Question$1$:

a$)$ The forces varies from $-2$ F to $5$ F for a solid cylindrical as shown in Figure below. The ultimate strength of the material is to be $700$ MPa with a factor of safety of $2.$ Determine the magnitude of $\text{'}$ F $\text{'}$ when $\backslash (\backslash$mathrm$\{$k$\}\_\{\backslash$mathrm$\{$b$\}\}\backslash )$ is $\backslash (0\mathrm{.}85,\backslash$mathrm$\{$k$\}\_\{\backslash$mathrm$\{$c$\}\}\backslash )$ is $0\mathrm{.}89,$ q is $0\mathrm{.}9$ and $\backslash (\backslash$mathrm$\{$k$\}\_\{\backslash$mathrm$\{$t$\}\}\backslash )$ is $1\mathrm{.}42.$ b$)$ The forces varies from $-2$ F to $5$ F for a solid cylindrical as shown in Figure below. The ultimate strength of the material is to be $700$ MPa with a factor of safety of $2.$ Determine the magnitude of $\text{'}$ F $\text{'}$ when $\backslash (\backslash$mathrm$\{$k$\}\_\{\backslash$mathrm$\{$b$\}\}\backslash )$ is $0\mathrm{.}85,\backslash (\backslash$mathrm$\{$k$\}\_\{\backslash$mathrm$\{$c$\}\}\backslash )$ is $0\mathrm{.}89,$ q is $0\mathrm{.}9$ and $\backslash (\backslash$mathrm$\{$k$\}\_\{\backslash$mathrm$\{$t$\}\}\backslash )$ is $1\mathrm{.}42.$