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LearnEdexcelYPH112018 specificationWPH11 · Unit 1: Mechanics and MaterialsMaterials

WPH11 · Module

Materials

4 subtopics≈ 135 min in total

Start the module: Stress, strain and the Young modulus Open graphing calculator

Stress, strain and the Young modulus
A spring or wire obeys Hooke's law, $F=kx$ , up to its limit of proportionality. To compare materials rather than particular objects, use stress ( $\sigma=\tfrac FA$ ) and strain ( $\varepsilon=\tfrac xL$ ). Their ratio in the linear region is the Young modulus, $E=\dfrac\sigma\varepsilon$ , a property of the material alone.
≈ 35 min
Density, pressure and upthrust
Pressure in a fluid increases with depth: $\Delta p=\rho g\Delta h$ . Because the pressure on the bottom of a submerged object is greater than on its top, there's a net upward force, the upthrust, equal to the weight of fluid displaced: $F=\rho gV$ . An object floats when the upthrust equals its weight.
≈ 35 min
Elastic and plastic behaviour
Below its elastic limit, a material returns to its original shape when the load is removed; beyond it, it's permanently (plastically) deformed. The work done stretching a material is the area under its force–extension graph, and within the limit of proportionality the stored elastic potential energy is $E_P=\tfrac12Fx=\tfrac12kx^2$ . Ductile materials deform plastically a lot before breaking; brittle ones snap.
≈ 30 min
Fluid flow and viscosity
Viscosity $\eta$ measures a fluid's resistance to flow. In laminar flow the layers slide smoothly; in turbulent flow they mix in eddies. A small sphere moving slowly through a fluid feels drag $F=6\pi\eta rv$ (Stokes' law). A falling sphere reaches terminal velocity when weight = upthrust + drag.
≈ 35 min