Illustrated · 1 min
What is a force, anyway?
Forces are a consequence of the conservation of energy. Exerting a net force on an object changes its kinetic energy; but that energy must come from somewhere else. Forces are produced by changes in potential energy with position - described in terms of derivatives as gradients.
An Example
Consider the following schematic, giving the potential energy (y) of an object as a function of position (x):
This might describe a hill on the right, with a barrier near the bottom.
Place an object at a point on the hill. The potential energy decreases leftward, so the force is in that direction. But when an object encounters the barrier, potential energy is changing the opposite way. The object experiences a force in the opposite direction - and unless it has sufficiently high kinetic energy to start with, it will not pass the barrier.
If there is no change in potential energy with position, as on the left, then there is no force.