527 Appendix B Sample Calculation of the Elastic Modulus The sample calculation below was done assuming a circular hair with a diameter of 60 μm using typical numbers for a virgin hair extended at 50% relative humidity. 1) E = Stress/Strain = Δ F*L/(ΔL*A) a) Δ F is change in force during length change ΔL b) L is length of fiber c) A is the cross-sectional area 2) Assume circular hair is 60 μ in diameter: a) A = 2.83 x 10-5 cm2 = 2.83 x 10-9m2 3) A 10-cm length is extended to 10.2 cm a) 2% extension 4) Force change is 22 grams-force = 0.216 N a) 1 Gram force = 980 dynes = 9.8 x 10-3 N 5) E = (0.216 x 10 cm)/(0.2 cm x 2.83 x 10-9 m2) 6) E = 3.8 x 109 N/m2 7) 1 Pascal = 1Newton/m2 , 1N = 105 dynes, 1m2 = 104 cm2 8) E = 3.8 x 109 Pa = 3.8 x 109 N/m2 = 3.8 GPa 9) In older papers E is usually called Y and is reported in dynes/ cm2 10) Y = E = 3.8 x 1010 dynes/cm2 APPENDIX B