Page 160 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 12

Simple Machines

MACHINES

A machine is a device that changes the magnitude, direction, or mode of application of a force or torque while
transmitting it for a particular purpose. There are only three basic machines, of which all others are developments:
the lever, the inclined plane, and the hydraulic press. The hydraulic press is described in Chapter 16.

MECHANICAL ADVANTAGE
The actual mechanical advantage (AMA) of a machine is the ratio between the output force F out it exerts and
the input force F in that is applied to it:

F out
AMA =
F in
output force
Actual mechanical advantage =
input force
An AMA greater than 1 means that F out exceeds F in ; an AMA less than 1 means that F out is smaller than F in .
The ideal mechanical advantage (IMA) of a machine is its mechanical advantage in the absence of friction.
If the input force acts through the distance s in when the output force acts through the distance s out , then according
to the principle of conservation of energy

Work input = work output

F in s in = F out s out
F out s in
and so =
F in s out
when there is no friction present. Because friction acts to decrease the ratio F out /F in in an actual machine but
does not change the ratio s in /s out , it is customary to define ideal mechanical advantage in terms of the latter:

s in
IMA =
s out
input distance
Ideal mechanical advantage =
output distance
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