Problem $4$

Numerical Problem $(20$ points$)$: While moving to the UC Davis dorms, you bring a box weighing $625$ lbf full of your stuff. Unfortunately, you have to move this heavy box to the third floor of the dorms. Luckily, you have ropes and metal stakes that you can use to pull the box up$.$

Using the cartesian component method in $3$D to calculate the following assuming that the system is in equilibrium:

Determine the internal normal forces in all the members $($AF$,$ AD$,$ AC$,$ AB$)$ assuming that the box is suspended at $F.$

Determine the maximum weight of the box that the ropes can support, such that no single cord develops a tension exceeding $325lbf.$