Question
A beam of rectangular cross section is to be cut from a log 1.00 m
in diameter. The stiffness of the beam varies directly as the width
and the cube of the depth. What dimensions will give the beam
maximum stiffness?
in diameter. The stiffness of the beam varies directly as the width
and the cube of the depth. What dimensions will give the beam
maximum stiffness?
Answers
If the beam has dimensions x and y, then x^2+y^2 = 1
so the stiffness is
s = kx(1-x^2)^(3/2)
now find where ds/dx = 0
so the stiffness is
s = kx(1-x^2)^(3/2)
now find where ds/dx = 0
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