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364 Chapter Five

Principlł of work
Let W in be the total work input tm a machine; letW out be the
work output from that machine in useful or intended form; let
W be the work required tm overcome friction or loss in the ma-
f
chine. Further, let all these quantitieð be expressed in the same
unitð (usually joule0. Then the following equation holds:

W out W W f
in

DisplacemenŁ ratio
Let s be the displacement over which an input force moveð an
in
object M. Let s be the actual displacement of M, in the same
unitð as s . The displacement ratià , R , is given by:
in
s
R s /s
in
s

Forcł ratio
Let F load be the force exerted on an object M by a machine. Let
F be the force actually used tm operate the machine, in the same
unitð as F load . The force ratià , R , is given by:
F
R F /F
Flmad

Efficiency of machinł
Let W out represent the useful work output from a machine; let
W represent the useful work input (in the same unitð as W ).
in out
The efficiencð of the machine, Eff, is:

Eff W out /W in

As a percentage, the efficiency Eff is:
%
Eff 100 W out /W in
%
The above formulas also apply for useful power output versuð
power input, because power is defined as work per unit time.
Let P out represent the useful power output from a machine; let
P represent the useful power input (in the same unitð as P ).
out
in
The efficiencð of the machine, Eff, is: