ELEMENTARY GENERAL SCIENCE 



CHAP. 



to each other at an angle which is not a right angle, the calcula- 

 tion involves an elementary knowledge of trigonometry. This 

 can' be obviated, however, by the simple expedient of what is 

 called the graphical method. This consists in drawing two lines 

 inclined at the angle at which the directions of the forces are 

 inclined, and making them of such length that they contain as 

 many units of length as the force does units of force. The 

 parallelogram is then completed by drawing AR and BA parallel 

 respectively to OB and OA and joining the diagonal OR, whose 

 direction will be that of the resultant, and whose length will 

 be as many units as there are units of force in the resultant 

 force. 



Resolution of Forces. A single force can be replaced by 

 other forces which will together produce the same effect. Such 

 a substitution is called resolving the 

 force or a resolution of the force. The 

 parts into which it is resolved are 

 spoken of as components. When this 

 has been done it is clear that we have 

 made the original force become the 

 resultant of certain other forces which 

 have replaced it. Referring back to 

 what has been said about the paral- 

 lelogram of forces, it will be seen that 

 any single force can have any two 

 components in any directions we like ; 

 for by trying, the student will be able 

 to make any straight line become the 

 diagonal of any number of different 

 parallelograms. The most convenient 

 components into which a force can 

 be resolved are those the directions 

 of which are at right angles to each 

 other. In this method of resolution, 

 neither component has any part in the 

 other. 



An interesting example of the resolution of a force into two 

 components at right angles is afforded by a pendulum. Consider 

 a pendulum at any point in its swing, as shown in Fig. 26. The 

 pendulum-bob is pulled downwards in consequence of the attrac- 

 tion of gravity, and this vertical force is represented by the line 

 BD. The force can, however, be resolved into two forces, one 



FIG. 26. Resolution of a 

 Force. 



