What does \lambda represent?

The modulus of elasticity of the string or spring, in newtons.

What is the extension of a string?

Its stretched length minus its natural length.

Which can exert a thrust, a string or a spring?

A spring can (when compressed); a string cannot.

What do you do with two strings and an unknown position?

Let one extension be x, express the other string's extension in terms of x, then resolve forces.

What happens to tension in a remaining string when the other is cut?

It is unchanged at that instant because the length has not changed.

How do you find the acceleration of a particle on an elastic string?

Find T from Hooke's law, then apply F=ma to the resultant force.

Hooke's lawEdexcel A-Level Further Maths: Flashcards

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State Hooke's law for an elastic string.

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State Hooke's law for an elastic string.: $T=\frac{\lambda x}{l}$ : tension is proportional to extension.
What does $\lambda$ represent?: The modulus of elasticity of the string or spring, in newtons.
What is the extension of a string?: Its stretched length minus its natural length.
What is the tension in a string whose length is less than its natural length?: Zero: the string is slack.
Spring stiffness in terms of $\lambda$ and $l$ ?: $k=\frac{\lambda}{l}$ , so $T=kx$ .
Which can exert a thrust, a string or a spring?: A spring can (when compressed); a string cannot.
Tension in a string hanging a particle of mass $m$ in equilibrium?: $T=mg$
Thrust in a spring compressed by $x$ ?: $\frac{\lambda x}{l}$
Unit of modulus of elasticity?: Newton (N).
What do you do with two strings and an unknown position?: Let one extension be $x$ , express the other string's extension in terms of $x$ , then resolve forces.
What happens to tension in a remaining string when the other is cut?: It is unchanged at that instant because the length has not changed.
How do you find the acceleration of a particle on an elastic string?: Find $T$ from Hooke's law, then apply $F=ma$ to the resultant force.

Exam questions on Hooke's law

A particle of mass $2$ kg is attached to one end of a light elastic string of natural length $0.8$ m and modulus of elasticity $40$ N. The other end of the string is fixed to a ceiling and the particle hangs in equilibrium. Take $g=9.8$ m s $^{-2}$ .
The particle is replaced by a particle of mass $3$ kg. Find the length of the string when this particle hangs in equilibrium.2 marks
A light spring has natural length $0.6$ m and modulus of elasticity $30$ N. Take $g=9.8$ m s $^{-2}$ .
The spring stands vertically with one end fixed to the ground. A block of mass $1.5$ kg rests in equilibrium on its upper end. Find the length of the spring.2 marks
A particle $P$ of mass $0.5$ kg is attached to one end of a light elastic string of natural length $1.2$ m and modulus of elasticity $24$ N. The other end of the string is fixed to a point $O$ on a ceiling. Take $g=9.8$ m s $^{-2}$ .
The particle hangs in equilibrium. Find the extension of the string.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).