Force

Force produces a change in the momentum of a mass on which it acts, according to F=ma (Newton's Second Law). Forces result from various types of physical interactions, which always generate a pair of opposite forces acting on two different objects (Newton's Third Law).

Historically the first mathematical description of interactions was by forces and force laws, and this formulation is still the most commonly used in Newtonian Mechanics. In the traditional approach to Newtonian Mechanics, all other descriptions of interactions (e.g. potential energy) are defined in terms of force. In this WIKI, "force" is often used interchangeably with "interaction". For example, the earth and the moon are attracted by the force of gravity, OR by their gravitational interaction.

Properties of forces:

• Forces satisfy Newton's Second Law (for a point particle) 
• The definition of force and its unit of measurement (Newton = kg m s-2) follow from this law
• Various forces combine linearly according to laws of vector addition to give the Net Force acting on a body.
• Interactions between bodies generate opposite forces on each of the two different bodies (Newton's Third Law)
• Four fundamental interactions give rise to the four fundamental forces, but only gravity and the electromagnetic forces are ficant at distance scales larger than a micron.
• Phenomenological Forces such as contact forces, friction, spring force, tension, drag from a moving fluid, etc. result from these fundamental forces plus quantum mechanics and often follow mathematical laws reasonably accurately.  (e.g. Hooke's Law, viscous drag, form drag)
• Conservative forces can be expressed as the (negative) gradient of the associated potential energy.

Motivation for Concept

Consider a bowling ball (or some other heavy object that moves with little resistance). If you want a stationary ball to move, you have to exert a force on it in the direction you want it to move, which will accelerate it. If you want the moving ball to turn, you have to exert a force on it toward the side you want it to turn toward. If you want the ball to stop moving, you have to exert a force opposite to its velocity.  To change the motion of the bowling ball, you will probably apply a force by using your hands or feet or some object you push against the ball. There are other kinds of forces, however. The earth, for example, can alter the ball's motion through the invisible action-at-a-distance of gravity, often represented as a gravitational field acting on the body at the site of the body.

Newton's Laws

Newton's famous Three Laws of Motion together comprise his definition of force.

• Newton's First Law: If an object is moving with no force acting upon it, then it will move with constant velocity. Note that velocity is a vector, so this statement implies that the object will keep the same speed and the same direction of motion.  This directly contradicts the animistic view of motion in which the natural condition of a body is at rest with respect to its surroundings - the First Law says the natural state of a body is moving with zero acceleration, not zero velocity.
• Newton's Second Law: The mathematical relationship between force and momentum, or, for systems with constant mass, the relationship between force and acceleration.
• Newton's Third Law: Every force exerted on one body by a second body is paired with another force of equal magnitude and opposite direction exerted on the second body by the first.

Classification of Forces

There are many ways to classify forces. For the purposes of the modeling approach to physics, the most important classifications to understand are Internal vs. External and Conservative vs. Non-Conservative. Another commonly encountered classification of forces is by their status as "fundamental" vs. phenomenological.

Internal vs. External

• Internal Force: A force exerted on one constituent of a specified system by another constituent of the same system. Internal forces do not affect the momentum of the system's center of mass, because their effects always cancel as required by Newton's Third Law.

• External Force: A force exerted on a constituent of a system by the environment.

Conservative vs. Non-Conservative

• Conservative Force: A force which has an associated potential energy. In introductory mechanics, the only conservative forces generally encountered are gravitation (universal) and elastic forces which satisfy Hooke's Law for elastic interactions.

• Non-Conservative Forces: A force which does work on an object in a path-dependent manner. For example, any force that has more than one possible value at a specific position is non-conservative.

Fundamental vs. Phenomenological

• Fundamental Forces: Forces which can influence the motion of at least one class of elementary fermionic particle. The only fundamental force which is studied directly in introductory mechanics is gravity.

• Phenomenological Forces: The page phenomenological force could not be found.