# Question #90503

Dec 21, 2016

$61.22 N$

#### Explanation:

Refer to the figure below

As the mass slides down the inclined plane, we see that Normal reaction $N$ is equal and opposite to the $\cos \theta$ component of the weight. The other two forces acting on the mass are, $\sin \theta$ component acting along the plane and force of friction acting up the plane and opposing the motion of the mass. _"net"

As there is movement in sliding down there is net force given as
${F}_{\text{net}} = m g \sin \theta - f$
Using Newton's second law this net force can be written as

${F}_{\text{net}} = m a$ .......(1)
Where $m$ is mass $\mathmr{and} a$ is acceleration produced.

Using the kinematic equation
$s = u t + \frac{1}{2} a {t}^{2}$ and inserting given quantities in SI units we get
$1.2 = 0 \times 0.42 + \frac{1}{2} a {\left(0.42\right)}^{2}$
Solving for $a$
$a = 1.2 \times \frac{2}{0.42} ^ 2 = 13.605 m {s}^{-} 2$, rounded to three decimal places

Inserting value of $a$ in (1)
${F}_{\text{net}} = 4.5 \times 13.605$
$\implies {F}_{\text{net}} = 61.22 N$