Question

Write the relation between the mechanical advantage (MA) and velocity ratio (VR) of an ideal machine.

Answer 1

Ideal machine:

1. An ideal machine is a machine whose parts are weightless and frictionless.
2. Thus there is no dissipation of energy in any manner.
3. Its efficiency is 100%, i.e. the work output is equal to work input.
4. An ideal machine can also be stated as a machine in which no part of the work done on the machine is wasted.
5. Mathematically it can be stated as, $Workinput=Workoutout$

Mechanical advantage and its SI unit:

1. Mechanical advantage is a parameter that describes how much of the effort that is put into a simple machine, goes into manipulating the load.
2. In other words, it is the ratio of the output work to the input work of a machine.
3. It can also be stated as the ratio of the load to the effort.

The formula of mechanical advantage(M.A.):

1. $Mechanicaladvantage(M.A)=\frac{Load\left(L\right)}{Effort\left(E\right)}$
2. This ratio is a measure of the advantage that one obtains by using the machine.
3. Since it is the ratio of two identical quantities, it has no units.

Velocity ratio(V.R):

1. It is the ratio of the velocity at which the effort is applied to the machine to the velocity at which the load moves.
2. It is also defined as the ratio of displacement of effort to the displacement to load.

The formula for velocity ratio:

$$\begin{gathered} Velocityratio(V.R)=\frac{Velocityofeffort\left(V_E\right)}{Velocityofload\left(V_L\right)} \\ If,d_E=displacementcausedbyeffortintimet \\ {d}_L=displacementcausedbyloadinsametimet \\ then, \\ Velocityeffort=\frac{d_E}{t} \\ Velocityload=\frac{d_L}{t} \\ Therefore, \\ Velocityratio=\frac{d_{E/t}}{d_L/t}=\frac{d_E}{d_L} \end{gathered}$$

2. Since velocity ratio is the ratio of two similar quantities, hence it has no unit.

Relation between the mechanical advantage (MA) and velocity ratio (VR) of an ideal machine:

1. $Effeciency=Mechanicaladvantage/velocityratio$
2. For the ideal machine $Effeciency=1$
3. So, for the ideal machine, $Mechanicaladvantage=velocityratio$

Hence, the relation between the mechanical advantage (MA) and velocity ratio (VR) of an ideal machine $Mechanicaladvantage=velocityratio$