Angle of a\mathbf{i}+b\mathbf{j} with \mathbf{i}?

\tan\theta=\frac{b}{a} (check the quadrant)

What is the resultant of a set of forces?

The single force with the same effect as all of them; the vector sum.

How do you find the resultant of forces in component form?

Add the \mathbf{i} components and the \mathbf{j} components separately.

What does it mean to resolve a force?

To replace it by two perpendicular components with the same effect.

Components of a weight W on a slope of angle \alpha?

W\sin\alpha down the slope; W\cos\alpha into the slope.

A 20 N force at 60^\circ above the horizontal: horizontal and vertical components?

10 N and 10\sqrt{3}\approx17.3 N

Equilibrant of (-4\mathbf{i}+6\mathbf{j}) N?

(4\mathbf{i}-6\mathbf{j}) N, the same size and opposite direction.

Why must you state the direction you are resolving in?

Components can be positive or negative depending on the chosen direction.

Forces as vectors and resolving forcesEdexcel International A Level Maths: Flashcards

Card 1 of 120 of 12 known

Question

Component of a force $F$ at angle $\theta$ to a direction, along that direction?

Tap or press Space to reveal

Tap card or press Space to flip

See all 12 cards

Component of a force $F$ at angle $\theta$ to a direction, along that direction?: $F\cos\theta$
Component of $F$ perpendicular to that direction?: $F\sin\theta$
Magnitude of $a\mathbf{i}+b\mathbf{j}$ ?: $\sqrt{a^2+b^2}$
Angle of $a\mathbf{i}+b\mathbf{j}$ with $\mathbf{i}$ ?: $\tan\theta=\frac{b}{a}$ (check the quadrant)
What is the resultant of a set of forces?: The single force with the same effect as all of them; the vector sum.
How do you find the resultant of forces in component form?: Add the $\mathbf{i}$ components and the $\mathbf{j}$ components separately.
What does it mean to resolve a force?: To replace it by two perpendicular components with the same effect.
Components of a weight $W$ on a slope of angle $\alpha$ ?: $W\sin\alpha$ down the slope; $W\cos\alpha$ into the slope.
SI unit of force?: The newton (N).
A 20 N force at $60^\circ$ above the horizontal: horizontal and vertical components?: $10$ N and $10\sqrt{3}\approx17.3$ N
Equilibrant of $(-4\mathbf{i}+6\mathbf{j})$ N?: $(4\mathbf{i}-6\mathbf{j})$ N, the same size and opposite direction.
Why must you state the direction you are resolving in?: Components can be positive or negative depending on the chosen direction.

Exam questions on Forces as vectors and resolving forces

A force $\mathbf{F}$ of magnitude 20 N acts in the $x$ – $y$ plane at $60^\circ$ above the positive $x$ -axis. The unit vectors $\mathbf{i}$ and $\mathbf{j}$ are in the directions of the positive $x$ -axis and $y$ -axis.
Write $\mathbf{F}$ in the form $a\mathbf{i}+b\mathbf{j}$ , giving $a$ and $b$ exactly.2 marks
Two forces act on a particle: $\mathbf{F}_1=(3\mathbf{i}+4\mathbf{j})$ N and $\mathbf{F}_2=(-7\mathbf{i}+2\mathbf{j})$ N.
Find the angle between the resultant and the vector $\mathbf{j}$ , giving your answer to 1 decimal place.2 marks
Three forces act on a particle: $\mathbf{F}_1=(2\mathbf{i}-3\mathbf{j})$ N, $\mathbf{F}_2=(p\mathbf{i}+q\mathbf{j})$ N and $\mathbf{F}_3=(-\mathbf{i}+5\mathbf{j})$ N, where $p$ and $q$ are constants. The resultant of the three forces is $(6\mathbf{i}+4\mathbf{j})$ N.
Find the values of $p$ and $q$ .3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).