Question

A force of 40 N acts upon a body whose weight is 9.8 N. What is the mass of the body and how much is its acceleration?

Answer 1

Step 1: Given:

Weight of the body, $\mathit{W}\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{8}\mathit{N}$

Acceleration due to gravity, $\mathit{g}\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{8}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$

Mas of the body, $m=?$

Force, $\mathit{F}\mathbf{=}\mathbf{40}\mathit{N}$

Step 2: Finding mass

The formula for weight, W can be expressed as

$$\begin{gathered} \mathit{W}\mathbf{=}\mathit{m}\mathit{g} \\ \mathit{m}\mathbf{=}\frac{\mathbf{W}}{\mathbf{g}} \end{gathered}$$

Substituting the values,

$\mathit{m}\mathbf{=}\frac{\mathbf{9}\mathbf{.}\mathbf{8}}{\mathbf{9}\mathbf{.}\mathbf{8}}\mathbf{=}\mathbf{1}\mathit{k}\mathit{g}$

Step 3: Finding acceleration

The formula for force is

$\mathit{F}\mathbf{=}\mathit{m}\mathit{a}$

where $a=$acceleration

Substituting the values

$$\begin{gathered} \mathbf{40}\mathbf{=}\mathbf{1}\mathbf{\times }\mathit{a} \\ \mathit{a}\mathbf{=}\mathbf{40}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}} \end{gathered}$$

So, the mass of the body is $1kg$ and acceleration is $40m/s^2$.