A three-legged wooden bar stool made out of solid Douglas fir has legs that are 2.0 in diameter?
Tuesday, January 24th, 2012 at
9:07 pm
When a 75 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.
Tagged with: legs • simplicity
Filed under: Your Community Center
Like this post? Subscribe to my RSS feed and get loads more!
I’ll assume that you mean a 75 kg man?
You’ll need to know the elastic modulus (or "Young’s" modulus) for douglas fir. That’s the stiffness in tension and compression for a material. I looked it up in a couple of places: http://www.csudh.edu/oliver/chemdata/woods.htm has it at 1357 kg/mm^2 for "coast type" and 981 kg/mm^2 for "mountain type"; http://www.engineeringtoolbox.com/young-modulus-d_417.html lists it at 13,000,000,000 N/m^2 (which is 13,000 N/mm^2, or a lot closer to "coast type", so let’s use that here. I’d look in your text to see if there is a value given and use that.
The key formula is modulus = stress / strain, where strain is change in length/original length.
Stress = Force / Area.
The 75 kg man exerts a force of 75kg x 9.81 m/s^2 = 736 N on the stool.
The total area of the legs (in mm^2) is 3 x pi x R^2 = 3 x pi x (50.8/2)^2 = 6080 mm^2
So stress = 736 N / 6080 mm^2 = 0.121 N/mm^2
now the Strain = stress/modulus = 0.121 N/mm^2 / 13,000 N/mm^2 = 0.0000093, or 0.00093% change in length.