A three-legged wooden bar stool made out of solid Douglas firhas legs that are 2

Question

A three-legged wooden bar stool made out of solid Douglas firhas legs that are 2.5 cm in diameter. When a 70 kg man sits on thestool, by what percent does the length of the legs decrease?Assume, for simplicity, that the stool's legs are vertical and thateach bears the same load. A three-legged wooden bar stool made out of solid Douglas firhas legs that are 2.5 cm in diameter. When a 70 kg man sits on thestool, by what percent does the length of the legs decrease?Assume, for simplicity, that the stool's legs are vertical and thateach bears the same load. When a 70 kg man sits on thestool, by what percent does the length of the legs decrease?Assume, for simplicity, that the stool's legs are vertical and thateach bears the same load.

Explanation / Answer

Mass   m = 70 kg , diameter of the stool d = 2.5 cm                                                                        = 0.025 m    Y = F /A ( L0/L )         L /L0 = F / A Y                     = ( w / 3 ) / r2 Y = mg / 3( d/2 )2 Y                                                   = 4 mg / 3 d2 Y           Y is the young's modulus Y =1*1010 N /m2                                   = 4 * 70 kg * 9.81 m/s2 / 3 * ( 0.025 m)2 * 1*1010 N/m2                                 = 4.665 *10-5 m                 percentange of decrease in length L =4.665*10-3 m              

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