Question

With reference to the terms mechanical advantage, velocity ratio and efficiency of a machine, name and define the term that will not change for a machine of a given design.

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, go 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.

Efficiency:

1. The efficiency of a machine is the ratio of the work done on the load by the machine to the work done on the machine by the effort.
2. Thus, it is the ratio of useful work done by the machine output to the work done by the machine input.
3. It is represented by the Greek symbol$\eta \left(eta\right)$.

The formula of efficiency:

1. $\eta =\frac{Output}{Inout}$
2. It is usually expressed as a percentage $\eta =\frac{Output}{Inout}\times 100\%$
3. Since it is a ratio of two similar quantities, it has no unit.

The term that will not change for a machine of a given design:

1. It is the velocity ratio that will not change for a machine of a given design
2. While mechanical advantage and efficiency can vary according to circumstances.

Hence, the velocity ratio will not change for a machine of a given design.