...at the walls due to those forces. Now, it is known that if any number of forces act on a point, and are in equilibrium, they may be represented in magnitude and direction by the sides of a polygon drawn parallel to the direction of those forces, taken in regular succession. Thus if А BCDE,...

...a similar way it can be shown that if any number of forces, in the same plane, acting at a point, r are in equilibrium, they may be represented, in magnitude and direction, by the H sides of a polygon taken in- order. Thus let BC, BH, BF, BD, and BG be in equilibrium. By combining...

...triangle, as a, b, c, Fig. 123. Since the forces at C, Fig. 122, including the strains in the bars, are in equilibrium, they may be represented in magnitude and direction by the three sides of a triangle. In Fig. 123, draw the lines 1 and 2 from the extremities of P, , parallel...

...Ibs., then R 2 = (15)" + (8) 2 = 225 + 64 289, therefore R = 17. 2. // three forces acting on a point be represented in magnitude and direction by the sides of a triangle taken in order, they will keep the point in equilibrium. Let ABC be the triangle, and let P,Q and R be three...

...this proposition is true, that is, if three forces, acting at a point be in equilibrium, they can bo represented in magnitude and direction by the sides of a triangle, taken in order. This is a particular case of a more general theorem, which wo now proceed to prove. 39. If three...

...adding, we have /» + ft — jp as before. The forces P and Fare called component forces. 44. TRIANGLE OF FORCES. If three concurrent forces are in equilibrium,...resultant of the other two. Thus, in Fig. 19, if AB and BC lepresent two forces in magnitude and direction, AC will represent the resultant. parallelogram of...

...several forces which are applied at the several angles as shown. These forces being in equilibrium may be represented in magnitude and direction by the sides of a Wangle, as a, b, e, Fig. 123. Since the forces at C, Fig. 122, including the strains in the bars, are...

...225-424-26 = 20074 .-. 11 = 14-1. 33. The Triangle of Forces. — If three forces acting at a point be represented in magnitude and direction by the sides of a triangle taken in order, they will be in equilibrium. This proposition follows as a matter of course from the Parallelogram...

...with velocity AC. 13. Triangle of Velocities.—If a point have three component velocities, which are represented in magnitude and direction by the sides of a triangle taken in order, the point is at rest. Let a point have three uniform velocities represented by the sides AB,...

...the resultant of P and Q, both in magnitude and direction. 20. TRIANGLE OF FOBCES. If three forces, represented in magnitude and direction by the sides of a triangle taken in order, act upon a point, they will be in equilibrium ; and, conversely, if three forces acting upon...