7.2MechanicsStretch

Modelling with Statics

Real situations — a hanging sign, a suspended mass, a sloped support — are modelled with static equilibrium. The skill is drawing a clear force diagram and choosing helpful directions to resolve in.

22 min Video by Zeeshan Zamurred Applications of Forces

Edexcel A Level Maths: 7.1-7.2 Statics and ModellingWatch the full walkthrough before the notes below.

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What you'll be able to do

Draw a force diagram for a model
Identify all forces acting
Choose convenient resolving directions
Solve the resulting equations

Building the model

Start with a force diagram showing weight, tensions, reactions and any applied forces. Then resolve in directions that make the algebra simplest — often along and perpendicular to a string or slope.

force diagram \to resolve \to \sum F = 0

Modelling workflow.

1Weight downward, two tensions along the strings.

2Resolve horizontally and vertically; set each to zero.

AnswerWeight + two tensions; ΣF = 0 in two directions.

Tip — Choose resolving directions along unknown forces to simplify the equations.

Formula recap

\sum F = 0

Equilibrium of the model.

W = m g

Weight of a mass.

Common mistakes to avoid

Omitting a force from the diagram.

Include weight, tensions, reactions and applied forces.

Always resolving horizontally/vertically even when awkward.

Resolve along the most convenient directions.

Key takeaways

Draw a complete force diagram first.
Resolve in convenient directions; set ΣF = 0.
Weight of a mass is W = mg.

Test yourself

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