My book mentions that A simple machine with Mechanical Advantage (MA) less than 1 acts as a speed multiplier. But I could not understand why is it so and I searched on the internet and some books but I found no Useful insights for why a simple machine with MA less than 1 acts as a speed multiplier.
[Physics] Why does a simple machine with Mechanical Advantage (MA) less than 1 acts as speed multiplier
forcesnewtonian-mechanics
Best Answer
It would be more accurate to say that a machine with a mechanical advantage less than $1$ can act as a speed multiplier - whether it does or not depends on the efficiency of the machine.
If the input to the machine is force $F_{in}$ at speed $v_{in}$ then the input power is $P_{in}=F_{in}v_{in}$. If the output is force $F_{out}$ at speed $v_{out}$ then the output power is $P_{out}=F_{out}v_{out}$. If the efficiency of the machine is $\eta$ then
$P_{out} = \eta P_{in} \\ \displaystyle \Rightarrow v_{out} = \left ( \frac {\eta F_{in}}{F_{out}}\right ) v_{in}$
But $\frac {F_{out}}{F_{in}}$ is the mechanical advantage of the machine $MA$, so
$v_{out} = \frac \eta {MA} v_{in}$
So if $MA < \eta$ then $v_{out} > v_{in}$.