Question

What is the magnitude of mechanical advantage and velocity ratio of an actual machine?

Answer 1

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. 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:

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

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

For actual machine :

1. For an actual machine the mechanical advantage is always less than its velocity ratio.
2. It can also be stated as the output work is always less than the input work as some of the input energy is lost due to the force of friction etc.

$$\begin{gathered} MA<VR \\ Thus,\eta <1 \end{gathered}$$

Hence, the mechanical advantage is always less than the velocity ratio for an actual machine.