Page 161 - Schaum's Outline of Theory and Problems of Applied Physics

146 SIMPLE MACHINES [CHAP. 12

EFFICIENCY
The efficiency (Eff) of a machine is the ratio between its work output and work input. From the preceding
discussion,
work output F out s out F out s out AMA
Eff = = = =
work input F in s in F in s in IMA
Since the efficiency is also the ratio between the power output of the machine and its power input, in general
work output power output AMA
Eff = = =
work input power input IMA
If we know the ideal mechanical advantage and the efficiency of a machine,
F out = (Eff)(IMA)(F in )

COMPOUND MACHINES

When two or more machines are coupled together so that the output of one is the input of the next, the overall
mechanical advantage (IMA or AMA) of the combination is the product of the mechanical advantages of each
one:

MA = (MA 1 )(MA 2 )(MA 3 ) ···

The overall efficiency of two or more machines in combination is similarly
Eff = (Eff )(Eff 2 )(Eff 3 ) ···
1
SOLVED PROBLEM 12.1

Find the IMA of the pulley system shown in Fig. 12-1.

Fig. 12-1

To raise the load through a height h, a length of rope equal to 4h must be pulled through the pulley system since
the load is supported by four strands of rope. Hence

s in 4h
IMA = = = 4
s out h