9E - University Physics with Modern Physics

Question

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 N to the box and produces an acceleration of magnitude $\mathbf{2}\mathbf{.}\mathbf{2}\mathbf{ }\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$, what is the mass of the box?

Step-by-Step Solution

Answer

The mass of the box which undergoes an acceleration of $2.2 \mathrm{m}/{\mathrm{s}}^2$ when a force of 48 N is applied on it is 21.8 kg.

Step 1: Given data

The force on the box is, $\mathrm{F}=48 \mathrm{N}$   

The acceleration of the box is

 $\mathrm{a}=2.2 \mathrm{m}/{\mathrm{s}}^2$. 

Step 2: Second law of motion

The second law of motion relates the net force  , mass   and acceleration   as

$\mathbf{F}\mathbf{=}\mathbf{ma}$                                                                                                                         …(1)

Step 3: Mass of the box

From equation (1), the mass of the box is

  

$\begin{array}{rcl}\mathrm{m}& =& \frac{\mathrm{F}}{\mathrm{a}}\\ & =& \frac{48 \mathrm{N}}{2.2 \mathrm{m}/{\mathrm{s}}^2}\\ & =& 21.8 \mathrm{kg}\end{array}$

 

Thus, the mass of the box is 21.8 kg.