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1 markMechanical Properties of Materials

CAPE Physics Unit 1 · May/June 2026 · Paper 2 · Question 3(d)(iii)

A bench has two wooden cylindrical legs differing in length by d = 0.50 mm. The shorter leg has length 1.0 m. The bench is loaded with 290 kg so that both legs are compressed and no wobbling occurs. The legs have cross-sectional area a = 1.0 cm² and Young's modulus E = 1.3 × 10¹⁰ N m⁻². The short and long legs are compressed by ΔL_short and ΔL_long respectively.

Assume that the force acting on the long leg is F_long. Deduce the equation to show the relationship between F_long and ΔL_long.

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Other parts of this question

  1. 3(a)Complete the table by inserting ONE difference between crystalline and non-crystalline solids in terms of structure and properties, and give ONE example of…[6 marks]
  2. 3(b)With the aid of a diagram, describe a simple experimental procedure that could be used to determine the Young's modulus of a length of sample wire.[6 marks]
  3. 3(c)Define the terms 'tensile stress' and 'tensile strain'.[4 marks]
  4. 3(d)(i)Write an expression to show the relationship between ΔL_short and ΔL_long.[1 mark]
  5. 3(d)(ii)Assume that the force acting on the short leg is F_short. Deduce the equation to show the relationship between F_short and ΔL_short.[2 marks]
  6. 3(d)(iv)Calculate the values of ΔL_short and ΔL_long.[7 marks]
  7. 3(d)(v)Hence, determine the values of F_short and F_long.[3 marks]

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