Question

A pulley system has three pulleys. A load of $120\mathrm{N}$ is overcome by applying an effort of $50\mathrm{N}$. Calculate the mechanical advantage and efficiency of this system.

Answer 1

Step 1: Given data

Velocity ratio $\left(\mathrm{VR}\right)$ is equal to the number of pulleys i.e. $3$

$$\begin{gathered} \mathrm{L}=120\mathrm{N} \\ \mathrm{E}=50\mathrm{N} \end{gathered}$$

Step 2: Find the mechanical advantage

Mechanical Advantage $\mathrm{MA}$: It is the ratio of the load $\left(\mathrm{L}\right)$to the effort $\left(\mathrm{E}\right)$.

It is expressed as $\mathrm{MA}=\frac{\mathrm{L}}{\mathrm{E}}$

Substitute the given values in $\mathrm{MA}=\frac{\mathrm{L}}{\mathrm{E}}$

$$\begin{gathered} \mathrm{MA}=\frac{120\mathrm{N}}{50\mathrm{N}} \\ \mathrm{MA}=2.4 \end{gathered}$$

The mechanical advantage of the system is $2.4$

Step 3: Find the efficiency.

Efficiency $\eta =\frac{\mathrm{MA}}{\mathrm{VR}}\times 100\%$

Substitute the value of $\left(\mathrm{MA}\right)$ and $\left(\mathrm{VR}\right)$ in the formula for efficiency

$\begin{array}{rcl}\eta & =& \frac{\mathrm{MA}}{\mathrm{VR}}\times 100\%\\ & =& \frac{2.4}{3}\times 100\%\\ & =& 80\%\end{array}$

So, the efficiency is $80\%$.

Thus, the mechanical advantage and efficiency of the given system is $2.4$ and $80\%$.