How do you calculate the force when you know the mass and vertical distance?

Answer 1

The force required to lift a given mass perpendicularly to, just at, and at a constant velocity (including zero velocity) from, the Earth's surface may be determined from Newton's Second Law of Motion, F=MA, by substituting 'G', the acceleration of gravity, for A. So, F=MG Which essentially defines the distinction between mass and weight. I gave this definition because of the use of "vertical" in the question. As long as the "distance" is small compared to the radius of the Earth and the other conditions are met, the distance is irrelevant to the force required to lift the object. The distance does figure in the amount of "work" expended in lifting the object however, according to the relationship W=FD. If you are moving a mass on a ramp, under the effects of friction, under acceleration, or in any other way that doesn't meet the conditions described above, then the force calculated as shown will still apply, and must be added to the total force as a vector contribution. (The above applies to objects NOT moving at relativistic speeds, but if you are designing a particle accelerator you probably shouldn't be getting your advice from Wikianswers!)