Question

What is the condition for mechanical advantage to be less than 1 and velocity ratio to be greater than 1?

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.

The condition for mechanical advantage to be less than 1:

1. If the effort applied is greater than the load, then$M.A.<1$.
2. For example, if a load is 20 N is moved by applying an effort of 40 N then,

$$\begin{gathered} Mechanicaladvantage(M.A)=\frac{Load\left(L\right)}{Effort\left(E\right)} \\ =\frac{20N}{40N}=0.5 \end{gathered}$$

Thus, the mechanical advantage is 0.5 N.

Hence, the mechanical advantage is less than 1.

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.

The condition for velocity ratio to be greater than 1:

1. If the displacement of effort is more than the displacement of load, then $V.R.>1$

Hence, the velocity ratio is greater than 1.