354 



Introduction to the Study of Science 



' C 



Exercise : Relation of forces as in pushing a wagon. Assume that 

 the angle in the illustration, Fig. 121 (A), is 45V A pushing force of 

 ten pounds 2 is exerted on the stick. As is evident 

 from the direction of the stick, part of the pushing 

 force is expended upon the ground, or downwards, 

 and may be regarded as wasted or ineffective 

 effort. Only a part of the effort serves in moving 

 the wagon forward. The problem now is to find 

 how much of the total effort, ten pounds, is wasted 

 in the downward push, and how much is applied 

 to the wagon effectively. 



Graphic solution. The problem may be solved 

 graphically, 3 that is, by representing the forces by 

 lines drawn to scale. As in Fig. 121 (B), draw a 

 line parallel to the surface of the ground as a base 



1 Angles may be measured with a protractor. Or 

 take a square piece of paper, fold in half diagonally ; 

 the acute angle formed is 45. To find an angle of 15, 

 cut the paper on the crease, then fold the 45 angle into 

 three equal parts and cut. Each will be 15. How can 

 you find an angle of 60? 



2 Measuring force. Force is measured by its pressure 

 or pull, and the quantities may be stated in ounces and 

 pounds (or in grams and kilograms in the metric system). 

 A sack of flour placed on the platform of a balance is 

 weighed. The flour is removed, but the weights are left 

 unchanged. One may grasp the platform with the hands 

 and exert a pressure sufficient to balance the weights 

 that measured the weight of the flour. Plainly the force 

 exerted in the pressure is exactly as many pounds as the 

 flour weighed. Consequently we speak of a pressure of 

 fifty pounds just as properly as of a weight of fifty 

 pounds of any commodity. So with the pull exerted by 

 a force. A spring balance (Fig. 122) registers the pull 

 which an applied force or a given weight of iron or sugar 

 may exert. Weight and force are then equivalent. And 

 it is a common practice to speak of a pull or a push of 

 ten, twenty, or a thousand pounds whether the force be 

 exerted by man, animal, or anything else, such as falling 

 water, wind, steam, or electricity. 



3 Graphic representation of force. Both force and 

 weight may be represented graphically. A given length 

 of line may be taken to represent a given amount or 

 measure of force or weight. A line one fourth of an inch 

 long may represent a force of ten pounds ; a line four 

 times as long will represent by the same scale forty pounds 

 of force. The length of a line may thus show the magni- 

 tude of a force. The direction in which the force is act- 

 ing may be shown by arrows. It is equally simple to 

 show the point at which a given force is applied. Thus 

 the magnitude, direction, and point of application of a force 

 may be represented by a line drawn to scale. 



FIG. 122. Spring 

 balance. What is 

 the equivalent of 64 

 ounces in grams? 



