Direction of the normal reaction?

Perpendicular to the surface, away from it.

What is a light string?

A string with negligible mass; the tension is the same throughout.

The compressive force along a rod.

When does F=\mu R apply?

In limiting equilibrium, when the particle is on the point of slipping.

Effect on the normal reaction of pulling up at an angle?

It is reduced: R=W-T\sin\theta.

Effect on the normal reaction of pushing down at an angle?

It is increased: R=W+P\sin\theta.

What do you do for a particle on two strings?

Resolve horizontally and vertically and solve the two equations simultaneously.

Equilibrium of a particleEdexcel International A Level Maths: Flashcards

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Condition for a particle to be in equilibrium?

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Condition for a particle to be in equilibrium?: The resultant force is zero, so components sum to zero in every direction.
Formula for weight?: $W=mg$ , with $g=9.8$ m s $^{-2}$
Direction of the normal reaction?: Perpendicular to the surface, away from it.
What is a light string?: A string with negligible mass; the tension is the same throughout.
What is thrust?: The compressive force along a rod.
When does $F=\mu R$ apply?: In limiting equilibrium, when the particle is on the point of slipping.
What is the general friction condition?: $F\le\mu R$
Smooth slope at angle $\alpha$ : force $P$ up the slope holds weight $W$ . Find $P$ and $R$ .: $P=W\sin\alpha$ , $R=W\cos\alpha$
Horizontal force $H$ holds weight $W$ on a smooth slope at $\alpha$ . Find $H$ .: $H=W\tan\alpha$
Effect on the normal reaction of pulling up at an angle?: It is reduced: $R=W-T\sin\theta$ .
Effect on the normal reaction of pushing down at an angle?: It is increased: $R=W+P\sin\theta$ .
What do you do for a particle on two strings?: Resolve horizontally and vertically and solve the two equations simultaneously.

Exam questions on Equilibrium of a particle

A crate of mass 20 kg rests on a rough horizontal floor. A rope attached to the crate is pulled with a force of 50 N at $30^\circ$ above the horizontal, and the crate remains at rest. Take $g=9.8$ m s $^{-2}$ and model the crate as a particle.
The crate is on the point of slipping. Find the coefficient of friction between the crate and the floor.2 marks
A particle of weight 30 N is held in equilibrium on a smooth plane inclined at $30^\circ$ to the horizontal by a force of magnitude $P$ N acting up the slope, parallel to the line of greatest slope.
The force $P$ is removed and replaced by a horizontal force of magnitude $H$ N, so that the particle is still in equilibrium on the plane. Find $H$ .2 marks
A particle of weight 80 N is in equilibrium, supported by two light inextensible strings. One string has tension $T_1$ N and makes an angle of $30^\circ$ with the horizontal. The other has tension $T_2$ N and makes an angle of $60^\circ$ with the horizontal, on the opposite side of the particle.
By resolving horizontally, show that $T_2=\sqrt{3}\,T_1$ .3 marks

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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).