9231 · 3.4
Hooke's law flashcards
Revision flashcards for Cambridge 9231 Hooke's law (syllabus 3.4). Flip, recall, then mark a real past-paper question.
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What is Hooke's Law for an elastic string/spring?
The tension $T$ is proportional to the extension $x$. The formula is $T = \frac{\lambda x}{l_0}$, where $\lambda$ is the modulus of elasticity and $l_0$ is the natural length.
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What is the modulus of elasticity, $\lambda$?
A measure of the stiffness of an elastic object. It is the tension required to double the natural length of the string/spring, assuming it remains elastic. Its unit is Newtons (N).
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What is the 'natural length', $l_0$?
The length of an elastic string or spring when no forces are acting on it.
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How is 'extension', $x$, calculated?
Extension is the difference between the current (stretched) length and the natural length. $x = L - l_0$. It must be positive.
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What is the difference between tension and thrust?
Tension is the pulling force in a stretched string/spring. Thrust is the pushing force in a compressed spring. Elastic strings cannot experience thrust.
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What are the units of the modulus of elasticity, $\lambda$?
Newtons (N). This can be seen from the formula $T = \frac{\lambda x}{l_0}$, as $\lambda = \frac{T l_0}{x}$, giving units of $\frac{\text{N} \cdot \text{m}}{\text{m}} = \text{N}$.
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Common Trap: What value is often used incorrectly for $x$?
Using the total stretched length instead of the extension. Always calculate the extension $x = L - l_0$ first.
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What does it mean if an elastic string 'goes slack'?
The string's length has returned to or is less than its natural length. The tension in it immediately becomes zero.
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How does the modulus of elasticity $\lambda$ relate to the spring constant $k$?
The spring constant $k$ is the force per unit extension ($F=kx$). By comparing $T = kx$ with $T = \frac{\lambda x}{l_0}$, we see that $k = \frac{\lambda}{l_0}$.
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When does Hooke's Law not apply?
When the material is stretched beyond its 'elastic limit'. At this point, it deforms permanently and the linear relationship between force and extension breaks down.
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What is compression in a spring?
The reduction in length from its natural length. If a spring is compressed by an amount $x$, it exerts an outward thrust $T = \frac{\lambda x}{l_0}$.