Edexcel International A Level Maths: Mechanics 1

Revision Notes

3.1.3 Equilibrium in 2D

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Equilibrium in 2D

What does two dimensions (2D) mean in mechanics?

  •  In two dimensions, a particle may be considered as existing and being able to move around two-dimensional space rather than in a single straight line (1D)
    • This 2D space is called a plane – so you may see the 0xy plane mentioned
  • The directions of the two dimensions are chosen so that they are perpendicular to each other
  • The two directions are usually
    • horizontal and vertical, or
    • parallel and perpendicular to an inclined plane

What is the resultant force in 2D and an unbalanced force in 2D?

  • The resultant force in 2D is the sum of forces acting on a particle but this will now need to be considered in two parts – one for each direction
  • An unbalanced force is a force acting on a particle that whereby one or both parts are not cancelled by another force acting in the opposite direction
  • So a non-zero resultant force will be non-zero in at least one of the two dimensions, is therefore unbalanced and the particle will accelerate

What does equilibrium in 2D mean?

  • In two dimensions a particle is in equilibrium if the resultant force acting on it is zero
    • For example, if the two dimensions involved are the horizontal and vertical directions, a particle will be in equilibrium if any forces acting left are balanced by any forces acting right and any forces acting up are balanced by any forces acting down
  • When a particle has several forces (at least 3 – have a think as to why!) acting on it – and it is in equilibrium – the forces can be drawn “nose-to-tail” such that they form a polygon

3-1-3-fig1-four-forces-polygon

Worked example

3.1.3_WE_Equilibrium in 2D_1

(a)  Write down the resultant forces acting on the particle in both the horizontal and vertical directions.

3-1-3-fig2-we-solution-1

3-1-3-fig2-we-solution-a

(b)  Find the value of F.

3-1-3-fig2-we-solution-b

Exam Tip

  • Fnet is often used for resultant force in equations.
  • Sketching diagrams, or adding to any given in a question, can help you to understand a problem and pick up some marks.

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Paul

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Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.