...proportional to these forces. 133. If three forces acting on a particle keep it in equilibrium, each force is proportional to the sine of the angle between the other two. Let P, Q, S, represented by AB, AC, AD respecFro. 56. tively (Fig. 56), be three forces acting on the...

...directions are not parallel:— (i) Their lines of action must meet in a point, Art. (22). (ii) Each force is proportional to the sine of the angle between the other two, the direction of each force lying without the angle formed by the other two, Art. (23). For this latter...

...give the ratios of the forces. To express this algebraically, let ij, ¿ 2 , be the angles made by the of action of the supporting forces with that of the resultant of the load ; then Pr Rj : Rj : : sin (4 + i%) • s * n ^2 • s ' n ^i (^-)The same piece in a frame may act at once...

...often stated as follows :— When three forces act on a point and keep it at rest, each one of them is proportional to the sine of the angle between the other two forces. It also takes another form, which was an early invention in mechanics, and is known as the...

...sides of that triangle will give the ratios of the forces. To express this algebraically, let %, ¿ 2 , be the angles made by the lines of action of the supporting...forces with that of the resultant of the load; then : E 2 .(4.) The same piece in a frame may act at once as a beam and tie, or as a beam and strut; or...

...often stated as follows :— When three forces act on a point and keep it at rest, each one of them is proportional to the sine of the angle between the other two forces. It also takes another form, which was an early invention in mechanics, and is known as the...

...that triangle will give the ratios of the forces. — QEI To express this algebraically, let i,, i.,, be the angles made by the lines of action of the supporting...proportional to the sine of the angle between the other two, P : RI : R, : : sin (i + t,) : sin f, : sin t,. 143. l,oi d supported by Three Parallel force*. —...

...of forces in another form. Prop. If three forces acting on a particle, keep it in equilibrium, each ‘is proportional to the sine of the angle between the other two. Let OA, OB, OG represent three forces ‘F, Q, B which, acting on a particle, keep it in equilibrium....

...along EF, W along EW and a force, opposite to their resultant, along E B. From Art. 44, each force is proportional to the sine of the angle between the other two. Hence, P: W :: (sin WEB=) sin BED: (sin BEF=) 2 BED. 123. Change in the Ratio of Power and Weight.—...

...than the third. 40. Lami's Theorem. If three forces acting on a particle keep it in equilibrium, each is proportional to the sine of the angle between the other two. Taking Fig., Art. 38, let the forces P, Q, R be in equilibrium. As before, measure off lengths OL,...