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anonymous

  • 5 years ago

The strenght of a rectangular beam is proportion to its width (w) and its square thickness (t) that is S=kwt^2, where k is a constant. Find the dimensions of the strongest beam that can be cut from a cylindrical log of radius 20cm.

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  1. anonymous
    • 5 years ago
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    It's been a long time since we reviewed optimization, so I might be wrong.... Solve for S'=0 to get the max strength and use this: (w^2+t^2)/2=r

  2. anonymous
    • 5 years ago
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    that should be w^2 + t^2 = (2r)^2 right?

  3. anonymous
    • 5 years ago
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    thank you for replyin but where did you get the (w^2+t^2)/2=r from? I understand to find the max strength we set s' to zero, but the second part you mentioned confused me o.0

  4. anonymous
    • 5 years ago
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    i dont think what he gave you is correct. draw a cross-section of the beam, a circle, a square inscribed in the circle, so the sides of the rectangle should be the width and thickness, and the diagonal of the rectangle is the diameter

  5. anonymous
    • 5 years ago
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    Yeah my bad. sorry. half the diagonal of a enclosed rectangle is the radius of the outside circle is what I was aiming for.

  6. anonymous
    • 5 years ago
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    hey INT are you sure you got that series question?

  7. anonymous
    • 5 years ago
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    okay no i understand, thank you guys so much!!

  8. anonymous
    • 5 years ago
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    *now

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