EXAMPLE: $1-3$

The sphere shown in the figure weighs $20$ kg $,$ and is supported and held in equilibrium by cable CBA over a friction$-$less pulley and a spring CD $($spring CD is horizontal$).$

$[$a$]$ Draw free body diagrams for the sphere, and for the chord CE$.$

$[$b$]$ Draw free body diagrams for points, C and B $.$

$[$c$]$ Determine the cable forces and spring force.

$[$d$]$ If the largest permissible change in spring length is $0\mathrm{.}1$ mm $,$ determine the necessary spring stiffness.

$[$e$]$ Determine the support reaction at the pulley support B$.$