Question

$\text{(a)}$ Express the full relation among the mechanical advantage, velocity ratio, and efficiency of a machine. $\left[3\text{marks}\right]$

$\text{(b)}$ If the velocity ratio of a machine is $3.6$ and the load of the machine is thrice the effort in magnitude, find out how efficient the machine is. $\left[2\text{marks}\right]$

Answer 1

$\text{(a)}$ The mechanical advantage $\left(\text{MA}\right)$, velocity ratio $\left(\text{VR}\right)$, and efficiency $\left(\eta \right)$ of a machine are related to each other as:
$\text{MA}=\text{VR}\times \eta$ $\left[1\text{mark}\right]$

$\eta =\frac{\text{MA}}{\text{VR}}=\frac{\frac{L}{E}}{\frac{V_E}{V_L}}=\frac{L\times V_L}{E\times V_E}$ $\left[1\text{mark}\right]$

where, $L$ and $E$ are the load and effort of the machine, $V_L$ is the velocity of the load to the corresponding velocity $V_E$ of the effort. $\left[1\text{mark}\right]$

$\text{(b)}$ Given the velocity ratio $\left(\text{VR}\right)=3.6$
The load is thrice the effort, $L=3E$ $\left[0.5\text{mark}\right]$
$⟹$ Mechanical advantage $\left(\text{MA}\right)=\frac{L}{E}=3$ $\left[0.5\text{mark}\right]$
The efficiency of the machine, $\eta =\frac{\text{MA}}{\text{VR}}=\frac{3}{3.6}=\frac{5}{6}$
$=0.8333$ $\left[0.5\text{mark}\right]$
So, the machine is $83.33\%$ efficient. $\left[0.5\text{mark}\right]$