Problem $1$: The $90-$degree bar $\backslash (\backslash$mathbf$\{$A B$\}\backslash )$ has a mass of $50$ kg $,$ acting through its centroid. What are the reactions at $\backslash ($ A $\backslash$& B $\backslash )?$ The support at $\backslash ($ B $\backslash )$ is a roller.

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

PLEASE INCLUDE THE TABLE AND SHOW HOW YOU GOT THE VALUES IM CONFUSED $-$ thanks!

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 AB 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.