Statics, a branch of mechanics, deals with bodies at rest which do not move under the influence of forces. In these statics problems we investigate the relationship between the forces acting on the bodies to determine why there is no resulting movement.
Equilibrium
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.
Solution
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:
