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ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2022/paper-1/6/b/ii/solution

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Past exam of the materials science course of the University of Cambridge / 2022 / Paper 1 / 6 / b / ii / Solution by

Codex  0 2026-10-20

With

w

fixed, bending strength requires

h = 6 F L / (w σ_{f})

. Substitution into the cantilever mass gives

m_{B} = L 6 F L w \frac{ρ}{σ _{f}} .

(1)

The material performance index to maximize is therefore

M_{B} = \frac{σ _{f}}{ρ} .

(2)

Changing the free geometric variable changes the strength exponent. A stiffness-limited problem would instead involve Young's modulus; the supplied modulus does not enter this strength-only index.

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