Question

Question:A $\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{kg}$object undergoes an acceleration given by $\mathbf{a}\mathbf{=}\left(2.00\hat{i}+5.00\hat{j}\right)\mathbf{}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. Find (a) the resultant force acting on the object and (b) the magnitude of the resultant force.

Short answer

(a) The resultant force acting on the object is $(6\hat{i}+5\hat{j})\mathrm{N}$.

(b) The magnitude of resultant force acting on the object is $16.2\mathrm{N}$.

Step-by-step solution

Concept and identification of given data

The acceleration of the object is the variation in the velocity of the object with position and time.

Consider the given data as below.

The mass of object is $m=3\mathrm{kg}$.

The acceleration of object is $\mathrm{a}=(2.00\hat{\mathrm{i}}+5.00\hat{\mathrm{j}})\mathrm{m}/{\mathrm{s}}^2$.

(a) Determination of resultant force acting on object

The resultant force acting on the object is given as:

$\overrightarrow{F}=m\overrightarrow{a}$

Substitute all the values in the above equation.

$\begin{array}{l}\overrightarrow{\mathrm{F}}=\left(3\mathrm{kg}\right((200\hat{\mathrm{i}}+5.00\hat{\mathrm{j}})\mathrm{m}/{\mathrm{s}}^2)\\ \overrightarrow{\mathrm{F}}=(6\mathrm{i}+5\mathrm{j})\mathrm{N}\end{array}$

Therefore, the resultant force acting on the object is $\overrightarrow{\mathrm{F}}=(6\mathrm{i}+5\mathrm{j})\mathrm{N}$.

(b) Determination of magnitude of the resultant force acting on the object

The magnitude of resultant force acting on the object is given as:

$\begin{array}{c}F=\overrightarrow{\left|F\right|}\\ =\left(6\hat{\mathrm{i}}+15\hat{\mathrm{j}}\right)\mathrm{N}\\ =\sqrt[]{{\left(6\mathrm{N}\right)}^2+{\left(15\mathrm{N}\right)}^2)}\\ =16.2\mathrm{N}\end{array}$

Hence, the magnitude of resultant force acting on the object is $16.2\mathrm{N}$.