40 



APPLIED SCIENCE 



6-in. drum is the axle. If a boy turns the handle P uniformly 

 with a force of 50 Ibs., what weight can he lift at W! 



2. Suppose in problem 

 1, 15% were lost in friction, 

 what would be the answer 

 to the problem? 



3. If 26 ft. 8 in. of rope 

 were wound up on the drum 

 in Fig. 24, how many turns 

 and parts of turns did the 

 crank P make? (Take 



w 



FIG. 24. Hoist. 



- = ~) 



4. lii Fig. 24, what is the ratio between the weight lifted and 

 the force applied? 



5. A wheel and axle has the wheel 24 in. in diameter and the 

 axle 12 in. in diameter. If 10 ft. of rope are wound up on the wheel 

 how many feet will be unwound on the axle? 



NOTE. To do this problem it is necessary only to consider the 

 circumferences of the wheel and the axle. One turn of the wheel 

 will wind up 3.1416 X 24 in. of rope and at the same time unwind 

 3.1416 X 12 in. of rope from the axle. This is the same as saying 

 that the lengths of cord wound and unwound are proportional to 

 the circumferences of the wheel and axle. But we already know 

 that the circumferences of circles are proportional to their diameters 

 and so we can say that the lengths of rope wound and unwound are 

 proportional to the diameters of the wheel and axle and in the 

 above problem we will have, 



or 



24 : 12 

 12 X 10 



24 



= 10 : rope unwound from axle. 

 - f> ft. rope unwound from axle. 



A simple rule for this would read : To find the length of rope un- 

 wound from the axle multiply the length of rope wound on the wheel 

 by the diameter of the axle and divide this by the diameter of the wheel. 



If we wanted to find the length of rope wound up on the wheel 

 the rule would read; To find the length of rope wound on the wheel 



