Learning Goal:

To be able to solve for unknown forces and moments in rigid$-$

body problems using the equations of equilibrium.

For a rigid body to be in equilibrium, both the sum of the forces

and the sum of the moments about an arbitrary point $O$ must

be zero.

${\displaystyle \underset{?}{\overset{?}{}}}F=0$

${\displaystyle \underset{?}{\overset{?}{}}}{M}_O=0$

When all of the forces lie in the $x-y$ plane, the forces can be

resolved into their $x$ and $y$ components, which results in the

equations of equilibrium in two dimensions:

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0$

${\displaystyle \underset{?}{\overset{?}{}}}{M}_O=0$

Part A

As shown, a uniform beam of length $d=5\mathrm{.}60ft$ and weight $36\mathrm{.}6$ lb is attached to a wall with a pin at point $B.($Figure $1)$ A cable attached at point $A$

supports the beam. The beam supports a distributed weight $w_2=16\mathrm{.}0l\frac{b}{f}t.$ If the support cable can sustain a maximum tension of $300$ lb $,$ what is

the maximum value for $w_1?$ Under this maximum weight, what is $F_{B_y},$ the vertical component of the support's reaction force at point $B?$

Express your answers numerically in pounds per foot and pounds to three significant figures separated by a comma.

View Available Hint$($s$)$

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