Force Required to Move an Object on an Inclined Plane I was reviewing some basic concepts in physics. I was reading a concept that says “the force needed to push/pull an object on an inclined plane (suppose friction is zero) is
$$F= m\,g\,\sin(\theta)$$
My question is, if we exert the force on that object with that amount of force, wouldn’t we end up preventing the object from sliding down rather than move the object up?
Because the forces would cancel each other out and thus, no motion is made. Shouldn't the force required to move the object upwards be greater? I am thinking the force should be $F_p = m\,a + m\,g\sin(\theta)$.
 A: See if the body was sliding on the inclined plane ( considering frictionless surface) with only gravitational force then it would be accelerating along the plane with an acceleration of $g\sin \theta $.
Now if you apply the same amount of force along the plane then it wouldn't come at rest but will continue its motion in the same direction but this time with a constant velocity ( which is the velocity the body had gained (since it's velocity was changing at every moment due to gravity) when the external force was applied ) .
So in order to move the body upward i.e. in opposite direction , YES you will have to apply a greater amount of force .
As @ohneVal mentioned if the body was initially going upward (because of any push ) then we just need to apply force equal to its gravitational component along the plane and the body will move upward with a constant velocity.
A: Yes the object would then be in equilibrium. If you give it some velocity and then apply the force ($mg\sin \theta$), it would move up the slope.
