An object with a mass of 2 kg is acted on by two forces. The first is F_1= < 3 N , 5 N> and the second is F_2 = < 7 N, -6 N>. What is the object's rate and direction of acceleration?

May 17, 2017

The rate of acceleration is $= 5.02 m {s}^{-} 2$ in the direction of 5.71º clockwise from the x-axis

Explanation:

The resultant force is

$\vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2}$

$= < 3 , 5 > + < 7 , - 6 >$

$= < 10 , - 1 >$

We apply Newton's second Law

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

Mass, $m = 2 k g$

$\vec{a} = \frac{1}{m} \cdot \vec{F}$

$= \frac{1}{2} < 10 , - 1 > = < 5 , - \frac{1}{2} >$

The magnitude of the acceleration is

$| | \vec{a} | | = | | < 5 , - \frac{1}{2} > | |$

$= \sqrt{{\left(5\right)}^{2} + {\left(- \frac{1}{2}\right)}^{2}}$

$= \sqrt{25.25} = 5.02 m {s}^{-} 2$

The direction is $\theta = \arctan \left(\frac{- \frac{1}{2}}{5}\right)$

The angle is

theta=arctan(1/10)=5.71º clockwise from the x-axis