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

Practise applying Hooke's law to elastic strings and springs, equating tensions, resolving forces, finding equilibrium positions and calculating acceleration at release.

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: 4]
Figure 1

Figure 1

A light elastic spring has natural length l and modulus of elasticity λ\lambda.
One end of the spring is attached to a point A on a smooth plane.
The plane is inclined at angle θ\theta to the horizontal, where tan⁡θ=512\tan\theta=\frac5{12}.
A particle P of mass m is attached to the other end of the spring.
Initially P is held at the point B on the plane, where AB is a line of greatest slope of the plane.
The point B is lower than A and AB=2l, as shown in Figure 1.
The particle is released from rest at B and first comes to instantaneous rest at the point C on AB, where AC=0.7l.

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

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