# Force

(Redirected from Forcing) In physics, force is anything that can cause a mass to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force). In an extended body, force may also cause rotation, deformation, or an increase in pressure for the body. Rotational effects are determined by the torques, while deformation and pressure are determined by the stresses that the forces create.

Net force is mathematically equal to the rate of change of the momentum of the body. Since momentum is a vector quantity (has both a magnitude and direction), force also is a vector quantity.

The concept of force has formed part of statics and dynamics since ancient times. Ancient contributions to statics culminated in the work of Archimedes in the 3rd century BC, which still forms part of modern physics. In contrast, Aristotle's dynamics incorporated intuitive misunderstandings of the role of force which were eventually corrected in the 17th century, culminating in the work of Isaac Newton. Following the development of quantum mechanics it is now understood that particles influence each another through fundamental interactions, making force a redundant concept. Only four fundamental interactions are known: strong, electromagnetic, weak (unified into one electroweak interaction in 1970s), and gravitational. (in order of decreasing strength).

## History

Aristotle and his followers believed that it was the natural state of objects on Earth to be motionless and that they tended towards that state if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g. for heavy bodies to fall), which lead to "natural motion", and unnatural or forced motion, which required continued application of a force. But this theory, although based on the everyday experience of how objects move (e.g. a horse and cart), had severe trouble accounting for projectiles, such as the flight of arrows. Several theories were discussed over the centuries, and the late medieval idea that objects in forced motion carried an innate force of impetus was influential on the work of Galileo. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the Aristotelian theory of motion early in the 17th century. He showed that the bodies were accelerated by gravity to an extent which was independent of their mass and argued that objects retain their velocity unless acted on by a force - usually friction.

Isaac Newton is recognised as having argued explicitly for the first time that, in general, a constant force causes a constant rate of change (time derivative) of momentum.

In 1784 Charles Coulomb discovered the inverse square law of interaction between electric charges using a torsion balance, which was the second fundamental force. The weak and strong forces were discovered in the 20th century.

With the development of quantum field theory and general relativity it was realized that “force” is a redundant concept arising from conservation of momentum (4-momentum in relativity and momentum of virtual particles in QED). Thus currently known fundamental forces are more accurately called “fundamental interactions”.

## Types of force

Although there are apparently many types of forces in the Universe, they are all based on four fundamental forces. The strong and weak forces only act at very short distances and are responsible for holding certain nucleons and compound nuclei together. The electromagnetic force acts between electric charges and the gravitational force acts between masses. The Pauli exclusion principle is responsible for the tendency of atoms not to overlap each other, and is thus responsible for the "stiffness" or "rigidity" of matter, but this also depends on the electromagnetic force which binds the constituents of every atom.

All other forces are based on these four. For example, friction is a manifestation of the electromagnetic force acting between the atoms of two surfaces, and the Pauli exclusion principle, which does not allow atoms to pass through each other. The forces in springs modeled by Hooke's law are also the result of electromagnetic forces and the exclusion principle acting together to return the object to its equilibrium position. Centrifugal forces are acceleration forces which arise simply from the acceleration of rotating frames of reference.

There is currently some debate to whether there are five forces not four. The discovery of dark energy which acts on an even larger scale than gravity (with an opposing effect) and is a unique and separate force.

The modern quantum mechanical view of the first three fundamental forces (all except gravity) is that particles of matter (fermions) do not directly interact with each other but rather by exchange of virtual particles (bosons). This exchange results in what we call electromagnetic interaction (Coulomb force is one example of electromagnetic interaction).

In general relativity, gravitation is not strictly viewed as a force. Rather, objects moving freely in gravitational fields simply undergo inertial motion along a straight line in the curved space-time - defined as the shortest space-time path between two points. This straight line in space-time is a curved line in space, and it is called the ballistic trajectory of the object. For example, a basketball thrown from the ground moves in a parabola shape as it is in a uniform gravitational field. Similarly, planets move in ellipses as they are in an inverse square gravitational field. The time derivative of the changing momentum of the body is what we label as "gravitational force".

## Examples

• A heavy object is in free fall. Its momentum changes as dp/dt = mdv/dt = ma =mg (if the mass m is constant), thus we call the quantity mg a "gravitational force" acting on the object. This is the definition of weight (w=mg) of an object.
• A heavy object on a table is pulled (attracted) downward toward the floor by the force of gravity (i.e., its weight). At the same time, the table resists the downward force with equal upward force (called the normal force), resulting in zero net force, and no acceleration. (If the object is a person, he actually feels the normal force acting on him from below.)
• A heavy object on a table is gently pushed in a sideways direction by a finger. However, it doesn't move because the force of the finger on the object is now opposed by a new force of static friction, generated between the object and the table surface. This newly generated force exactly balances the force exerted on the object by the finger, and again no acceleration occurs. The static friction increases or decreases automatically. If the force of the finger is increased (up to a point), the opposing sideways force of static friction increases exactly to the point of perfect opposition.
• A heavy object on a table is pushed by a finger hard enough that static friction cannot generate sufficient force to match the force exerted by the finger, and the object starts sliding across the surface. If the finger is moved with a constant velocity, it needs to apply a force that exactly cancels the force of kinetic friction from the surface of the table and then the object moves with the same constant velocity. Here it seems to the naive observer that application of a force produces a velocity (rather than an acceleration). However, the velocity is constant only because the force of the finger and the kinetic friction cancel each other. Without friction, the object would continually accelerate in response to a constant force.
• A heavy object reaches the edge of the table and falls. Now the object, subjected to the constant force of its weight, but freed of the normal force and friction forces from the table, gains in velocity in direct proportion to the time of fall, and thus (before it reaches velocities where air resistance forces becomes significant compared to gravity forces) its rate of gain in momentum and velocity is constant. These facts were first discovered by Galileo.

## Quantitative definition

We have an intuitive grasp of the notion of force, since forces can be directly perceived as a push or pull. As with other physical concepts (e.g. temperature), the intuitive notion is quantified using operational definitions that are consistent with direct perception, but more precise. Historically, forces were first quantitatively investigated in conditions of [static equilibrium where several forces cancelled each other out. Such experiments prove the crucial properties that forces are additive vector quantities: they have magnitude and direction. So, when two forces act on an object, the resulting force, the resultant, is the vector sum of the original forces. This is called the principle of superposition. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. As with all vector addition this results in a parallelogram rule: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector which is equal in magnitude and direction to the transversal of the parallelogram.

As well as being added, forces can also be broken down (or 'resolved'). For example, a horizontal force pointing northeast can be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Force vectors can also be three-dimensional, with the third (vertical) component at right-angles to the two horizontal components.

The simplest case of static equilibrium is when two forces are equal in magnitude but opposite in direction. This remains the most usual way of measuring forces, using simple devices such as weighing scales and spring balances. Using such tools, several quantitative force laws were discovered: that the force of gravity is proportional to volume for objects made of a given material (widely exploited for millennia to define standard weights); Archimedes' principle for bouyancy; Archimedes' analysis of the lever; Boyle's law for gas pressure; and Hooke's law for springs: all these were all formulated and experimentally verified before Isaac Newton expounded his three laws of motion.