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?

1 Answer
Feb 13, 2018

"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.

enter image source here

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

G=mg=2*9.81=19.62N

enter image source here

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

enter image source here

G_x=mg*cos theta=2*9.81*cos(pi/8)=18.13 N

G_y=mg*sin (theta)=2.9.81*sin (pi/8)=7.51N

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

N=-G_y=-mg*cos theta
N+(-G_y)=0

enter image source here

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

enter image source here

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

F_("net")=G_x-F

F_("net")=18.13-8

F_("net")=10.13N

enter image source here