Question

In a lifting machine, an effort of $500\;N$ is to be moved by a distance of $20\;m$ to raise a load of $10000\;N$ by a distance of $0.8\;m$. Determine the velocity ratio and mechanical advantage?
(A) $10\;$ and $\;35$
(B) $20\;$and $\;35$
(C) $10\;$ and $\;25$
(D) $25\;$ and $\;20$

Answer 1

To solve this question we have to find the velocity ratio and mechanical advantage. The velocity ratio can be defined as the ratio of the distance that is moved by the effort to the distance which is being moved by load. Mechanical advantage can be defined as the ratio of the weight of the load to the weight of the effort.

Formula used:
The velocity ratio formula
$\Rightarrow {V_R} = \dfrac{{{d_E}}}{{{d_L}}}$
Where ${d_E}$ is the distance of effort and ${d_L}$ is the distance of load.
Machine advantage formula
$\Rightarrow M.A = \dfrac{{load}}{{effort}}$.

Complete answer
In the question, it is given that the distance moved by the effort is ${d_E} = 20\;m$ and the distance moved by the load is given as ${d_L} = 0.8\;m$.
As we know that velocity ratio is defined as the ratio of the distance that is moved by the effort to the distance which is being moved by load. Hence
$\Rightarrow {V_R} = \dfrac{{{d_E}}}{{{d_L}}}$ ……….$(1)$
Substituting the values of ${d_E} = 20\;m$ and ${d_L} = 0.8\;m$ in the equation $(1)$, we get
$\Rightarrow {V_R} = \dfrac{{20}}{{0.8}}$
$\therefore {V_R} = 25$
Now let us find the value of mechanical advantage of the machine which is defined as the ratio of the weight of the load to the weight of the effort which can be expressed as
$\Rightarrow M.A = \dfrac{{load}}{{effort}}$ ……..$(2)$
In the question, it is already given that weight of $effort = 500\;N$, and the weight of $load = 10000\;N$, hence substituting these values in the equation $(2)$ we get
$\Rightarrow M.A = \dfrac{{10000}}{{500}}$
$\therefore M.A = 20$
Hence we concluded that the velocity ratio is ${V_R} = 25$ and machine advantage is given as $M.A = 20$.
Therefore option (D) is the correct answer.

Note:
The velocity ratio is also defined as the ratio of the distance by which a machine component moves to the distance by which a driving machine component is moving during the same time. Machine advantages can also be defined as a quantity that is being used to calculate the force of amplification which is produced by a mechanical system.