Resultant Systems

Thema:Vektoren 2D (zweidimensional), Vektoren

The following frame consists of couple moments M₁and M₂, and external forces F₁ and F₂. Click and drag the red dots of each external force to move it to a new location on the diagram. Click and drag to set the resultant system to any location O on the diagram. For all questions below, the following coordinate system will be used. x is positive to the right

y is positive toward the top of the page

positive moments produce a counterclockwise rotation

Conceptual Questions - Resultant Systems

Use the interactive Figure above to answer the following questions.

Assuming no change in magnitude or angle, how does the location of an external force affect the resultant force (F_r)?

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A
It changes the magnitude of F_r
B
It changes the direction of F_r
C
It changes the magnitude and direction of F_r
D
It has no effect on F_r

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If all external forces stay the same, what happens to the magnitude of the resultant moment (M_r)_Oas the couple moments M₁ and M₂ are moved?

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A
The magnitude of (M_r)_Oincreases
B
The magnitude of (M_r)_Odecreases
C
The magnitude of (M_r)_Oincreases or decreases depending on where the couple moments are moved
D
The magnitude of (M_r)_Odoes not change

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Why does the magnitude of the resultant moment (M_r)_Oremain unchanged as the couple moments are moved on the diagram?

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A
Because the system is in static equilibrium
B
Because couple moments are free vectors
C
Because the couple moments cancel each other out
D
Because couple moments are scalar quantities

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Which of the following statements regarding the resultant moment (M_r)_O is true?

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A
(M_r)_Odepends only on the sum of all couple moments ΣM
B
(M_r)_Odepends only on the sum of the moments produced by all forces ΣM_O about point O
C
(M_r)_Odepends on both the sum of all couple moments ΣM and the moments produced by all forces ΣM_O about point O

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Use the Figure to Determine the Resultant Moment and Force

In the interactive Figure above, click and drag the red dot to move each of the external forces, couple moments, and the location of the resultant equivalent system. Use the following information and interactive Figure to answer the following questions.

Set F₁ = 300 N at an angle of 75^oat point B, and F₂ = 100 N at an angle of 0^olocated at 3m in the +y direction from A. Use this information to answer the questions below.

What is the approximate magnitude of the resultant force F_r and its angle θ_r?

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A
F_r = 340 N, θ_r = 58^o
B
F_r = 340 N, θ_r = -58^o
C
F_r = 340 N, θ_r = 32^o
D
F_r = 340 N, θ_r = -32^o

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As the angle of F₁ decreases, what happens to the magnitude of F_r?

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A
It increases
B
It decreases
C
It stays the same

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For what angle of F₁, is the magnitude of θ_r a maximum?

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A
0^o
B
45^o
C
90^o
D
180^o

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If the location of force F₂ is moved to A, what happens to the magnitude of F_r?

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A
It increases
B
It decreases
C
It stays the same

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Assuming all forces and their directions remain unchanged from above and M₁ and M₂ both equal 0, what is the correct expression for the resultant moment (M_r)_Cat C?

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If M₁ produces a clockwise rotation and M₂ counterclockwise, and if F₁ is set to 90^o at point B, and F₂ remains unchanged, which expression for the resultant moment at D, (M_r)_D is correct?

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A
(M_r)_D= -M₁ + M₂ + 5F₁ - 2F₂
B
(M_r)_D= M₁ + M₂ + 5F₁ + 2F₂
C
(M_r)_D= M₁ - M₂ - 5F₁ + 2F₂
D
(M_r)_D= -M₁ + M₂ + 5F₁ - 2F₂

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Set F₂ and M₂ to 0. If F₁ = 100 N at B at an angle of 90^o, what will be the required direction and magnitude of M₁for a resultant moment M_r = 0 at point D?

Assuming everything stays the same, what will be the required direction and magnitude of M₁ for a resultant moment M_r = 0 at point A?

Resultant Systems

Conceptual Questions - Resultant Systems

Use the Figure to Determine the Resultant Moment and Force

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