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Pearson Edexcel IAL Mathematics M3.2 Elastic strings & springs Question Bank

Practise modelling elastic strings and springs with Hooke's law, equilibrium, acceleration and energy changes for particles released from rest.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • form Hooke's law tensions from extensions and use equilibrium to prove lengths
  • resolve forces along a string or plane to find acceleration after release from rest
  • use elastic energy with GPE and KE to find speeds or prove a modulus value

Covered syllabus points

M3.2.1 - Elastic strings and springsM3.2.2 - Energy stored in elastic strings and springs

M3.2 - Elastic strings and springs question 1

[Maximum number: 4]
Figure 2

Figure 2

A smooth bead of weight 12 N is threaded onto a light elastic string of natural length 3 m. The points A and B are on a horizontal ceiling, with AB=3 mA B=3 \mathrm{~m}. One end of the string is attached to A and the other end of the string is attached to B.

The bead hangs freely in equilibrium, 2 m below the ceiling, as shown in Figure 2.

Question (a)

(a)

Show that the modulus of elasticity of the string is 11.25 N .

The bead is now pulled down to a point vertically below its equilibrium position and released from rest.

[ 2 ]

Question (b)

(b)

Find the elastic energy stored in the string at the instant when the bead is moving at its maximum speed.

[ 2 ]
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