shown, three forces act on the tip of a pole. F₁ = -50 i +75j +45 k lb. F₂ = 100 lb and forms the following angles with the x, y, and z axes, respectively: a =51.7°, 8= 71.1°, and 7= 135.6°. F3 = 120 lb, forms the angle o 26° with the z axis, and forms the angle 8= 25° between the x axis and the projection of F3 in the zy plane. 0 F. Part A - Resultant of adding F₁ and F3 Find the resultant of adding F₁ and F3. Express your answer in component form. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) R₁3 = F₁ AE Ivec ? i lb, j lb, k lb Part B - Resultant of adding F₁ and F₂ and F3 Find the resultant of adding F₁, F₂. and F₁. Express your answer in component form. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) R₁21= Part C- Direction of a resultant ■ 195] ΑΣΦ | It | vec ▸ View Available Hint(s) For the given forces, F₁, F₂, and F3, find the three direction angles aR. BR. and Yr between the resultant force R123 found in Part B and the x, y, and z axes, respectively. Express your answers, separated by commas, in degrees to three significant figures. aR, BR. YR= 3 → C P ? ARE- 195] ΑΣΦ... 11/vocl 4 between the x axis and the force. Express your answer in degrees to three significant figures. View Available Hint(s) ■VA‰¢ it vec | | 1 Part D. Find the direction angle a when given direction angles p and y As shown, a force of 300 lb acts at the tip of a tower. Two of the force's direction angles are known. m - 40° and YRI-65", that define the angles between the force and the y and z axes, respectively. Find the angle ca. A O i lb, j lb, klb. C www ? R₁ ?
2.6.1 To find the resultant of multiple forces using Cartesian components and to determine the direction of this resultant from its components. As shown, three forces act on the tip of a pole. F₁ = -50 i +75j +45 k lb. F₂ = 100 lb and forms the following angles with the x, y, and z axes, respectively: a =51.7°, 8= 71.1°, and 7= 135.6°. F3 = 120 lb, forms the angle o 26° with the z axis, and forms the angle 8= 25° between the x axis and the projection of F3 in the zy plane. 0 F. Part A - Resultant of adding F₁ and F3 Find the resultant of adding F₁ and F3. Express your answer in component form. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) R₁3 = F₁ AE Ivec ? i lb, j lb, k lb Part B - Resultant of adding F₁ and F₂ and F3 Find the resultant of adding F₁, F₂. and F₁. Express your answer in component form. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) R₁21= Part C- Direction of a resultant ■ 195] ΑΣΦ | It | vec ▸ View Available Hint(s) For the given forces, F₁, F₂, and F3, find the three direction angles aR. BR. and Yr between the resultant force R123 found in Part B and the x, y, and z axes, respectively. Express your answers, separated by commas, in degrees to three significant figures. aR, BR. YR= 3 → C P ? ARE- 195] ΑΣΦ... 11/vocl 4 between the x axis and the force. Express your answer in degrees to three significant figures. View Available Hint(s) ■VA‰¢ it vec | | 1 Part D. Find the direction angle a when given direction angles p and y As shown, a force of 300 lb acts at the tip of a tower. Two of the force's direction angles are known. m - 40° and YRI-65", that define the angles between the force and the y and z axes, respectively. Find the angle ca. A O i lb, j lb, klb. C www ? R₁ ?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
![2.6.1
To find the resultant of multiple forces using
Cartesian components and to determine the
direction of this resultant from its components.
As shown, three forces act on the tip of a pole.
F₁ = -50 i +75j +45 k lb. F₂ = 100 lb
and forms the following angles with the x, y, and z
axes, respectively: a = 51.7°, B = 71.1°, and
Y
135.6°. F3 = 120 lb, forms the angle
$
26° with the z axis, and forms the angle
0 = 25° between the x axis and the projection of
F3 in the xy plane.
0
F₂
Part A - Resultant of adding F₁ and F3
R₁3 =
F₁
Find the resultant of adding F₁ and F3. Express your answer in component form.
Express your answers, separated by commas, to three significant figures.
► View Available Hint(s)
AΣo↓vec
y
?
i lb,j lb, k lb
Part B - Resultant of adding F₁ and F2 and F3
Find the resultant of adding F₁ F₂, and F3. Express your answer in component form.
Express your answers, separated by commas, to three significant figures.
► View Available Hint(s)
R₁23 =
IVE] ΑΣΦ | 11
Part C - Direction of a resultant
aR, BR, YR=
vec
For the given forces, F₁, F2, and F3, find the three direction angles R. BR. and YR between the resultant force
R123 found in Part B and the x, y, and z axes, respectively.
Express your answers, separated by commas, in degrees to three significant figures.
▸ View Available Hint(s)
ΨΕΙ ΑΣΦ ↓↑ vec 5
Ri=
Part D - Find the direction angle a when given direction angles B and y
?
between the x axis and the force.
Express your answer in degrees to three significant figures.
▸ View Available Hint(s)
As shown, a force of 300 lb acts at the tip of a tower. Two of the force's direction angles are known, BR 40° and
YR₁ = 65°, that define the angles between the force and the y and z axes, respectively. Find az, the angle
B₁
-ΓΙ ΑΣΦ ↓↑ vec
i lb,j lb, k lb
?
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Transcribed Image Text:2.6.1
To find the resultant of multiple forces using
Cartesian components and to determine the
direction of this resultant from its components.
As shown, three forces act on the tip of a pole.
F₁ = -50 i +75j +45 k lb. F₂ = 100 lb
and forms the following angles with the x, y, and z
axes, respectively: a = 51.7°, B = 71.1°, and
Y
135.6°. F3 = 120 lb, forms the angle
$
26° with the z axis, and forms the angle
0 = 25° between the x axis and the projection of
F3 in the xy plane.
0
F₂
Part A - Resultant of adding F₁ and F3
R₁3 =
F₁
Find the resultant of adding F₁ and F3. Express your answer in component form.
Express your answers, separated by commas, to three significant figures.
► View Available Hint(s)
AΣo↓vec
y
?
i lb,j lb, k lb
Part B - Resultant of adding F₁ and F2 and F3
Find the resultant of adding F₁ F₂, and F3. Express your answer in component form.
Express your answers, separated by commas, to three significant figures.
► View Available Hint(s)
R₁23 =
IVE] ΑΣΦ | 11
Part C - Direction of a resultant
aR, BR, YR=
vec
For the given forces, F₁, F2, and F3, find the three direction angles R. BR. and YR between the resultant force
R123 found in Part B and the x, y, and z axes, respectively.
Express your answers, separated by commas, in degrees to three significant figures.
▸ View Available Hint(s)
ΨΕΙ ΑΣΦ ↓↑ vec 5
Ri=
Part D - Find the direction angle a when given direction angles B and y
?
between the x axis and the force.
Express your answer in degrees to three significant figures.
▸ View Available Hint(s)
As shown, a force of 300 lb acts at the tip of a tower. Two of the force's direction angles are known, BR 40° and
YR₁ = 65°, that define the angles between the force and the y and z axes, respectively. Find az, the angle
B₁
-ΓΙ ΑΣΦ ↓↑ vec
i lb,j lb, k lb
?
000
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