70 . STATICS OF SYSTEMS OF PARTICLES 



There are four quantities which it is required to find. So far we have obtained 

 only three equations. We can, of course, obtain other equations by resolving 

 in other directions and by taking moments about other points, but it will be 

 found that the equations so obtained will not be new equations, but simply 

 equations of which the truth is already implied in the equations already 

 obtained. Thus we cannot, by resolving and taking moments, obtain more than 

 three independent equations, and these do not suffice to determine the four 

 unknown quantities. 



Here we have illustrated a problem which cannot be solved by the methods 

 explained in this chapter, and which requires for its solution a consideration 

 of the systems of forces set up between the separate particles of the bodies acted 

 upon. It is important that the student should realize that such problems exist, 

 although he may not yet be able to solve them. 



5. Force required to drag a car along. To simplify the problem as far as 

 possible, let us suppose that the car is mpunted on four equal wheels, each of 

 radius a and revolving round an axle of radius 6, the coefficient of friction 

 between wheel and axle being the same for each wheel. Let us suppose that a 

 force P applied horizontally is found to be just sufficient to start the car into 

 motion. 



1*1 



FIG. 38 



Let us consider first the equilibrium of the whole car. We are most con- 

 veniently able to enumerate the forces acting on any system by taking a tour, 

 in imagination, over the whole surface of a cover made just to fit the system, 

 and noting the forces which act across this cover at its different points. These, 

 together with the weight of the whole system, will give the whole system of 

 forces. The forces acting on the car are in this way found to be 



(a) its weight, say W; 



(b) the horizontal applied force P ; 



(c) the reactions between the wheels and the ground. Let us resolve each 

 reaction into a vertical component R and a horizontal component F', let us 

 denote the components of the reaction between the first wheel and the ground 

 by J?i, RI ; let the corresponding quantities for the second wheel be F 2 , R 2 ', and 

 so on. 



