Question

A three-legged wooden bar stool made out of solid Douglas fir (the Young's modulus is 1.0×1010N/m2) has legs that are 2.0 cm in diameter.

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.

Express your answer in percent.

Answer 1

Mass   m = 85 kg

diameter of the stool d = 2.0 cm

= 0.020 m

   Y = F /A ( L₀/ΔL )

        ΔL /L₀ = F / A Y

                    = ( w / 3 ) / pi r^2 Y = mg / 3pi( d/2 )^2 Y

                                                  = 4 mg / 3pi d^2 Y

          Y is the young's modulus Y =1*10^10 N /m²

= (4 * 85 * 9.81) / (3 pi * 0.020^2 * 1 * 10^10)

                              = 8.847 *10^-5 m

  percentage change = 0.0088 % (Answer)

I hope help you.....!!