Problem $4($P$5\mathrm{.}7$ in textbook$)$

Determine the reactions at the supports, and the tension in each segment of the cable.

Problem $5$

Consider the cable shown below. The cable is supporting two distributed loads at its

extremities, and it is pre$-$tensioned by a force of $50$ k $.$ Neglecting its self$-$weight:

Derive an expression for the tension of the cable as a function of $x$ and $w.$ Identify

the locations of minimum and maximum tensions.

Derive an expression for the deflection shape of the cable as a function of $x$ and $w.$

Determine the location of the maximum deflection.

Determine the maximum allowable load $w$ such that the cable's maximum

deflection is limited to $5$ ft $.$