THE WHEEL AND AXLE. 81 



apply a force of -TT^T = O kgr *l, for the work done by 



this force must be equal to the work done in raising G, 

 and since work = force x space, we can conversely find 

 the force by dividing the work by the space, in this 

 case by dividing 0*03 kilogrammetres by O m *3. 



Instead of pulling the cord by theiiand, the necessary 

 work may be done by a descending weight. This 

 weight, <7, must in our case be O kgr *l, In general, if the 

 wheel is three times as large as the axle, the weight to 

 be suspended from it must be one -third of the weight to 

 be raised by the axle. If the weights are correctly 

 suspended, the wheel and axle will be jit- rest, but a 

 small force will be sufficient to set it in motion. This 

 force is solely applied to overcome the resistance of 

 friction. The work of raising one of the weights is 

 entirely performed by the other which descends. 



If the weights are suspended at. the smallest and 

 middle-sized cylinders, the weights will have to be in 

 the proportion of 2 : 1 ; similarly, if the middle-sized 

 and largest cylinders are used, the weights will have to 

 bear the proportion of 3 : 2. In any case, there will be 

 quilibrium if the forces are such that the work done by 

 hem. if motion takes place, is equal. If one of the forces 

 ^ greater than what is required by this condition, the 

 *ther force will be overcome, and motion will ensue. 



Figs. 55 and 56 (p. 82) show two forms of the wheel 

 nd axle which are practically used for raising weights, 

 n fig. 56 the wheel is replaced by a handle. Suppose 

 he weight to be raised by the wheel and axle, repre- 

 entecl in fig. 55, to be 50 kgr , the radius of the axle 

 ound which the rope is wound to be O m *l, and the 



G 



