Flashcards · 9702 · AS Topic 6

Deformation of solids (AS Level) flashcards

12 cards on AS Topic 6, subtopics 6.1 to 6.2. Pick a subtopic or study them all.

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Hooke’s law, in full: The force applied is directly proportional to the extension produced, up to the limit of proportionality: F = kx, where k = F ÷ x is the spring constant (N m⁻¹).
Stress and strain: definitions and units: Stress = force ÷ cross-sectional area (Pa). Strain = extension ÷ original length (no unit).
Young modulus: E = stress ÷ strain = FL ÷ (Ax). Unit Pa. Found from the gradient of the straight-line region of a stress–strain graph.
Two wires of the same metal have different diameters. Which has the greater Young modulus?: Neither: the Young modulus is a property of the material. Only their spring constants (stiffness as objects) differ.
A wire 1.5 m long, area 2.0 × 10⁻⁶ m², extends 1.2 mm under 80 N. Find the Young modulus.: Stress = 80 ÷ 2.0 × 10⁻⁶ = 4.0 × 10⁷ Pa. Strain = 1.2 × 10⁻³ ÷ 1.5 = 8.0 × 10⁻⁴. E = 5.0 × 10¹⁰ Pa.
Young modulus experiment: why a long, thin wire, and why a reference wire?: Long: a measurable extension. Thin: a large stress for a modest load. Measure the diameter at several points with a micrometer. An unstretched reference wire alongside cancels effects such as thermal expansion.

Elastic deformation: The material returns to its original shape when the load is removed.
Plastic deformation: A permanent extension remains when the load is removed.
Put in order on a loading graph: elastic limit, breaking point, limit of proportionality, yield point: Limit of proportionality → elastic limit → yield point → breaking point. The elastic limit comes after the limit of proportionality.
Elastic potential (strain) energy: The area under the force–extension graph. Within the limit of proportionality, Ep = ½Fx = ½kx². For a non-linear graph, find the area.
A material is stretched beyond its elastic limit and unloaded. What does the area between the loading and unloading curves represent?: Energy dissipated (mostly as thermal energy) in permanently deforming the material. Only the area under the unloading curve is recoverable.
Brittle, ductile and polymeric materials: Brittle: breaks at the elastic limit with no plastic deformation (glass). Ductile: large plastic deformation before breaking (copper). Polymeric: very large extensions; loading and unloading curves differ (rubber).