All subjects · Mathematics · WME01 (M1)

Modelling assumptions in mechanics

Mechanics turns real objects into simple models. Every word such as light, smooth or particle is an assumption that changes the maths, and M1 questions often ask you to state or explain one.

Bodies

Strings, surfaces and pulleys

Pearson's conventions

M1 papers say: whenever a numerical value of g is required, take g = 9.8 m/s2, and give your answer to 2 or 3 significant figures. The reason is that 9.8 is only given to 2 s.f., so more figures would claim accuracy you do not have. Exact answers that do not use g (for example 13 m/s) can be left as they are. Always draw a clear force diagram and show the equation you form, because method marks depend on it.

Worked example

A box is pulled across a floor by a rope. State what is assumed by modelling the box as a particle and the rope as light and inextensible.

  1. Particle: the size of the box is ignored, so it does not rotate and all forces act at one point.
  2. Light: the rope has no mass, so the tension is the same throughout.
  3. Inextensible: the rope does not stretch, so the box moves with the rope.

Answer: Box: no size or rotation. Rope: same tension throughout and no stretching.

Key idea: Light means no mass (same tension), inextensible means same acceleration, smooth means no friction, uniform means weight at the centre. Use g = 9.8 and give 2 or 3 s.f.

Check yourself

  1. A string is modelled as light. What does this tell you?
    • The string cannot stretch
    • The tension is the same throughout the string
    • There is no friction on the string
    • The string has no length
    Show answer

    The tension is the same throughout the string. With no mass, there is no resultant force needed to accelerate the string, so the tension is constant along it.

  2. Two particles are joined by an inextensible string that stays taut. What follows?
    • They have equal masses
    • The tension in the string is zero
    • They experience equal friction
    • They have accelerations of equal size
    Show answer

    They have accelerations of equal size. The string does not stretch, so the particles move together with the same speed and acceleration magnitude.

  3. Where does the weight of a uniform rod act?
    • At the heavier end
    • At its midpoint
    • At either end
    • It depends on where it is supported
    Show answer

    At its midpoint. Uniform means the mass is spread evenly, so the centre of mass is at the midpoint.

  4. A particle slides on a surface modelled as smooth. Which force is ignored?
    • Weight
    • Normal reaction
    • Friction
    • Tension
    Show answer

    Friction. Smooth means friction is zero. The normal reaction still acts.

  5. Using g = 9.8 m/s2, find the weight of a particle of mass 0.35 kg, to 3 significant figures.
    Show answer

    3.43 N. W = mg = 0.35 × 9.8 = 3.43 N.

  6. Why do Pearson M1 mark schemes expect answers using g to 2 or 3 significant figures?
    • Calculators cannot show more figures
    • Answers to 4 s.f. are always wrong by a large amount
    • g = 9.8 is given to only 2 significant figures
    • The formulae booklet requires it
    Show answer

    g = 9.8 is given to only 2 significant figures. An answer cannot be more accurate than the data it uses, and g = 9.8 has 2 s.f.

  7. A ball is modelled as a particle. Which effect is therefore ignored?
    • The ball spinning
    • The weight of the ball
    • The mass of the ball
    • The ball's velocity
    Show answer

    The ball spinning. A particle has no size, so it cannot rotate, and effects of its size (such as spin) are ignored.

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Last updated 7 November 2026. Spotted a mistake? Tell us.