Chapter 5, Problem 5.1CYU

Check Your Understanding Find the magnitude and direction of the net force in the ice skater example just given.

To determine

The magnitude and direction of the net force.

Answer to Problem 5.1CYU

$14\text{N, }{56}^0\text{from}\text{x}\text{axis}$

Explanation of Solution

Given info:

The resultant force,

${\overrightarrow{F}}_{net}=8\widehat{i}+12\widehat{j}\text{N}$

Here, $F_1=8\text{N and }{F}_2=12\text{N}$

Formula used:

The magnitude is given by

$F_{net}=\sqrt{{\left(F_1\right)}^2+{\left(F_2\right)}^2}$

The direction is given by

$\theta ={\tan }^{-1}\left(\frac{F_2}{F_1}\right)$

Calculation:

The magnitude of net force is

$\begin{array}{l}{F}_{net}=\sqrt{{\left(8\right)}^2+{\left(12\right)}^2}\\ =\sqrt{208}=14.4\approx 14\text{N}\end{array}$

The direction is

$\begin{array}{l}\theta ={\tan }^{-1}\left(\frac{12}{8}\right)={\tan }^{-1}\left(1.5\right)\\ ={56}^0\text{from}\text{x}\text{axis}\end{array}$

Conclusion:

Thus, the magnitude of net force and its direction are 14 N and ${56}^0\text{from}\text{x}\text{axis}$ respectively.