544 MACHINES, WORK, AND ENERGY 



TION OR OF POSITION. Examples: By using a single fixed 

 pulley the direction of the force is changed and the operator 

 may choose his own position. The handle of the common 

 pump, the key of the typewriter, the wheel or handle of the 

 washing machine, the common door knob all these and many 

 other devices are advantageous because they aid in changing 

 the direction of the applied force or they enable the operator 

 to choose his position, or both. 



A machine may have mechanical advantage of two or more 

 kinds at the same time. It is impossible, however, for a 

 machine to have both mechanical advantage of force and 

 mechanical advantage of speed at the sa.me time. What ad- 

 vantages are afforded by the sewing machine over those of 

 the hand needle? 



642. Numerical Expression of Mechanical Advantage. 

 Mechanical advantage of force and mechanical advantage of 

 speed are each frequently expressed numerically, i.e., in num- 

 bers. The ratio of the force delivered by a machine to the 

 force applied to the machine is said to express the mechanical 

 advantage of force of the machine. 



Mechanical advantage of force = 



Number of units of force delivered 

 Number of units of force applied 



Example: A man by using a crowbar exerts a force of 

 1000 Ib. upon a rock while exerting a force of 100 Ib. upon 

 the handle of the crowbar. In this case the mechanical 



. 1000 Ib. 

 advantage of force is == 10- 



The ratio of the speed with which the force acts to the 

 speed of the applied force is said to express the mechanical 

 advantage of speed of the machine. 

 Mechanical advantage of speed = 



Number of units of speed of the force delivered- 



Number of units of speed of force applied 

 Example: The knives of an egg beater pass 5 times around 

 a 2-in. circle while the handle on the drive wheel passes once 



