calculate the moment of a force about a specified axis is as follows: The magnitude of a moment about a line segment connecting points P and Q due to a force F applied at point R (with R not on the line through P and Q) can be calculated using the scalar triple product, MpQ = upq.rx F, where r is a position vector from any point on the line through P and Q to R and upo is the unit vector in the direction of line segment PQ. The unit vector upo is then multiplied by this magnitude to find the vector representation of the moment. As shown in the figure, the member is anchored at A and section AB lies in the x-y plane. The dimensions are ₁ = 1.6 m, y₁ = 1.8 m, and z₁ = 1.6 m. The force applied at point Cis F = [-235 i+ 135 j + 155 k] N. (Figure 1) Figure B 1 of 1 Part B - Calculating the moment about AB using the position vector AC Using the position vector from A to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. ► View Available Hint(s) MAB =[ Submit 96 MAB =[ AΣ vec ▼ Part C - Calculating the moment about AB using the position vector BC Submit Using the position vector from B to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. ► View Available Hint(s) ? 17| ΑΣΦ | Η vec i, j, k N-m ? i, j, k] N.m Review
calculate the moment of a force about a specified axis is as follows: The magnitude of a moment about a line segment connecting points P and Q due to a force F applied at point R (with R not on the line through P and Q) can be calculated using the scalar triple product, MpQ = upq.rx F, where r is a position vector from any point on the line through P and Q to R and upo is the unit vector in the direction of line segment PQ. The unit vector upo is then multiplied by this magnitude to find the vector representation of the moment. As shown in the figure, the member is anchored at A and section AB lies in the x-y plane. The dimensions are ₁ = 1.6 m, y₁ = 1.8 m, and z₁ = 1.6 m. The force applied at point Cis F = [-235 i+ 135 j + 155 k] N. (Figure 1) Figure B 1 of 1 Part B - Calculating the moment about AB using the position vector AC Using the position vector from A to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. ► View Available Hint(s) MAB =[ Submit 96 MAB =[ AΣ vec ▼ Part C - Calculating the moment about AB using the position vector BC Submit Using the position vector from B to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. ► View Available Hint(s) ? 17| ΑΣΦ | Η vec i, j, k N-m ? i, j, k] N.m Review
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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I need help with parts A,B, and C. The learning goal starts in the first screenshot and continues on the second one.
![calculate the moment of a force about a specified axis
is as follows:
The magnitude of a moment about a line segment
connecting points P and Q due to a force F applied
at point R (with R not on the line through P and Q)
can be calculated using the scalar triple product,
Mpq = upq ·r × F,
where r is a position vector from any point on the line
through P and Q to R and up is the unit vector in
the direction of line segment PQ. The unit vector upo
is then multiplied by this magnitude to find the vector
representation of the moment.
As shown in the figure, the member is anchored at A
and section AB lies in the x-y plane. The dimensions
are x₁ = 1.6 m, y₁ = 1.8 m, and 2₁ = 1.6 m. The
force applied at point C is
F = [-235 i+ 135 j + 155 k] N.
(Figure 1)
Figure
B
1 of 1
Part B - Calculating the moment about AB using the position vector AC
Using the position vector from A to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
► View Available Hint(s)
MAB =[
Submit
Π| ΑΣΦ
MAB =[
↓↑
Submit
vec
▼ Part C - Calculating the moment about AB using the position vector BC
www
Using the position vector from B to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
View Available Hint(s)
15| ΑΣΦ11
vec
i, j, k] N.r
• m
www
i, j, k] N. r
.m
Review](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6aa72a1b-7be3-4dcd-bcb5-7886fdb6dafd%2Fd3cf8a45-604e-47fc-a723-ec53cb35d218%2F96tzubc_processed.png&w=3840&q=75)
Transcribed Image Text:calculate the moment of a force about a specified axis
is as follows:
The magnitude of a moment about a line segment
connecting points P and Q due to a force F applied
at point R (with R not on the line through P and Q)
can be calculated using the scalar triple product,
Mpq = upq ·r × F,
where r is a position vector from any point on the line
through P and Q to R and up is the unit vector in
the direction of line segment PQ. The unit vector upo
is then multiplied by this magnitude to find the vector
representation of the moment.
As shown in the figure, the member is anchored at A
and section AB lies in the x-y plane. The dimensions
are x₁ = 1.6 m, y₁ = 1.8 m, and 2₁ = 1.6 m. The
force applied at point C is
F = [-235 i+ 135 j + 155 k] N.
(Figure 1)
Figure
B
1 of 1
Part B - Calculating the moment about AB using the position vector AC
Using the position vector from A to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
► View Available Hint(s)
MAB =[
Submit
Π| ΑΣΦ
MAB =[
↓↑
Submit
vec
▼ Part C - Calculating the moment about AB using the position vector BC
www
Using the position vector from B to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
View Available Hint(s)
15| ΑΣΦ11
vec
i, j, k] N.r
• m
www
i, j, k] N. r
.m
Review
![<Lecture 10 Assignment
Moment of a Force About a Specified Axis
Learning Goal:
To gain insight into the independence of the scalar
triple product from the point on the line chosen as the
reference point of the calculation.
The general process (not referenced to Figure 1) to
calculate the moment of a force about a specified axis
is as follows:
The magnitude of a moment about a line segment
connecting points P and Q due to a force F applied
at point R (with R not on the line through P and Q)
can be calculated using the scalar triple product,
= upQ rx F,
MPQ
where r is a position vector from any point on the line
through P and Q to R and upq is the unit vector in
the direction of line segment PQ. The unit vector upQ
is then multiplied by this magnitude to find the vector
representation of the moment.
As shown in the figure, the member is anchored at A
and section AB lies in the x-y plane. The dimensions
Figure
B
1 of 1
Part A - Finding the scalar triple product
Which of the following equations correctly evaluates the scalar triple product of three Cartesian vectors R, S, and T?
► View Available Hint(s)
R.S× T = Rx (SyTz – SzTy) i – Ry (SxTz − SzTx) j+ Rz(SxTy − SyTx) k
R.SXT= R(SyTz – SzTy) + Ry(SxTz − SzTx) + Rz(SxTy — SyTx)
○ R.SXT = R₂ (SyTz - S₂Ty) i+ Ry(S₂T₂ — S₂Tz)j + R₂(SzTy - SyTz) k
R. S × T = Rx (SyTz – SzTy) – Ry(SxTz − SzTx) + Rz(SzTy – SyTx)
Submit
Part B - Calculating the moment about AB using the position vector AC
Using the position vector from A to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
View Available Hint(s)
MAB =[
VE ΑΣΦ
↓↑
vec
wwwwwww
?
i, j, k] N.m
1 of 5
Review](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6aa72a1b-7be3-4dcd-bcb5-7886fdb6dafd%2Fd3cf8a45-604e-47fc-a723-ec53cb35d218%2Fjt3xz9_processed.png&w=3840&q=75)
Transcribed Image Text:<Lecture 10 Assignment
Moment of a Force About a Specified Axis
Learning Goal:
To gain insight into the independence of the scalar
triple product from the point on the line chosen as the
reference point of the calculation.
The general process (not referenced to Figure 1) to
calculate the moment of a force about a specified axis
is as follows:
The magnitude of a moment about a line segment
connecting points P and Q due to a force F applied
at point R (with R not on the line through P and Q)
can be calculated using the scalar triple product,
= upQ rx F,
MPQ
where r is a position vector from any point on the line
through P and Q to R and upq is the unit vector in
the direction of line segment PQ. The unit vector upQ
is then multiplied by this magnitude to find the vector
representation of the moment.
As shown in the figure, the member is anchored at A
and section AB lies in the x-y plane. The dimensions
Figure
B
1 of 1
Part A - Finding the scalar triple product
Which of the following equations correctly evaluates the scalar triple product of three Cartesian vectors R, S, and T?
► View Available Hint(s)
R.S× T = Rx (SyTz – SzTy) i – Ry (SxTz − SzTx) j+ Rz(SxTy − SyTx) k
R.SXT= R(SyTz – SzTy) + Ry(SxTz − SzTx) + Rz(SxTy — SyTx)
○ R.SXT = R₂ (SyTz - S₂Ty) i+ Ry(S₂T₂ — S₂Tz)j + R₂(SzTy - SyTz) k
R. S × T = Rx (SyTz – SzTy) – Ry(SxTz − SzTx) + Rz(SzTy – SyTx)
Submit
Part B - Calculating the moment about AB using the position vector AC
Using the position vector from A to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
View Available Hint(s)
MAB =[
VE ΑΣΦ
↓↑
vec
wwwwwww
?
i, j, k] N.m
1 of 5
Review
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