Free Practice Quiz Question List

4 Force System Resultants Online Quiz Questions

Use this free practice quiz with 20 questions to review 4 Force System Resultants, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

True or false: If a force system has zero resultant force but a nonzero resultant moment about a point, it reduces to a pure couple.

A
True
B
False

Choose one

1 point

An equivalent force-couple system at O has resultant force $\mathbf{R}$ and moment $\mathbf{M}_O$ . If $\mathbf{r}_{OP}$ points from O to P, which equation gives the equivalent moment at P?

A
$\mathbf{M}_P = \mathbf{M}_O + (\mathbf{r}_{OP} \times \mathbf{R})$
B
$\mathbf{M}_P = \mathbf{M}_O - (\mathbf{r}_{OP} \times \mathbf{R})$
C
$\mathbf{M}_P = \mathbf{M}_O$ for every point P
D
$\mathbf{M}_P = \mathbf{M}_O - \mathbf{R}$

Fill in the blank

1 point

In words, the resultant moment about O is the sum of each force's about O and all applied .

Choose all

1 point

Select all statements that correctly describe reducing a force system to an equivalent force-couple system.

A
The resultant force is the vector sum of all forces.
B
The resultant moment about a point includes the moments of the forces and all applied couples.
C
An applied couple contributes to the resultant force.
D
The position of each force relative to the reference point is needed to calculate its moment about that point.
E
An applied couple's moment changes when the reference point changes.

Choose one

1 point

A system contains several forces and one or more applied couples. Which statement about its resultant force is correct?

A
The resultant force is the same vector sum of forces, whether or not applied couples are present.
B
An applied couple must be added to the resultant force.
C
An applied couple changes the force components but not the moment.
D
The resultant force depends on the reference point used for the moment calculation.

Written response

1 point

A force with components $(F_x,F_y)=(3,4)\ \text{kN}$ acts at $(x,y)=(2,-1)\ \text{m}$ . Taking counterclockwise as positive, what is its moment about O? Enter the signed value in kN·m.

Fill in the blank

1 point

For a planar force system with $\mathbf{R}=0$ and $\mathbf{M}_O\ne 0$ , the reduced system is a .

True or false

1 point

True or false: Two statically equivalent force systems must produce the same local stresses and internal forces in a rigid body.

A
True
B
False

Choose all

1 point

Select all statements that correctly describe special cases or reductions of force systems.

A
If $\mathbf{R}=0$ and $\mathbf{M}_O\ne 0$ , the system reduces to a pure couple.
B
If $\mathbf{R}\ne 0$ and the moment is zero at a point, the resultant force acts through that point.
C
If $\mathbf{R}=0$ and $\mathbf{M}_O=0$ , the loading system is in rigid-body equilibrium.
D
Every three-dimensional force-couple system can be replaced by a single force.

Written response

1 point

At O, an equivalent system has $M_O=-12\ \text{kN·m}$ and $\mathbf{R}=(0,3)\ \text{kN}$ . Point P is at $\mathbf{r}_{OP}=(2,0)\ \text{m}$ from O. Using the stated transfer relation, what is the signed moment at P? Enter the value in kN·m.

Choose one

1 point

What is the name of the general reduced form for a three-dimensional force-couple system when it cannot be represented by a single force alone?

A
A single force through the reference point
B
A pure couple only
C
A wrench consisting of a force and a moment parallel to it
D
A force and a moment that must be perpendicular

Open ended

1 point

Explain how a planar force-couple system with a nonzero resultant force can sometimes be represented by a single force, and state why the same reduction is not always possible in three dimensions.

Choose one

1 point

Two forces have components $(2,3)\ \text{kN}$ and $(3,-4)\ \text{kN}$ . An applied couple is also present. What is the resultant force of the system?

A
$\mathbf{R}=(5,-1)\ \text{kN}$
B
$\mathbf{R}=(5,1)\ \text{kN}$
C
$\mathbf{R}=(2,-1)\ \text{kN}$
D
$\mathbf{R}=(2,1)\ \text{kN}$

True or false

1 point

True or false: A force system with both zero resultant force and zero resultant moment is in equilibrium as a rigid-body loading system.

A
True
B
False

Written response

1 point

At $O$ , a $4\ \text{kN}$ force acts in the positive $x$ -direction at $(0,2)\ \text{m}$ , a $3\ \text{kN}$ force acts downward at $(3,0)\ \text{m}$ , and a $2\ \text{kN}\cdot\text{m}$ counterclockwise couple is applied. What is the signed resultant moment about $O$ , taking counterclockwise as positive?

Written response

1 point

An equivalent planar system has $M_O=10\ \text{N}\cdot\text{m}$ , $\mathbf{r}_{OP}=(2,0)\ \text{m}$ , and $\mathbf{R}=(0,3)\ \text{N}$ . Using counterclockwise moments as positive, what is the moment $M_P$ at point $P$ ?

Choose one

1 point

A force’s position vector from O points along $+x$ , and the force points along $+y$ . In which direction does the moment about O point?

A
$-z$ direction
B
$+y$ direction
C
$+z$ direction
D
$-x$ direction

Choose one

1 point

A force acts at a point whose position vector from O is parallel to the force. What is the force’s moment about O?

A
The moment is zero because the position vector and force are parallel.
B
The moment has its greatest possible magnitude because the vectors are parallel.
C
The moment is nonzero and points along the force.
D
The moment is nonzero and points opposite to the position vector.

Choose one

1 point

A force of fixed magnitude acts at a point a fixed distance from O. As the force direction changes, when is the magnitude of its moment about O greatest?

A
It is largest when the vectors are parallel.
B
It is the same for every angle because $r$ and $F$ are fixed.
C
It is largest when the angle is $0^\circ$ .
D
It is largest when the vectors are perpendicular.

Choose one

1 point

A resultant force has components $\mathbf{R}=(-6,8)$ kN. Which choice gives both its magnitude and its quadrant in the standard $x$ - $y$ coordinate system?

A
10 kN in Quadrant II
B
10 kN in Quadrant IV
C
14 kN in Quadrant II
D
10 kN in Quadrant III