147.] PLANE STATICS. 8/ 



146. The following examples will illustrate the application of 

 the conditions of equilibrium. To establish these conditions in 

 any particular problem it will generally be found best to resolve 

 the forces along two rectangular directions and equate the sums 

 of the components to zero; and then to "take moments," i.e. 

 equate to zero the sum of the moments of all the forces with 

 respect to some point conveniently selected as origin. 



147. A homogeneous straight rod AB= 2! (Fig. 38) of weight W 

 rests with one end A on a smooth horizontal plane AH, and with the 

 point E(AE = e) on a cylindrical support, the axis of the cylinder being 

 at right angles to the vertical plane containing the rod. Determine what 

 horizontal force F must be applied at a given point F of the rod (AF 

 = f>e) to keep the rod in equilibrium when inclined to the horizon at an. 

 angle 6. 



The rod exerts a certain unknown pressure on each of the supports at 

 A and E, in the direction of the normals to the surfaces of contact, pro- 

 vided there be no friction, as is here assumed. The supports may 

 therefore be imagined removed if forces A, E, equal and opposite to 

 these pressures, be introduced ; these forces A, E are called the 

 reactions of the supports. The rod itself is here regarded as a straight 

 line ; its weight W is applied at its middle point C. 



Taking A as origin and AH as axis of x, the resolution of the forces 

 gives 



o, (i) 



o. (2) 



Taking moments about A, we find 



E-e-W- /cos & - /Vsin = o. (3) 



