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A three-legged wooden bar stool made out of solid Douglas fir (the Young's modulus is 1.0×1010N/m2)...

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Physics

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 indiameter.

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

Express your answer in percent.

Answer & Explanation Solved by verified expert
4.1 Ratings (863 Votes)

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.....!!
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