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CAIE A-Level Further Mathematics 3.2 Rigid Body Equilibrium

Practise locating centres of mass, resolving coplanar forces and taking moments, then applying limiting friction or contact-edge conditions to sliding and toppling.

Syllabus
2028–2030
Course
Further Mathematics 9231
Level
AS

Exam points

  • take moments of component areas or volumes to locate the combined centre of mass
  • resolve forces and set the net moment to zero about a point that removes unknown reactions
  • at limiting equilibrium, apply friction or move the weight line through the contact edge

Covered syllabus points

3.2.1—Moments3.2.2—Centre of mass3.2.3—Centre of mass3.2.4—Centre of mass3.2.5—Rigid body equilibrium3.2.6—Toppling and sliding

3.2 Equilibrium of a rigid body question 1

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Figure for Question 3.2 Equilibrium of a rigid body question 1 — CAIE A-Level Further Math AS

A uniform square lamina ABCD has sides of length 10 cm. The point E is on BC with EC=7.5 cmE C=7.5 \mathrm{~cm}, and the point F is on DC with CF=x cmC F=x \mathrm{~cm}. The triangle EFC is removed from ABCD (see diagram). The centre of mass of the resulting shape ABEFD is a distance xˉ cm\bar{x} \mathrm{~cm} from CB and a distance yˉ cm\bar{y} \mathrm{~cm} from CD.

Question (a)

(a)

Show that xˉ=400−x280−3x\bar{x}=\frac{400-x^{2}}{80-3 x} and find a corresponding expression for yˉ\bar{y}.

The shape ABEFD is in equilibrium in a vertical plane with the edge DF resting on a smooth horizontal surface.

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Question (b)

(b)

Find the greatest possible value of x, giving your answer in the form a+b2a+b \sqrt{2}, where a and b are constants to be determined.

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