Question

1. if you needed to put 16 n of work into a machine to get 12 n of work out, what is the mechanical efficiency of the machine?

Explanation:

Step1: Recall the formula for mechanical efficiency

Mechanical efficiency ($\eta$) is calculated as the ratio of output work ($W_{out}$) to input work ($W_{in}$), multiplied by 100 to get a percentage. The formula is $\eta=\frac{W_{out}}{W_{in}}\times100\%$.

Step2: Substitute the given values

We know that $W_{out} = 12\space N$ (output work) and $W_{in}=16\space N$ (input work). Substituting these values into the formula:
$\eta=\frac{12}{16}\times 100\%$

Step3: Simplify the fraction and calculate the percentage

First, simplify $\frac{12}{16}=\frac{3}{4}$. Then, $\frac{3}{4}\times100\% = 0.75\times100\%=75\%$.

Answer:

The mechanical efficiency of the machine is $75\%$.