Directions: solve the following problems using the knowledge and skills acquired in class. Each student shall deliver a separate solution sheet. The solution shall be handed as a soft copy $($scanned PDF$)$ and hand$-$written $().$ The homework will be graded $5\mathrm{.}0$ points in total. Show your calculations step by step. Write down your name on each page.

Due date: in two weeks. Upload the PDF file on the Moodle platform $($on the "Homework $1"$ assignment tab$)$ by $8^{th}$ December $2024.$

Problem $1$:

Three chains act on the bracket such that they create a resultant force having a magnitude of $500lb.$ If two of the chains are subjected to known forces, as shown, determine the angle $$ of the third chain measured clockwise from the positive x axis, so that the magnitude of force $F$ in this chain is a minimum. All forces lie in the $x-y$ plane. What is the magnitude of $F?$ Hint: First find the resultant of the two known forces. Force $F$ acts in this direction.

Name: $q,$

Problem $2$:

If the magnitude of the resultant force acting on the bracket is $600N,$ directed along the positive $u$ axis, determine the magnitude of $F$ and its direction