# An object with a mass of 2 kg is on a plane with an incline of pi/8 . If the object is being pushed up the plane with  8 N  of force, what is the net force on the object?

Feb 13, 2018

$\text{please see the explanation section.}$

#### Explanation:

• drawing a free-body diagram will make it easier to understand.
• blue and red dotted lines will be useful to separate the weight of the object from the components.

• The vector drawn with green symbolizes the weight of the body.

$G = m g = 2 \cdot 9.81 = 19.62 N$

• we now have to find the components of the weight on the red and blue axes.

${G}_{x} = m g \cdot \cos \theta = 2 \cdot 9.81 \cdot \cos \left(\frac{\pi}{8}\right) = 18.13 N$

${G}_{y} = m g \cdot \sin \left(\theta\right) = 2.9 .81 \cdot \sin \left(\frac{\pi}{8}\right) = 7.51 N$

• The blue vector is acting vertically. We know that the inclined plane will react against the effect(Newton's third law).

$N = - {G}_{y} = - m g \cdot \cos \theta$
$N + \left(- {G}_{y}\right) = 0$

• now,let's draw the Force of 8 N and Simplify the look of the diagram.

• we need to find the sum of the black and red vectors.

${F}_{\text{net}} = {G}_{x} - F$

${F}_{\text{net}} = 18.13 - 8$

${F}_{\text{net}} = 10.13 N$