FORCE AND MOTION. 35 



(2.) W^^en the given forces act in opposite di- 

 rections. The resultant is then the difference 

 between the given forces. Motion will be pro- 

 duced in the direction of the greater force. Ex- 

 ample : Rowing a boat up stream. 



(3.) When the given forces act at an angle. The re- 

 sultant is then ascertained by the parallelogram of 

 forces. Example : Rowing a boat across a stream. 



81. Graphic Representation of Forces. 



Forces may le represented by lines, the point of 

 application determining one end of the line, the direc- 

 tion of the force determining the direction of the line, 

 and the magnitude of the force determining the length 

 of the line. 



(a.} It will be noticed that these three elements of a force ( 65) 

 are the ones that precisely define a line. By drawing the line as 

 above indicated, the units of force being numerically equal to the 

 units of length, we have a complete graphic representation of the 

 given force. The unit of length adopted in any such representation 



may be determined by convenience; 



A. but the scale once determined, it 



must be adhered to throughout the 

 problem. Thus the diagram rep- 

 resents two forces applied to the 

 point B. These forces act at right 

 angles to each other. The arrow- 

 v J heads indicate that the forces rep 



FIG. 8. resented act from B toward A and 



C respectively. The force that 



acts in the direction BA being 20 pounds and the force acting in the 

 direction BC being 40 pounds, the line BA must be one-half as 

 long as BC. The scale adopted being 1 mm. to the pound, the 

 smaller force will be represented by a line 2 cm. long, and the greater 

 force by a line 4 cm. long. 



(&.) The graphic determination or representation of the resultant 

 in the first two cases under the " Composition of Forces " is too 

 simple to need any explanation. 



