Question

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?

Answer 1

`sumF_x = 15.8` `"N"` directed down the ramp

Explanation:

We're asked to find the net force acting on an object on an incline plane.

![upload.wikimedia.org]()

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 `mgsintheta`

• 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` `"kg"`

• `g = 9.81` `"m/s"^2`

• `theta = pi/8`

• `F_"applied" = 3` `"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)