Mechanics 1: Statics and Vectors Flashcards

Comprehensive practice questions covering mechanics topics including vector addition, resolution of forces, moments, couples, equilibrium conditions, and stability based on the AQA specification.

What is the difference between a scalar quantity and a vector quantity?

A scalar quantity has magnitude ("size") only, whereas a vector quantity has both magnitude and direction.

List three examples of scalar quantities provided in the notes.

Examples include mass, distance, speed, time, energy, and temperature.

List three examples of vector quantities provided in the notes.

Examples include displacement, velocity, acceleration, force, and weight.

What does the term "resultant" mean in the context of forces?

It means finding the overall or total result, also sometimes referred to as the "net" force.

What does the term "coplanar" mean regarding vectors?

Coplanar means that the vectors lie in the same plane and can be drawn on a two-dimensional sheet of paper.

What is the standard rule for adding vectors graphically?

Vectors are added "nose-to-tail."

What are the two specific conditions that must be met for an object to be in equilibrium?

1. There is no resultant force acting on the object ($\Sigma F = 0$). 2. There is no resultant moment acting on the object ($\Sigma T = 0$).

How is a "moment of a force about a point" defined?

It is the product of the force and the perpendicular distance from the point to the line of action of the force ($\text{Moment} = F \times d$).

What is the unit of measurement for moments?

Newton-metres ($N \text{ } m$).

What is a "couple" in mechanics?

A pair of equal and opposite coplanar forces acting on a body that do not share a line of action.

How is the moment (torque) of a couple calculated?

It is the product of one of the forces ($F$) and the perpendicular separation ($d$) between the lines of action of the forces ($\text{Moment of a couple} = F \times d$).

State the Principle of Moments.

For an object in equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments taken about any point.

Define the "centre of mass" of an object.

The point at which the entire mass of the object can be considered to be concentrated.

Define the "centre of gravity" of an object.

The point through which the entire weight of the object can be said to act.

When resolving a force $F$ into components, what are the formulas for the horizontal and vertical components if the angle $\theta$ is measured from the horizontal?

$\text{Horizontal component} = F \times \text{cos}(\theta)$ and $\text{Vertical component} = F \times \text{sin}(\theta)$.

What is the general rule for an object toppling over?

An object will topple over if the centre of gravity is not directly above the base area.

What two features make an object less likely to topple over?

A wide base and a low centre of gravity.

When adding vectors that are not at right angles using a scale drawing, which tool is essential to quote the direction accurately?

A protractor.

On an inclined plane (ramp), what axes are typically chosen to simplify the resolution of forces?

Axes that are parallel and perpendicular to the slope.

If three coplanar forces are in equilibrium, what shape will they form when drawn nose-to-tail?

A closed triangle.