CAIE A-Level Further Math A2 3.4.3 Problems Involving Forces Due to Elastic Questions

Practise solving elastic-string and spring problems using extensions, energy, acceleration, friction and equilibrium with Further Mathematics Paper 2 questions and mark schemes.

Exam points

Apply de Moivre's theorem to powers and roots of complex numbers.

[Maximum number: 3]

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 speed of P when it is at a distance $\frac{3}{4} a$ below O.

$\frac{3 m g}{2 a}(2 a)^{2}$
Correct EPE term seen

$\frac{1}{2} m v^{2}+m g \times\left(3 a-\frac{3}{4} a\right)=\frac{3 m g}{2 a}(2 a)^{2}$
Dimensionally correct energy equation. Must have
one KE, one EPE term and at least one GPE.
Allow sign errors.

$v=\sqrt{\frac{15}{2} a g} \quad[2.74 \sqrt{a g}]$
AEF

3

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CAIE A-Level Further Math A2 3.4.3 Problems Involving Forces Due to Elastic Questions question 1