88 THE PULLEY. THE INCLINED PLANE. 



experiments are made with weights ; and as the weight 

 of the moveable pulley itself has to be supported, two 

 small cardboard boxes or scales are attached to the 

 free ends, into one of which sand or shot is placed until 

 equilibrium is produced ; this is done before the weights 

 to be experimented on are applied. 



Several pulleys may be combined in various ways. 

 A simple consideration will show that in the arrange- 

 ment fig. 60, (7, the force applied to the free end of the 

 cord passes over one and a half times the space of that 

 applied at the axis of the lowest pulley, while in the 

 arrangement D it passes over four times as great a space. 

 The force at C will therefore be f , at D ^, of the 

 force acting at the axis of the pulley. In fig. 61 there 

 are six pulleys ; the weight to be raised is thus sus- 

 pended by six cords, each of which must become shorter 

 by the space through which the weight is to be raised. 

 The free end of the cord will therefore have to be pulled 

 down through a space six times as great, and the force 

 acting at this end must be ^ of the weight. 



The inclined plane is chiefly used for raising 

 weights to a certain height by the application of a 

 smaller force than would be required for lifting them 

 to the same height vertically. 



The work done in drawing a carriage on the inclined 

 plane, fig. 62, from a to c is the same as that required 

 for lifting the carriage vertically upwards through the 

 space ab, or dc, but the force required will be 

 less than the weight of the carriage in the same pro- 

 portion in which the length of the inclined plane is 

 greater than its height. If the weight of the carriage 

 be 200 kgr , the height of the plane 3 m , its length 20 m , the 



