Force Diagrams (CIE A Level Maths: Mechanics)

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Force Diagrams

Why do we need force diagrams?

  • Force diagrams are used to help understand a given scenario and show which forces are acting on which particles and in which direction they are acting
  • In diagrams an arrow is used to represent a force acting on a particle which shows the direction in which the force is acting
  • The magnitude of the force is normally written next to its arrow

3-1-1-fig1-basic-force-diagrams

What types of forces could be involved?

  • Specific types of force encountered (which may not be mentioned in the question nor labelled on a given diagram) are: weight (W N), tension (T N), thrust (T N), friction (F N) and normal reaction (R N)

3-1-1-fig2-forces-on-a-block

  • Remember that the diagram is drawn to help understand the scenario - cars, blocks, etc are modelled as particles occupying a single point in space and so all forces acting on the car, block, etc act at that same single point
  • The main forces that you will see are:
    • tension (a “pulling” force) acts away from a particle,

      thrust (a “pushing” force) acts towards it

    • weight is W = mg where m kg  is the mass of the particle and g is the acceleration due to gravity – In the CIE A Level Mechanics modules the value of g is approximated to 10 space m space s to the power of negative 2 end exponent, unless told otherwise
    • friction acts parallel to the surface in the opposite direction to motion
    • the normal reaction acts perpendicular to the surface (and friction)

Worked example

3.1.1_WE_Force_1

3-1-1-fig3-we-solution

Examiner Tip

  • Always draw a force diagram if appropriate.
  • If a diagram is already given then add to it as you progress through the question.
  • If a diagram is too small or it gets too complicated then draw a new diagram.
  • You may be able to manage with just drawing the section of the diagram you are dealing with in any particular question part.

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Amber

Author: Amber

Expertise: Maths

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.