A rectangular slot of width $($w$/4)$ is cut through a piece of aluminum at half the total width $($w$)$ of the original bar as shown above. A force P is then applied at either end putting the bar into tension. Assume the material properties are known.

For this question, calculate all final numerical answers to THREE decimal places and submit these answers into the appropriate field in Blackboard.

a$)(4$ marks$)$ Find a formula$/$expression for the total elongation in the bar as a function of the force P $,$ Young's modulus E$,$ and the geometric quantities found in the diagram above.

b$)(2$ marks$)$ Assume $\backslash ($ E$=73\backslash$mathrm$\{$GPa$\}\backslash )$ and $\backslash ($ P$=50\backslash$mathrm$\{$kN$\}\backslash ).$ If $\backslash ($ L$=3\backslash$mathrm$\{$~m$\},$ w$=25\backslash$mathrm$\{$~mm$\}\backslash )$ and $\backslash ($ t$=10\backslash$mathrm$\{$~mm$\}\backslash ),$ calculate the total elongation of the whole bar from A to D$.$ Give your final numerical answer on Blackboard in $\backslash (\backslash$mathrm$\{$mm$\}^\{2\}\backslash ).$

c$)(2$ marks$)$ Calculate the internal axial stress in the bar in between A and B$.$ Give your final numerical answer on Blackboard in GPa.

d$)(2$ marks$)$ Calculate the internal axial stress in the section of the bar between B and C above the slot. Give your final numerical answer on Blackboard in GPa.

e$)(2$ marks$)$ Calculate the ratio of your answer in part d to your answer in part c$.$ Is this number greater, less or equal to $1?$ Choose the correct answer on Blackboard and enter in the numerical answer in the appropriate field.

f$)(1$ mark$)$ Explain what your answer to part e tells you about the presence of the slot. Can we improve the geometry of the slot to change the ratio calculated in part e$.$ If so$,$ how?