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CAIE A-Level Further Mathematics 3.4.1 Hooke's Law

Practise converting length into extension and applying the modulus form of Hooke's law, then using the tension in equilibrium or an initial-acceleration equation.

Syllabus
2028–2030
Course
Further Mathematics 9231
Level
AS

Exam points

  • subtract natural length to obtain extension before substituting in the modulus tension formula
  • insert the resulting tension into equilibrium or Newton's second law with a stated direction

3.4.1—Hooke's law question 1

[Maximum number: 2]

One end of a light elastic string, of natural length a and modulus of elasticity 3 m g, is attached to a fixed point O. The other end of the string is attached to a particle P of mass m. The string hangs with P vertically below O. The particle P is pulled vertically downwards so that the extension of the string is 2 a. The particle P is then released from rest.

Find the initial acceleration of P when it is released from rest.

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