Hooke’s Law


Hooke’s Law says extension is proportional to forc

Metal wire supported at the top with a weight attached at the bottom stretches. Weight pulls down with force (F), producing an equal and opposite force at the support.
Robert Hooke discovered extension of a stretched wire (x) is proportional to the load or force (F).
F = kx (k=force or stiffness constant in Nm^-1)
Stretching a material creates tension across it. Forces of tension act along same line as forces stretching material but in the opposite direction at each end - they ‘pull’ on the object at either end.

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Hooke’s Law also applies to springs

Metal springs change length when a pair of opposite forces are applied.
Extension of a spring is proportional to force applied. If forces are compressive, spring is squashed - extension is negative.
For springs, k can also = spring stiffness or spring constant.
Tensile forces stretch the spring.
Compressive forces squash the spring.
Hooke’s Law works for compressive forces as well as tensile forces. For a spring, k has the same value.
All other materials obey Hooke’s Law up to a point,

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Hooke’s Law stops working when the load is great e

Graph showing force against extension for a typical metal wire or spring.
First part shows Hooke’s Law being obeyed - straight line relationship between force and extension.
Force becomes great enough - graph begins to curve. Metals obey Hooke’s Law up to the limit of proportionality (P).
Elastic limit is exceeded - material will be permantley stretched. All forces removed - material will be longer than in the beginning.
Beyond elastic limit - material stretches further for a given force.
Some materials (e.g rubber) only obey Hooke’s Law for really small extensions.

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A stretch can be elastic or plastic

Materials show elastic deformation up to their elastic limit, and plastic deformation beyond it.

Deformation = elastic - material returns to original shape.
Material is put under tension - atoms of material are pulled apart from one another. Atoms can move slightly relative to their equilibrium positions without changing position. Load is removed - atoms return to their equilibrium distance apart.

Deformation = plastic - material is permanently stretched.
Some atoms move position relative to one another. Load is removed - atoms don’t return to original postitions.

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You can investigate extension by stretching an obj

Set up clamp stand with clamp and hang object under investigation off clamp and attach weights to it. Have a ruler attached to the clamp stand to measure extension.
Add masses one at a time, measure the new length then calculate extension: extension = new length - original length.
Plot a graph of force against extension. Where line of best fit = straight - object obeys Hooke’s Law, gradient = k. Loaded the object beyond limit of proportionality - graph starts to curve.

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