Stress, Strain, and Elastic Energy

Vocabulary flashcards covering stress, strain, Hooke's law, spring combinations, elastic strain energy, and the Young modulus.

Compressive Forces

Forces that squash a material, changing its shape or dimensions.

Tensile Forces

Forces that stretch a material, causing tensile stress and strain.

Tensile Stress

Force per unit cross-sectional area applied to a material, defined by $\sigma = \frac{F}{A}$ and measured in $\text{N}\,\text{m}^{-2}$ or $\text{Pa}$.

Tensile Strain

The extension of a material compared with its original length, defined by

$\varepsilon = \frac{e}{l}$, having no units.

Ultimate Tensile Stress

The largest stress a material can withstand before breaking.

Steel Breaking Strain

The strain value at which steel breaks, which is about $0.01$.

Spider Silk Breaking Strain

The strain range at which spider silk breaks, which is between about $0.15$ and $0.30$.

Stress-Strain Gradient Comparison

On a stress-strain graph, line a has a steeper gradient indicating a stiffer material with a higher Young modulus than line b.

Elastic Strain Energy Density

Energy stored per unit volume in a deformed material, equal to the area under a stress-strain graph and given by $E = \frac{1}{2} \times \text{stress} \times \text{strain}$ .

Hooke's Law

The principle stating that extension is directly proportional to applied force ($F \propto e$) within the elastic limit.

Spring Constant

A measure of the stiffness of a spring or material, defined as $k = \frac{F}{e}$ with units of $\text{N}\,\text{m}^{-1}$.

Area Under Force-Extension Graph

Represents the total work done on the material or stored elastic strain energy, calculated as $E = \frac{1}{2}Fe$.

Springs in Series

A spring arrangement where

$$\frac{1}{k_T} = \frac{1}{k_A} + \frac{1}{k_B}$$

; for two identical springs

$k_T = \frac{k}{2}$,

making the combination more stretchy.

Springs in Parallel

A spring arrangement where $k_T = k_A + k_B$; for two identical springs $k_T = 2k$, making the combination less stretchy.

Spring Combination Arrangements

Visual representation comparing a single spring, two springs connected in series (more stretchy), and two springs connected in parallel (less stretchy) under load.

Elastic Strain Energy Formulas

Formulas for total energy stored in a stretched material: $E = \frac{1}{2}Fe$ and $E = \frac{1}{2}ke^2$.

Young Modulus

A measure of material stiffness defined as the ratio of tensile stress to tensile strain

$$E=\frac{\text{stress }}{\text{strain}}=\frac{Fl}{Ae}$$

measured in $\text{N}\,\text{m}^{-2}$ or $\text{Pa}$.

Experimental Setup for Young Modulus

Laboratory arrangement consisting of a wire held by a G-clamp, passing over a pulley to carry loads, measured with a metre rule and sticky tape pointer.

Searle's Apparatus

An alternative experimental apparatus used to measure the Young modulus with higher precision using extension-force measurements.