If a 1-N force accelerates a 1-kg mass at 1 meter per second squared in a zero-gravity and zero-friction environment how do you calculate its motion in the presence of gravity and friction?

Answer 1

Your ideal scenario describes the near-perfect vacuum and weightlessness of space. As you said, a one-kilogram mass will accelerate at one meter per second squared if a net force of one newton is applied to it. But you wish to know what happens under real-world conditions, such as the existence of friction (air resistance, rolling friction, and sliding friction) and gravity. If the motion is in the horizontal plane and at low speeds, air resistance is negligible. Friction between surfaces and rolling friction are significant, however, and will act against any force used to accelerate an object. Gravity plays a role in the consideration of friction, as well, inasmuch as the frictional force is proportional to the Normal Force, which is related to the object's weight.1 For motion in two directions, such as the path of a kicked ball or the trajectory of a bullet fired from a gun, air resistance plays a large role as does the acceleration of gravity. Friction and the effects of gravity play a major role in calculations involving the motion in the vertical direction, whereas the acceleration of gravity plays no role in the calculations of the motion in the horizontal direction.2Basically, keep in mind that weight is a force directed downward. When determining the net force acting on an object, its weight is just one of the forces acting on it. 1. For an object resting on a flat surface with zero incline, the Normal Force is equal and opposite to the object's weight (W = mg). The frictional force is calculated to be uN, where u (the Greek letter mu) is the coefficient of friction. The frictional force opposes the direction of motion. For objects on an inclined plane, the Normal force is equal to W*cos(theta), where theta is the angle of incline. 2. Weight is a force perpendicular (orthogonal) to horizontal motion and, hence, can have no effect upon it.

Answer 2

In the presence of gravity, you would need to consider the weight of the mass by adding the force due to gravity acting on it (F = m*g). Friction would add an opposing force that affects the acceleration of the mass. To calculate the motion with these considerations, you would use Newton's second law (F = ma) and include the forces due to gravity and friction in your calculations.