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Pearson Edexcel IAL Mathematics M3.2.1 Elastic strings & springs

Practise using Hooke's law for elastic strings and springs to find tensions, extensions, equilibrium positions and initial accelerations.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • form T=λx/l from the extension and equate tensions or resolve forces
  • apply F=ma at release to find the initial acceleration from tension and weight

M3.2.1 - Elastic strings and springs question 1

[Maximum number: 2]
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.

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.

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