An object with a mass of #8 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?
- the plane is frictionless,
- the only forces at play are the weight of the mass (
- the direction of the pushing force is parallel to the plane.
For convinience, lets shift our coordinate system by
Along the x' axis we have:
And along y' we have:
Then lets just add the vectors per axis.
And for y'
Thus, the net force is just
From this we can tell that the net force is parallel to the plane and that the net force points against the direction of the pushing force.
*Note: Its best to use a free body diagram if you're confused about the direction of forces.
Hope this helps!