Engineering Mechanics - System of Forces Study Guide

Fill-in-the-blank practice flashcards generated from the System of Forces study guide.

Standard notation uses __________ for force, $m$ for distance, and $N\,m$ for moment.

$$N$$

For a force $F$ making an angle $\theta$ counterclockwise from the positive x-axis, its horizontal component is given by $F_x = {\_\_\_\_\_\_\_\_\_\_}$.

$$F \cos(\theta)$$

For a force $F$ making an angle $\theta$ counterclockwise from the positive x-axis, its vertical component is given by $F_y = {\_\_\_\_\_\_\_\_\_\_}$.

$$F \sin(\theta)$$

In component sign conventions, force arrows pointing right or up are assigned __________ values.

positive

The magnitude of the resultant force $R$ from components $R_x$ and $R_y$ is calculated as $R = {\_\_\_\_\_\_\_\_\_\_}$.

$$\sqrt{R_x^2 + R_y^2}$$

To keep the correct quadrant when calculating the direction angle $\theta$ of a resultant force, the two-argument function __________ is used.

$$\text{atan2}(R_y, R_x)$$

A force system is defined as __________ when all lines of action meet at one point.

concurrent

When combining Force A ($100\,N$ at $30^\circ$) and Force B ($80\,N$ at $120^\circ$), the calculated horizontal component $R_x$ equals __________.

$$46.60\,N$$

To locate the line of action $x_R$ for a set of vertical parallel forces, the moment balance equation gives $x_R = {\_\_\_\_\_\_\_\_\_\_}$, provided $R \neq 0$.

$$\frac{\sum M_O}{R}$$

Under the common sign convention for moments in a plane, a clockwise rotation sense is assigned a __________ value.

negative

The theorem stating that the moment of a force about a point equals the sum of the moments of its components about that same point is the __________.

Varignon theorem

A couple consists of two equal, opposite, parallel forces; its resultant force is __________.

zero

The moment magnitude of a couple formed by two forces of magnitude $F$ separated by distance $s$ is $M = {\_\_\_\_\_\_\_\_\_\_}$.

F s

The force that balances a force system is the equilibrant $E$, which relates to the resultant force $R$ by $E = {\_\_\_\_\_\_\_\_\_\_}$.

-R

Lami theorem states that for three coplanar, concurrent, and non-parallel forces in equilibrium, $\frac{F_1}{\sin(\alpha)} = \frac{F_2}{\sin(\beta)} = {\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{F_3}{\sin(\gamma)}$$

Lami theorem can only be used when a particle is held in equilibrium by exactly __________ coplanar, concurrent, and non-parallel forces.

three

For a rigid body in 2D equilibrium, the rotational equilibrium requirement about any point O is __________.

$$\sum M_O = 0$$