Question

When a 85 kg man sits on the stool, by what percent does the length of the legs decrease? assume, for simplicity, that the stool's legs are vertical and that each bears the same load?

Answer 1

Find stress using the formula Stress = Force / Area. Here, force exerted by 85kg person on stool is F = mg = 85kg * 9.8 m/s^2 = 833N. Find total area of 3 legs A = 3 π (D/2)^2 = 3 π (2.5 x 10^-2 / 2)^2 = 1.4726 x 10^-3 m^2. Now substitute in Stress = Force/Area. Stress = 833N / 1.4726 x 10^-3 m^2 = 5.656 x 10^5 N/m^2. Find strain using the formula strain = Stress / Young’s modulus. For wood, Y = 1.3 x 10^10 N/m^2. Thus, strain = 5.656x10^5 N/m^2 / 1.3x10^10 N/m^2 = 4.35 x 10^-5 = 0.00435%. 

Therefore, the legs decrease by 0.00435%