SIMPLE MACHINES 193 



the direction of the force with respect to the weight and do 

 not give any mechanical advantage. Only the movable 

 pulleys give mechanical advantage. We saw in division 

 (b) of this section that the mechanical advantage of a 

 movable pulley is 2, and that there are two strands of rope, 

 one going to the pulley and the other coming from it. 

 So in order to find the mechanical advantage of a block 

 and tackle, we count the number of movable pulleys and 

 multiply that number by 2, or count the number of strands 

 of rope going to and from the movable pulleys; the 

 results are the same, if the rope is first attached to the 

 fixed pulleys. In a system of two movable pulleys with 

 a mechanical advantage of 4, a force of 100 pounds can 

 lift a 4oo-pound weight. Since there are four strands of 

 rope, the force will move four times as fast as the 

 weight and also move four times as far as the weight; 

 hence the work done by the force will again be equal to 

 the work accomplished on the weight. 



Combinations of pulleys are used in moving heavy fur- 

 niture, pulling stumps, lifting heavy stones and timbers, 

 moving small buildings, and in various other applications. 



Problems. 1. What force will be required to lift a 2Oo-pound 

 weight with a single fixed pulley? With a single movable pulley? 



2. Find the force needed to lift a 6oo-pound piano to a second 

 story window with a block and tackle containing two movable 

 pulleys. If the window is 10 feet high, how far will the force move 

 while pulling the piano up? 



3. What is the least number of movable pulleys that can be 

 used in a block and tackle to lift a 24oo-pound weight with a force 

 of 300 pounds. How far will the weight move if the force moves 

 72 feet? 



4. What is the largest weight that can be lifted by a force of 

 250 pounds applied to a block and tackle containing six movable 

 pulleys? How far will the force have to move to lift the weight 

 5 feet? 



