On a force diagram, what does each arrow show, and where is the size of the force written?

Each arrow shows a force acting on the particle , and the way the arrow points is the direction in which that force acts. The magnitude of the force is written next to its arrow, in newtons.

True or False? A force diagram should show only the forces that the question mentions.

False. A force diagram shows every force acting on the particle, whether or not the question names it. Weight acts on anything with mass, a surface in contact always produces a normal reaction, and a rough surface produces friction. None of them has to be mentioned to be there.

Why are all the forces on a force diagram drawn acting at the same single point?

Forces are drawn at a single point because the object is modelled as a particle , which occupies a single point in space. That is why the normal reaction on a block is drawn from the middle of the block rather than from the surface it is resting on.

True or False? For a block resting on a slope, the weight is drawn perpendicular to the slope.

False. Weight always acts vertically downwards , whatever the surface underneath it is doing. It is the normal reaction that is perpendicular to the slope. On a slope the two are therefore not in opposite directions, which is why they do not simply cancel.

Define resultant force .

The resultant force is the sum of all the forces acting on a particle. It is the single force that would have exactly the same effect as all of those forces combined.

State Newton's first law of motion.

An object at rest stays at rest, and an object moving with constant velocity keeps moving with constant velocity, unless an unbalanced force acts on it . An unbalanced force is one that is not cancelled by another force in the opposite direction, so it leaves a resultant force that is not zero, and the object accelerates.

Define equilibrium , for a particle.

A particle is in equilibrium when the resultant force acting on it, the sum of all the forces, is zero . Every force is then cancelled by others, so the particle does not accelerate.

The resultant force on a particle is zero. What can you say about how it is moving?

The particle is either at rest or moving with constant velocity . A zero resultant force does not mean the particle is stationary. It means the particle is not accelerating, so whatever it was doing, it carries on doing.

Several forces acting on a particle in equilibrium are drawn one after another, nose to tail. What shape do they form, and why?

The forces form a closed polygon . Drawing them nose to tail takes you from the start of the first arrow to the end of the last, and that overall journey represents the resultant. In equilibrium the resultant is zero, so the path has to finish where it started.

True or False? The two perpendicular directions used in a two-dimensional problem must be horizontal and vertical.

False. Any two perpendicular directions can be used, and they are chosen to make the problem easiest. Horizontal and vertical are the usual choice, but for an object on a slope it is normally better to work parallel and perpendicular to the slope.

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Forces & Equilibrium (Edexcel A Level Maths: Mechanics): Flashcards

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On a force diagram, what does each arrow show, and where is the size of the force written?

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On a force diagram, what does each arrow show, and where is the size of the force written?
Each arrow shows a force acting on the particle, and the way the arrow points is the direction in which that force acts.
The magnitude of the force is written next to its arrow, in newtons.
Complete the letters normally used to label these forces on a force diagram:
weight $______$ N, friction $______$ N, normal reaction $______$ N.
Weight is labelled $W$ N, friction $F$ N and the normal reaction $R$ N.
A tension or a thrust is usually labelled $T$ N.
True or False?
A force diagram should show only the forces that the question mentions.
False.
A force diagram shows every force acting on the particle, whether or not the question names it.
Weight acts on anything with mass, a surface in contact always produces a normal reaction, and a rough surface produces friction. None of them has to be mentioned to be there.
Why are all the forces on a force diagram drawn acting at the same single point?
Forces are drawn at a single point because the object is modelled as a particle, which occupies a single point in space.
That is why the normal reaction on a block is drawn from the middle of the block rather than from the surface it is resting on.
A force diagram also carries an arrow labelled $a {m s}^{- 2}$ . What does it show, and why must it be kept separate from the force arrows?
The arrow shows the direction of the acceleration, not a force.
An acceleration must not be included when the forces are added up, so it is drawn differently from the force arrows to keep the two apart.
True or False?
For a block resting on a slope, the weight is drawn perpendicular to the slope.
False.
Weight always acts vertically downwards, whatever the surface underneath it is doing.
It is the normal reaction that is perpendicular to the slope. On a slope the two are therefore not in opposite directions, which is why they do not simply cancel.
Define resultant force.
The resultant force is the sum of all the forces acting on a particle.
It is the single force that would have exactly the same effect as all of those forces combined.
State Newton's first law of motion.
An object at rest stays at rest, and an object moving with constant velocity keeps moving with constant velocity, unless an unbalanced force acts on it.
An unbalanced force is one that is not cancelled by another force in the opposite direction, so it leaves a resultant force that is not zero, and the object accelerates.
Define equilibrium, for a particle.
A particle is in equilibrium when the resultant force acting on it, the sum of all the forces, is zero.
Every force is then cancelled by others, so the particle does not accelerate.
True or False?
Forces on a particle can only balance if the same number of forces act in each direction.
False.
What matters is the total force in each direction, not how many forces there are.
For example, forces of $7 N$ and $5 N$ acting to the right are balanced by a single force of $12 N$ acting to the left.
The resultant force on a particle is zero. What can you say about how it is moving?
The particle is either at rest or moving with constant velocity.
A zero resultant force does not mean the particle is stationary. It means the particle is not accelerating, so whatever it was doing, it carries on doing.
A sign hangs at rest, held up by two strings. Complete the equation used to find an unknown force:
total $______$ force = total $______$ force
total upward force = total downward force
For the sign, the two tensions added together equal its weight.
Complete the condition for a particle to be in equilibrium in two dimensions:
The resultant force must be $______$ in $______$ of the two perpendicular directions.
The resultant force must be zero in both of the two perpendicular directions.
If the forces balance in one direction but not the other, the particle is not in equilibrium: it accelerates in the direction that is unbalanced.
Several forces acting on a particle in equilibrium are drawn one after another, nose to tail. What shape do they form, and why?
The forces form a closed polygon.
Drawing them nose to tail takes you from the start of the first arrow to the end of the last, and that overall journey represents the resultant. In equilibrium the resultant is zero, so the path has to finish where it started.
True or False?
The two perpendicular directions used in a two-dimensional problem must be horizontal and vertical.
False.
Any two perpendicular directions can be used, and they are chosen to make the problem easiest.
Horizontal and vertical are the usual choice, but for an object on a slope it is normally better to work parallel and perpendicular to the slope.
A particle hangs in equilibrium, and a diagram shows the tensions in the strings holding it. Which force is missing from that diagram, and in which direction does it act?
The weight of the particle is missing, and it acts vertically downwards.
Its magnitude is $m g$ newtons. It is easy to leave out, because it is not one of the forces the diagram has labelled.
Before writing an equation for the forces acting in one direction, what must you decide, and how do you record it?
You must decide which direction you are taking as positive, and show that choice beside the equation.
An arrow such as $(\to)$ or $(↑)$ next to the working does it, and every force in that equation then takes a sign to match.
A force is $(- 2 i - 3 j) N$ . Find its magnitude.
The magnitude is $\sqrt{13} N$ , which is $3.61 N$ to 3 significant figures.
The two components are perpendicular, so Pythagoras' theorem gives:
$| F | = \sqrt{(- 2)^{2} + (- 3)^{2}} = \sqrt{13} N$
The signs disappear when the components are squared, so a magnitude is never negative.
How is the direction of a force in two dimensions usually given, and what is it measured from?
The direction is given as an angle, usually in degrees, measured anticlockwise from the positive horizontal direction.
So a direction of $216.9 °$ describes a force pointing down and to the left.
True or False?
A force given as $(3 i + 8 j) N$ tells you its magnitude and its direction straight away.
False.
Component form separates a force into its horizontal and vertical parts, so neither the magnitude nor the direction is shown directly.
The magnitude comes from Pythagoras' theorem, and the direction from a sketch and trigonometry.
A force is $(- 8 i - 6 j) N$ . Why does putting $\tan^{- 1} (\frac{- 6}{- 8})$ into a calculator not give its direction?
A calculator returns an angle between $- 90 °$ and $90 °$ , so it cannot distinguish between two opposite directions.
Sketch the components instead, find the acute angle from the sizes of the components, then adjust it. Here $\tan^{- 1} (\frac{6}{8}) = 36.9 °$ , and the force points down and to the left, so the direction is $180 ° + 36.9 ° = 216.9 °$ , measured anticlockwise from the positive horizontal direction.
What does the resultant force on a particle in equilibrium look like when the forces are written in component form?
The resultant force is the zero vector, written $0$ N.
In component form that is $0 i + 0 j$ , or as a column vector $(\begin{matrix} 0 \\ 0 \end{matrix})$ . Both components have to be zero separately, which is the vector form of the two equilibrium equations.
Two forces act on a particle and their resultant is $(- 2 i - 3 j) N$ . What third force would bring the particle into equilibrium?
The third force is $(2 i + 3 j) N$ .
All three forces must add to the zero vector, so the third force has both components of the existing resultant reversed.

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