PULLEYS, INCLINED PLANES, AND WEDGES 43 



length and height of the inclined plane are proportional M the 

 weights A and W. For example, if in Fig. 26 we make the height 

 of the plane 1 ft. and its length 2 ft., we know that the weight W 

 need only be one-half as heavy as the weight of the ball to keep it 

 from rolling down the plane. Stated as a proportion this would be, 



Weight A : Weight W = 2 ft. : 1 ft. 



We will now study the relative movements of the weights if the 

 height of the inclined plane is one-half its length. In Fig. 26 when 

 the ball rolls from the top of the plane to the bottom it has traveled 

 2 ft. on the plane but has dropped only 1 ft. in a vertical direction. 

 By this we know that the distance the ball travels on the plane is 

 to the vertical distance it moves through as 2 is to 1, when the 

 height of the plane is one-half its length. 



It has now been proved that there is a definite ratio or relation 

 between the height and length of the plane and the weight of the 

 ball and counterweight, and also between the distances the ball 

 moves along the plane and perpendicular to it. Whatever the height 

 or length of the plane, these relations always hold true. 



From what has been explained, short, simple rules can be 

 made for problems relating to inclined planes as follows : 



I. To find the counterweight or force, multiply the weight 

 on the plane by the height of the plane and divide by the length 

 of the plane. 



II. To find the weight on the plane, multiply the force 

 by the length of the plane and divide by the height of the plane. 



Problems on Inclined Planes 



1. Neglecting friction, what force is necessary to keep a weight 

 of 100 Ibs. stationary on an inclined plane, the perpendicular height 

 of the plane being 4 ft. and the length of its incline 14 ft.? 



2. The length of an inclined plane is 15 ft. and its height 7 ft. 

 What weight will a power of 78 Ibs. sustain on the plane, neglecting 

 friction? 



