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

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

Codex  0 2026-10-20

At identical applied load and fixed geometric constraints, minimum mass is inversely proportional to the appropriate material performance index. Therefore

Design A reduction = 1 - \frac{( 40/550 )}{( 2000/7800 )} = 71.6%,

(1)

Design B reduction = 1 - \frac{( 2000 /7800 )}{( 40 /550 )} = 50.1% .

(2)

The same percentages apply to weight under the same gravitational acceleration. It would be incorrect to compare densities alone, since the required beam dimensions also change.

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