Stress, Strain and the Young Modulus
Section: Deformation of Solids | Syllabus: Cambridge AS Level Physics 9702
Stress, Strain and the Young Modulus To compare materials independent of their dimensions, we use stress and strain. Figure 6.7: Effect of Dimensions ((a) Larger cross-sectional area extends less for same force.
(b) Longer wire extends more for same force.) Definitions Stress (σ) : Force per unit cross-sectional area. σ = fraction (Unit: Pa or N m^-2) Strain () : Extension per unit original length. = fraction (Dimensionless / %) Young Modulus (E) : Measure of stiffness.
Ratio of stress to strain (within limit of proportionality). E = fraction = fraction (Unit: Pa or GPa) Worked Example: Harp String Question: A nylon string (A = 8.11 × 10^-7 m^2, L = 0.477 m) extends by 6.2 mm under 67 N tension.
Calculate the Young Modulus. Answer E = fraction = fraction) × (8.11 × 10^-7) = 6.4 × 10^9 Pa (6.4 GPa). Experimental Skills 6.2: Finding Young Modulus Using a long suspended wire to measure small extensions.
Figure 6.8 & 6.10: Young Modulus Apparatus (Show wire clamped over a pulley with a marker and scale, OR Searle's apparatus with reference wire and vernier scale. Label: Micrometer, Test Wire, Load.) Measure diameter with a micrometer (multiple readings/orientations) to find Area.
Measure original length with a rule. Measure extension (using marker or vernier scale) for various loads. Plot Force vs Extension (or Stress vs Strain). Gradient helps find E. Experimental Skills 6.3: Oscillating Rod Another method involves measuring the period of oscillation (T) of a loaded rod.
T^2 1/E. Figure 6.11: Oscillating Rod (Cantilever rod clamped at one end, mass at other end oscillating vertically.)
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