IN NA TURAL PHIL OSOPHT. 2 I 



between them from a pole 10 feet in length. Where should it 

 be suspended so that one will lift only 50 Ibs. ? 



One lifts 50 Ibs. ; the other 200 Ibs. The proportionate length of the arms 

 of the lever should be the same as the proportionate weights i. ., 1 to 4. 

 10 * 5 = 2, the unit of measure. Hence one arm is 2 feet long and the other 

 8 feet long. PROOF. (See Prob. 7, p. 10.) 50 x 8 = 200 x 2. This is the 

 Bubstance also of the equation P x Pd = W x Wd. 



5. In a lever of the first class, 6 feet long, where should tht 

 F be placed so that a P of \ Ib. will balance a W of 2.3 Ibs. f 



6 feet = 72 inches. 72 -*- 24 = 3, the unit of distance. The W must be 

 placed 3 in. and the P 69 in. from the F. PROOF. 23 x 3 = 1 x 69 (Prob. 4). 



6. What P would be required to lift a barrel of pork with a 

 windlass whose axle is one foot in diameter and handle 3 ft. 



long? 



P : W : rad. of axle : : rad. of wheol. 



a; : 200 Ibs : : V a ft. : 3 ft. 

 x = 33Vs Ibs. 



7. What sized axle, with a wheel 6 feet in diameter, would 

 be required to balance a W of i ton by a P of 100 Ibs. f 



P : W : : rad. of axle : rad. of wheel. 



100 Ibs. : 2000 Ibs. : : x : 3 ft. 

 x = '/ao ft- = the r& d- ; hence the diameter = 8 /io ft- 



8. What number of movable pulleys would be required to 

 lift a W of 200 Ibs. with a P of 2$ Ibs. ? 



TTT 



W P x twice the no. of mov. pulleys ; hence = twice the no. of mov. pul's. 

 200 + 25 = 8. 8 -*- 2 = 4 = the no. required. 



9. How many Ibs. could be lifted with a system of '4 movable 

 pulleys, and one fixed pulley to change the direction of the 

 force, by a P of 100 Ibs. ? 



W= P x twice the no. of mov. pulleys. 

 100 Ibs. x (4 x 2) = 800 Ibs. = the W. 



10. What weight could be lifted with a single horse-power 

 ^33,000 Ibs.) acting on the tackle-block? (Fig. 62.) 



This block has 3 movable pulleys, and using the equation of the pulleys given 

 in the last two problems, we have, making no allowance for friction, 



33,000 Ibs. x (3x2) = 198,000 Ibs. 



