Learning Goal: To use the vector cross product to calculate the moment produced by a force, or forces, about a specified point on a member. Part A - Moment due to a force specified by magnitude and endpoints The moment of a force F about the moment axis passing through O and perpendicular to the plane containing O and F can be expressed using the vector cross product, Mo =r x F. In a properly constructed Cartesian coordinate system, the vector cross product can be calculated using a matrix determinant: As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 1) The force has magnitude F = 180 N and is directed as shown. The dimensions are r, = 0.350 m. r2 = 1.90 m. y1 = 2.30 m. and z1 = 1.20 m. What is the moment about the origin due to the applied force F? ijk Express the individual components of the Cartesian vector to three significant figures, separated by commas. M =rx F =|r. Ty ra. F F, F • View Available Hint(s) Notice that the order of the elements of the matrix determinant is important; switching rows 2 and 3 of the determinant would change the sign of the moment from positive to negative (or vice versa.) VO AZ 1 vec ? Mo =| i, j, k] N · m Submit Part B - Moment due to a force specified as a Cartesian vector As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 2) The force is given by F = 130 N i– 135 Nj+ 70NK The dimensions are a = 1.35 m, y1 = 1.90 m, and z = 1.05 m. . Figure 1 of 3 > What is the moment about the origin due to the applied force F? Express the individual components of the Cartesian vector to three significant figures, separated by commas. • View Available Hint(s) VO AEO It vec + + ? B Mo =[ i, j, k) N - m Submit
Learning Goal: To use the vector cross product to calculate the moment produced by a force, or forces, about a specified point on a member. Part A - Moment due to a force specified by magnitude and endpoints The moment of a force F about the moment axis passing through O and perpendicular to the plane containing O and F can be expressed using the vector cross product, Mo =r x F. In a properly constructed Cartesian coordinate system, the vector cross product can be calculated using a matrix determinant: As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 1) The force has magnitude F = 180 N and is directed as shown. The dimensions are r, = 0.350 m. r2 = 1.90 m. y1 = 2.30 m. and z1 = 1.20 m. What is the moment about the origin due to the applied force F? ijk Express the individual components of the Cartesian vector to three significant figures, separated by commas. M =rx F =|r. Ty ra. F F, F • View Available Hint(s) Notice that the order of the elements of the matrix determinant is important; switching rows 2 and 3 of the determinant would change the sign of the moment from positive to negative (or vice versa.) VO AZ 1 vec ? Mo =| i, j, k] N · m Submit Part B - Moment due to a force specified as a Cartesian vector As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 2) The force is given by F = 130 N i– 135 Nj+ 70NK The dimensions are a = 1.35 m, y1 = 1.90 m, and z = 1.05 m. . Figure 1 of 3 > What is the moment about the origin due to the applied force F? Express the individual components of the Cartesian vector to three significant figures, separated by commas. • View Available Hint(s) VO AEO It vec + + ? B Mo =[ i, j, k) N - m Submit
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![Review
Learning Goal:
To use the vector cross product to calculate the moment produced by
a force, or forces, about a specified point on a member.
Part A - Moment due to a force specified by magnitude and endpoints
The moment of a force F about the moment axis passing through O
and perpendicular to the plane containing O and F can be expressed
using the vector cross product, Mo =r x F. In a properly
constructed Cartesian coordinate system, the vector cross product can
be calculated using a matrix determinant:
As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B.
(Figure 1)
The force has magnitude F = 180 N and is directed as shown. The dimensions are ¤1 = 0.350 m, x2 = 1.90 m, y1 = 2.30 m, and z1 = 1.20 m.
What is the moment about the origin due to the applied force F?
i j
M =rx F =|rz
k
Express the individual components of the Cartesian vector to three significant figures, separated by commas.
ry
F F, F;
• View Available Hint(s)
Notice that the order of the elements of the matrix determinant is
important; switching rows 2 and 3 of the determinant would change the
sign of the moment from positive to negative (or vice versa.)
vec
Mo =[
i, j, k] N · m
Submit
Part B - Moment due to a force specified as a Cartesian vector
As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B
(Figure 2)
The force is given by F = 130NI- 135 Nj+ 70 Nk. The dimensions are æj = 1.35 m, y1 = 1.90 m, and z = 1.05 m.
Figure
< 1 of 3
What is the moment about the origin due to the applied force F?
Express the individual components of the Cartesian vector to three significant figures, separated by commas.
• View Available Hint(s)
ΥΠ ΑΣφ vec
F
Mo =[
i, j, k] N · m
Submit
y1
Part C - Moment due to two forces](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb1a8ba3-371b-48d7-95b6-c118f740fa83%2F08d3fde9-dd41-4326-8b03-c33c396a43bf%2F6myqjv_processed.png&w=3840&q=75)
Transcribed Image Text:Review
Learning Goal:
To use the vector cross product to calculate the moment produced by
a force, or forces, about a specified point on a member.
Part A - Moment due to a force specified by magnitude and endpoints
The moment of a force F about the moment axis passing through O
and perpendicular to the plane containing O and F can be expressed
using the vector cross product, Mo =r x F. In a properly
constructed Cartesian coordinate system, the vector cross product can
be calculated using a matrix determinant:
As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B.
(Figure 1)
The force has magnitude F = 180 N and is directed as shown. The dimensions are ¤1 = 0.350 m, x2 = 1.90 m, y1 = 2.30 m, and z1 = 1.20 m.
What is the moment about the origin due to the applied force F?
i j
M =rx F =|rz
k
Express the individual components of the Cartesian vector to three significant figures, separated by commas.
ry
F F, F;
• View Available Hint(s)
Notice that the order of the elements of the matrix determinant is
important; switching rows 2 and 3 of the determinant would change the
sign of the moment from positive to negative (or vice versa.)
vec
Mo =[
i, j, k] N · m
Submit
Part B - Moment due to a force specified as a Cartesian vector
As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B
(Figure 2)
The force is given by F = 130NI- 135 Nj+ 70 Nk. The dimensions are æj = 1.35 m, y1 = 1.90 m, and z = 1.05 m.
Figure
< 1 of 3
What is the moment about the origin due to the applied force F?
Express the individual components of the Cartesian vector to three significant figures, separated by commas.
• View Available Hint(s)
ΥΠ ΑΣφ vec
F
Mo =[
i, j, k] N · m
Submit
y1
Part C - Moment due to two forces
![Part C - Moment due to two forces
As shown, a member is fixed at the origin, point O, and has two applied forces, F, and F2, applied at the free end, point B.
(Figure 3)
The forces are given by F1 = 85 Ni- 110 Nj+75 N k and F2 has magnitude 165 N and direction angles a = 155.0°, B= 66.0°, and y = 83.4°. The
dimensions are x1 = 1.40 m, Y1 = 1.85 m, and z1 = 1.10 m.
What is the moment about the origin due to the applied forces?
Figure
3 of 3 >
Express the individual components of the Cartesian vector to three significant figures, separated by commas.
• View Available Hint(s)
nα ΑΣφ
?
vec
Mo =[
i, j, k] N · m
F2
Submit
Provide Feedback
Next >](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb1a8ba3-371b-48d7-95b6-c118f740fa83%2F08d3fde9-dd41-4326-8b03-c33c396a43bf%2Fio6vpz1_processed.png&w=3840&q=75)
Transcribed Image Text:Part C - Moment due to two forces
As shown, a member is fixed at the origin, point O, and has two applied forces, F, and F2, applied at the free end, point B.
(Figure 3)
The forces are given by F1 = 85 Ni- 110 Nj+75 N k and F2 has magnitude 165 N and direction angles a = 155.0°, B= 66.0°, and y = 83.4°. The
dimensions are x1 = 1.40 m, Y1 = 1.85 m, and z1 = 1.10 m.
What is the moment about the origin due to the applied forces?
Figure
3 of 3 >
Express the individual components of the Cartesian vector to three significant figures, separated by commas.
• View Available Hint(s)
nα ΑΣφ
?
vec
Mo =[
i, j, k] N · m
F2
Submit
Provide Feedback
Next >
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