Complete each problem on engineering paper, You do not need to use the Given$/$Find$/$Solation format, but your solutions must be fully developed and presented profenionally. Show all your work, incluing equatiens ured, and pertinent sketches. Final aswaers shall be bexed or diecled, mest include correct units, and thow concorn for significant digtis $($usually is ac $4).$ Your work is to be completed and submitsed lidividually.

Problem $1$: The $90-$degree bar $\backslash (\backslash$mathbf$\{$A B$\}\backslash )$ has a mass of $50$ kg $,$ acting through its centrold. What are the reartinns at $\backslash (\backslash$mathrm$\{$A$\}\backslash$boldsymbol$\{\backslash$ell$\}\backslash$mathrm$\{$R$\}\backslash ))$ The sument at A is a miller.

a$.$ Locate the center of gravity of bar AB relative to point $\backslash ($ A $\backslash ).$ Due to symmetry, we don't need to solve for both $\backslash (\backslash$times $\backslash )\backslash$& y coordinates. Use the tabular method to find $\backslash ($ X $\backslash ),$ Use units of $"$mm$"$ is your table and to express your final answer. Use the shapes shown below.

b$.$ Apply equilibrium equations and solve for the unknown reactions $($show direction, too$).$ Assume the total weight of the bar acts through the centroid you just computed.

c$.$ Is bar AB a two$-$force member in this problem? Explain your answer.

d$.$ Consider bar $\backslash ($ A B $\backslash )$ to be comprised of two pieces as shown below. Assume each piece weighs half the total weight $($acting through each respective centroid$).$ Re$-$compute the reactions with this system and compare to your previous answers.