# An object with a mass of 5 kg is on a plane with an incline of pi/8 . If the object is being pushed up the plane with  3 N  of force, what is the net force on the object?

Aug 14, 2017

$\sum {F}_{x} = 15.8$ $\text{N}$ directed down the ramp

#### Explanation:

We're asked to find the net force acting on an object on an incline plane. The vertical forces (perpendicular to the incline) cancel out, because the normal force equals the perpendicular component of the weight force; thus, we are only looking at forces parallel to the incline.

There are two forces acting on the object (assuming the surface is frictionless):

• the gravitational force (acting down the ramp), equal to $m g \sin \theta$

• the applied force directed up the ramp

The net force equation is thus

sumF_x = overbrace(F_"applied")^"upward force" - overbrace(mgsintheta)^"downward force"

(taking positive direction to be up the ramp)

We know:

• $m = 5$ $\text{kg}$

• $g = 9.81$ ${\text{m/s}}^{2}$

• $\theta = \frac{\pi}{8}$

• ${F}_{\text{applied}} = 3$ $\text{N}$

Plugging these in:

sumF_x = 3color(white)(l)"N" - (5color(white)(l)"kg")(9.81color(white)(l)"m/s"^2)sin(pi/8) = color(red)(ulbar(|stackrel(" ")(" "-15.8color(white)(l)"N"" ")|)

(negative because it is directed down the ramp)