General Science Quiz: Elasticity: Stress, Strain and Hooke's Law

Hooke found that so long as a body is not strained beyond its elastic limit, the restoring force per unit area rises in step with the fractional deformation, and the constant ratio of the two is called the modulus of elasticity.

Stress is the restoring force divided by the area over which it acts, so its unit is the newton per square metre, and that combination is given the special name pascal, the same unit used for pressure.

Strain is defined as the change in a dimension divided by the original value of the same dimension, a length divided by a length or a volume divided by a volume, so the units cancel and only a pure number survives.

It governs the stretching or compression of a wire or rod along its length and is obtained by dividing the force per unit area of cross section by the fractional change in length.

The bulk modulus measures how strongly a substance resists a change in volume under uniform pressure, so its reciprocal measures how readily the volume yields, and that quantity is called compressibility.

Elasticity in physics is not the ability to stretch far but the strength of the restoring tendency, measured by the stress needed to produce a given strain, and steel demands an enormously greater stress than rubber for the same fractional extension.

When a wire is pulled it lengthens and at the same time grows thinner, and Poisson's ratio records how large the sideways contraction is compared with the lengthwise extension; it is a pure number, with theoretical limits of minus one and one half and practical values of about 0.2 to…

The restoring force grows from zero to its final value as the wire is stretched, so the work done is the average force multiplied by the extension, and dividing by the volume of the wire leaves half the product of stress and strain as the energy stored in each unit…

Once a ductile specimen passes its ultimate tensile strength, the deformation stops being uniform and concentrates in one short length, which draws out into a narrow waist.

When the block is released suddenly it falls freely at first, so at the lowest point its speed is zero and all the gravitational potential energy it has lost has gone into the spring.

The two strips are joined and carry the load together, so they suffer the same strain. Since stress equals the modulus multiplied by the strain, the stress in steel is three times the stress in aluminium.

Breaking stress is the greatest force per unit area that a substance can bear before it snaps, and since both the force and the area are already accounted for in the definition, what remains is a constant of the substance itself, the same for a thin wire and a thick…