CHAPTER III 

 FORCES ACTING ON A SINGLE PARTICLE 



COMPOSITION AND RESOLUTION OF FORCES 



27. The second law of motion enables us to find the acceleration 

 produced when a particle of known mass is acted upon by a known 

 force. In nature, however, forces do not generally act singly. 



Consider, for example, the flight of the rifle bullet, discussed in 

 18. While the bullet is in the air it is acted on by its weight 

 and by the resistance of the air simultaneously. In addition to 

 these, there may be a cross wind blowing and acting on the bullet 

 with a horizontal pressure in a direction perpendicular to its 

 motion. The resistance of the air retards the motion of the bul- 

 let, i.e. produces an acceleration in a direction opposite to that of 

 the bullet's motion; the weight of the bullet drags it down, Le. 

 produces an acceleration towards the earth ; while the cross wind 

 will blow the bullet out of its course, i.e. will produce an accel- 

 eration in the direction in which the wind is blowing. Thus we 

 can regard the three forces as each producing its own acceleration. 

 The three accelerations can each be calculated from the second 

 law of motion, and on compounding these three accelerations we 

 shall have the resultant acceleration of the bullet. This resultant 

 acceleration could have been produced by the action of a certain 

 single force, so that we may say that this single force is equiva- 

 lent, as regards the acceleration produced, to the combination of 

 the three separate forces, or that the single force is the resultant 

 of the three separate forces. 



We must now put these ideas into exact mathematical form. 

 As a preliminary, let us notice that a force has magnitude and 

 direction, so that it can be represented by a straight line. We shall 

 show that forces may be compounded according to the parallelogram 



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