Question

Show how Efficiency of a simple machine is affected by velocity ratio and mechanical advantage?

Answer 1

Hint: Efficiency of a machine is ratio of its mechanical advantage to velocity ratio and it is always less than 1.

Complete answer:
Anything that simplifies our work is a simple machine. Effort is the amount of force put in to achieve the required task. Load is the force exerted by a machine for completing the task. So both effort and load are a type of force. Mechanical advantage is the term given to the ratio of load and effort.
Mechanical Advantage = Load (L) / Effort (E)
Velocity Ratio is defined as the ratio of displacement of point of application of effort to displacement of point of application of load. If we denote displacement of point of application of effort by ${{D}_{E}}$ and displacement of point of application of load by ${{D}_{L}}$ then
Velocity Ratio = \[\dfrac{{{D}_{E}}}{{{D}_{L}}}\]
Efficiency (e) is the ratio of amount of work by load to work done by effort. Work is the product of force and displacement of point of application of force. So work done by load (${{W}_{L}}$) is equal to
${{W}_{L}}=L\times {{D}_{L}}$
Similarly work done by load (${{W}_{E}}$) is equal to
${{W}_{E}}=E\times {{D}_{E}}$
So,
$e=\dfrac{{{W}_{L}}}{{{W}_{E}}}$
$e=\dfrac{L\times {{D}_{L}}}{E\times {{D}_{E}}}$
which can be written as
e = Mechanical Advantage / Velocity Ratio
Since work by effort i.e. work input is always greater than or equal to work by load i.e. work output (because so amount of work is utilized in compensating losses due to resistive forces), so efficiency is always less than or equal to 1.
So, $e < 1$


Note:
Velocity Ratio as well as Mechanical Advantage both can have any value. None of them is bound to have its value less than 1. This is often a misconception among students, but actually it is efficiency which is bound to have its value less than one in practical life and equal to one in ideal condition.