Question $2$

A $9\mathrm{.}5$ inch diameter basketball is inflated to $10$ psi. If the basketball material has a Young's modulus of $4$ MPa and a Poisson ratio of $0\mathrm{.}45$:

a$)(2$ marks$)$ Normal strain in a spherical pressure vessel can be related to the stress we studied in class with the following equation: $\backslash (\backslash$varepsilon$\_\{\backslash$text $\{$normal $\}\}=\backslash$frac$\{\backslash$sigma$(1-$v$)\}\{$E$\}\backslash ).$ The reason for the extra factor $\backslash (1-$v $\backslash )$ is to account for the fact that the normal strain occurs in both directions $($ie$.2$D$)$ across the skin of the spherical shell. Using this equation determine the wall thickness of the basketball if the normal strain in the ball must be kept below $0\mathrm{.}42.$ Provide your numerical answer on Blackboard in mm$,$ and use two decimal places.

The wall thickness of the basketball is Blank $1$ mm $.$

b$)(2$ marks$)$ If you were designing higher quality ball with a wall thickness of $2$ mm $,$ calculate the stress and normal strain in the ball. Assume the same parameters from earlier in the problem apply. Provide your numerical answer on blackboard for stress in MPa and provide both numbers to two decimal places.

The stress on the basketball is Blank $2$ MPa $.$

The normal strain on the basketball is Blank $3.$

B

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