Equilibrium in 2D (Edexcel A-Level Mathematics): Flashcards

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Equilibrium in 2D
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Equilibrium condition for horizontal forces

∑Fx=0\sum F_x = 0

Equilibrium condition for vertical forces

∑Fy=0\sum F_y = 0

Definition of a static body

Object in equilibrium where all forces sum to zero

Key approach for 2D equilibrium problems

Identify forces → Resolve components → Apply ∑F=0\sum F = 0 → Solve

Value of sin⁡30∘\sin 30^\circ

12\frac{1}{2}

Value of cos⁡30∘\cos 30^\circ

32\frac{\sqrt{3}}{2}

Value of cos⁡60∘\cos 60^\circ

12\frac{1}{2}

Do mechanics concepts apply in 3D as well as 2D?

Yes, all concepts (equilibrium, F=maF=ma, SUVAT) apply in 3D

Equilibrium condition for particle in 3D

Sum of all force vectors equals zero vector

Formula for magnitude of 3D vector (x,y,z)(x, y, z)

x2+y2+z2\sqrt{x^2 + y^2 + z^2}

Tension in a light inextensible string

Same throughout the string

Purpose of resolving forces into components

To split forces into horizontal and vertical parts

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