Read · 3 min
Force is the gradient of the potential energy of a system. Observationally, all forces we have observed are versions of four different fundamental forces, which give four different forms of potential energy - each of which are relevant in different contexts.
Two of these fundamental forces should be relatively familiar: gravity and electromagnetism. The other two are the strong nuclear force and the weak nuclear force. As suggested by their names, the last two are relevant only on the scales of atomic nuclei and smaller.
Gravity
Gravity is a long-range force. It has been measured over distances ranging from tens of meters to hundreds of millions of lightyears. The gravitational force between two objects is determined by the masses of the two objects; the distance between them; and a quantity called the gravitational constant (described by the law of gravitation). It is common to describe the gravity of a single object in terms of the acceleration it would produce on another object at a given position in the absence of any other forces, since the mass of the second object cancels out.
Gravity is a relatively weak force unless large masses are involved. The entire mass of Earth produces a gravitational acceleration of on your body, unless you happen to be reading this from space - in which case it is less than that. For many applications, you don't need to worry about the gravitational perturbations from standing next to a mountain or from a lake draining or from the Moon passing overhead.
We don't all fall into a point under the influence of gravity because conservation of angular momentum and potential energy barriers due to other fundamental properties of materials prevent that.
Electromagnetism
Unlike gravity, the magnitude of other fundamental forces is determined by properties of objects other than mass - although the mass of an object still determines the acceleration it experiences from a given force. For electromagnetism, frequently abbreviated E&M, the fundamental physical property is called charge.
Unlike mass, charge can be positive, negative, or zero. This means that unlike gravity, which is an attractive force, electromagnetic interactions can either push objects apart or pull them together. Objects with charge of the same sign repel one another, objects with charge of opposite signs attract one another. The distribution and motion of charge within an object can also produce forces, even if its overall charge is zero - this is how magnets work.
The most visible electromagnetic process is light. Light is electromagnetic energy propagating across space; emitted and absorbed by charged particles.
Electromagnetic interactions are also responsible for the contact forces that are considered in much of mechanics. This includes the forces that stop everything on Earth from falling inwards to a point; the forces that let you press keys and buttons and use a trackpad or touchscreen; and many others.
Strong & Weak Nuclear Forces
The strong and weak nuclear forces act only on extremely short length scales - usually within the nuclei of individual atoms. They are determined by properties of subatomic particles called color charge and weak isospin respectively. Do not confuse the former with anything to do with the usual meaning of "color" - it is simply an arbitrary label given to "the property of particles that describes their strong nuclear interactions".
The strong and weak nuclear forces determine the structures of individual atomic nuclei and other particles; and describe interactions in nuclear physics such as fusion and fission. Describing the details of how they operate requires working through areas of physics called quantum mechanics, quantum electrodynamics, electro-weak theory, and quantum chromodynamics. For our purposes here, it is enough to say that the strong and weak nuclear forces become stronger than electromagnetism within atomic nuclei - allowing, for example, six positively-charged protons and six uncharged neutrons to be bound to one another in a carbon atom even though electromagnetism by itself would force the protons apart.