Engineering Mechanics - Statics Notes Flashcards

Vocabulary flashcards covering core definitions, fundamental laws, force system classifications, equilibrium types, Varignon's principle, and truss classifications from engineering mechanics statics lecture notes.

Statics

A branch of engineering mechanics that deals with forces and their effects on objects or bodies at rest.

Dynamics

A branch of engineering mechanics that deals with forces and their effects on bodies in motion.

Kinetics

A branch of dynamics that deals with bodies in motion due to the application of forces.

Kinematics

A branch of dynamics that deals with bodies in motion without reference to the forces responsible for the motion (e.g., velocity, acceleration).

Scalar Quantities

Quantities that have only magnitude (size) and no specific direction, such as mass, volume, time, speed, energy, and density.

Vector Quantities

Quantities that possess both a magnitude and a specific direction, such as force, displacement, velocity, and acceleration.

Mass

A quantitative measure of an object's inertia and resistance to a change in motion.

Coplanar Force System

A force system in which all the forces acting on a body lie in a single plane.

Concurrent Force System

A force system in which the lines of action of all forces pass through a single point.

Collinear Forces

A system of forces whose lines of action all act along the same line.

Coplanar Like Parallel Forces

Forces that are parallel to each other, lie in a single plane, and act in the same direction.

Newton's First Law of Motion

States that every body continues in its state of rest or of uniform motion in a straight line unless it is compelled by an external agency acting on it.

Newton's Second Law of Motion

States that the rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of the force acting on it ($\text{Force} = \text{mass} \times \text{acceleration}$).

Newton's Third Law of Motion

States that when one body applies a force $F$ on another, a reactive force $R$ develops which is equal in magnitude to $F$ but acts in the opposite direction.

Newton's Law of Gravitation

States that the force of attraction between any two bodies of mass $m_1$ and $m_2$ separated by distance $d$ is directly proportional to the product of their masses and inversely proportional to the square of the distance between them ($F = G \frac{m_1 m_2}{d^2}$).

Principle of Transmissibility of Forces

States that the effect produced by a force on a body remains unchanged if the force is transmitted from one point to another point along the same line of action.

Parallelogram Law of Forces

States that if two forces acting simultaneously on a particle are represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant is represented in magnitude and direction by the diagonal starting from their common point.

Moment of a Force

The tendency of a force to rotate a body about a point or an axis.

Couple

A system formed by two equal parallel forces that act in opposite senses to produce a pure turning action on a rigid body without translation.

Equilibrium

The state of a body subjected to external forces where it remains in a state of rest or constant velocity, satisfying \text{\Sigma} F = 0 and \text{\Sigma} M = 0.

Stable Equilibrium

An equilibrium condition where, after a small displacement, the body tends to return to its original position.

Unstable Equilibrium

An equilibrium condition where, after a small displacement, the body moves farther away from its original position.

Neutral Equilibrium

An equilibrium condition where, after a small displacement, the body remains in its new position.

Lami's Theorem

States that if three forces acting at a point are in equilibrium, each force is directly proportional to the sine of the angle between the other two forces.

Varignon's Principle

Also known as the principle of moments, it states that the moment of a force about any point is equal to the algebraic sum of the moments of its components about the same point.

Problem 3.2 Moment Calculation

Calculation of the moment about point O for a $100\,\text{N}$ force acting at point A, where perpendicular distance $OB = OC \sin(60^\circ) = 3 \times 0.866 = 2.598\,\text{m}$, resulting in a clockwise moment of $100 \times 2.598 = 259.8\,\text{N}\cdot\text{m}$.

Perfect Truss (Rigid Truss)

A truss containing a sufficient number of members to resist external loads with minimal deformation, satisfying $m = 2j - 3$, where $m$ is the number of members and $j$ is the number of joints.

Deficient Truss (Non-Rigid Truss)

A truss in which the number of members is less than that required for a perfect truss ($m < 2j - 3$).

Redundant Truss (Over Rigid Truss)

A truss in which the number of members is greater than that required for a perfect truss ($m > 2j - 3$).