Sample problem: rod and sphere
A light rod AB supports a sphere of mass M. The rod is pivoted at A while B is supported by a cord, fixed to the vertical surface at C as shown in Fig. 1. The sphere touches the surface rod AB at D and the vertical surface AC at E. Assume lengths of AD and DB are 4 and 6 units respectively. Ð abc = Ð bac = 45бу and Ð acb = 90бу . If all contact surfaces are smooth find the tension of the cord, T.
The forces on the sphere and rod are shown in separate diagrams. Note: Let RV and RH are the vertical and horizontal reactions respectively at A.
Fig. 2 shows the forces acting on the sphere and rod in two separate diagrams
Forces acting on the sphere: