FORCE AND MOTION 57 



pounds is pulled upward by a force of 50 pounds. The 

 effect will be motion upward as if a force of 20 pounds were 

 acting alone. Forces and their resultants are described in 

 terms of weight and may be represented by lines. A force 

 of 10 pounds, for instance, may be represented by a line 1 

 inch long. In the same case, a force of 20 pounds would 

 be represented by a line 2 inches long. 



Forces also act horizontally and then produce motion in 

 a horizontal direction. Two forces acting in the same direc- 

 tion produce an effect equal to the sum of the two forces. 

 Acting in opposite directions, they produce an effect equal 

 to the difference of the two forces, the resultant being in the 

 direction of the greater force. For example, two horses 

 working together can move as great a load as the two horses 

 working singly. When a man rows a boat up stream, his 

 muscular force acts in a direction opposite to the force of the 

 current; he must therefore exert a force greater than that 

 of the current. 



If forces act obliquely or at right angles to each other, 

 the resultant will lie between them. Suppose the current of 

 a stream is directly east; a man in a motor boat sets out 

 exactly south with the rudder set. He will arrive at a place 

 down stream instead of opposite the point where he started. 

 The direction of the resultant can be determined by a simple 

 mathematical construction. 



Let two lines at right angles represent two forces acting 

 at the point A . If the horizontal line represents a force of 

 50 pounds acting east, and the vertical line a force of 25 

 pounds acting south, the resultant will be represented by 

 the diagonal of a rectangular figure constructed on these 

 lines. Its value can be found by measurement, letting each 

 inch of the diagonal represent the same number of pounds 

 as an inch in the other lines. (See Fig. 19, p. 58.) 



58. Friction. A ball is set rolling on a smooth floor; 

 a boy runs upon. a sheet of ice and then slides. Because of 



