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Edexcel A-Level Mathematics A2 M3.2.1 Elastic Strings and Springs Questions

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

Edexcel A-Level Mathematics A2 M3.2.1 Elastic Strings and Springs Questions 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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