Force

The force may be thought of as an influence which tends to change the motion of an object. Forces are inherently vector quantities, requiring vector addition to combine them.

The SI unit for force is the newton [N], which is defined by Newton = \(\dfrac{kg\cdot m}{s^2}\) as may be seen from Newton’s second law. In mechanics, forces are seen as the causes of linear motion, whereas the causes of rotational motion are called torques. The action of forces in causing motion is described by Newton’s Laws under ordinary conditions, although there are notable exceptions.

Types of force

Conservative and non-conservative forces

A good way to think of conservative forces is to consider what happens on a round trip. A conservative force is a force with the property that the total work is done in moving a particle between two points is independent of the taken path.

If a particle travels in a closed loop, and the kinetic energy is the same after a round trip, the force is a conservative force, or at least is acting as a conservative force. Informally, a conservative force can be thought of as a force that conserves mechanical energy.

A conservative force is dependent only on the position of the object. If a force is conservative, it is possible to assign a numerical value for the potential at any point. When an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken. If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points.

Consider gravity; you throw a ball straight up, and it leaves your hand with a certain amount of kinetic energy. At the top of its path, it has no kinetic energy, but it has a potential energy equal to the kinetic energy it had when it left your hand. When you catch it again it will have the same kinetic energy as it had when it left your hand. All along the path, the sum of the kinetic and potential energy is a constant, and the kinetic energy at the end, when the ball is back at its starting point, is the same as the kinetic energy at the start, so gravity is a conservative force.

Kinetic friction, on the other hand, is a non-conservative force, because it acts to reduce the mechanical energy in a system. Note that non-conservative forces do not always reduce the mechanical energy; a non-conservative force changes the mechanical energy, so a force that increases the total mechanical energy, like the force provided by a motor or engine, is also a non-conservative force.

For macroscopic systems, the non-conservative approximation is far easier to deal with than millions of degrees of freedom. Examples of non-conservative forces are friction and non-elastic material stress.

Other examples of conservative forces are: force in elastic spring, the electrostatic force between two electric charges, and magnetic force between two magnetic poles. The last two forces are called central forces as they act along the line joining the centers of two charged/magnetized bodies. Thus, all central forces are conservative forces.

Other examples of non-conservative forces are: frictional forces, viscous forces, induction forces, air resistance force, tension in a string, normal force, propulsion force of the rocket, propulsion force of the boat.

Forces that act on all objects

  • Weight (W, Fg) – The force of gravity acting on an object due to its mass. An object’s weight is directed down, toward the center of the gravitating body; like the Earth or moon, for example.

Forces associated with solids

  • Normal (N, Fn) – The force between two solids in contact that prevents them from occupying the same space. The normal force is directed perpendicular to the surface. A “normal” in mathematics is a line perpendicular to a planar curve or surface; thus the name “normal force”.
  • Friction (f, Ff) – The force between solids in contact that resists their sliding across one another. Friction is directed opposite the direction of relative motion or the intended direction of motion of either of the surfaces.
  • Tension (T, Ft) – The force exerted by an object being pulled upon from opposite ends like a string, rope, cable, chain, etc. Tension is directed along the axis of the object. (Although normally associated with solids, liquids and gases can also be said exert tension in some circumstances.)
  • Elasticity (Fe, Fs) – The force exerted by an object under deformation (typically tension or compression) that will return to its original shape when released like a spring or rubber band. Elasticity, like tension, is directed along an axis (although there are exceptions to this rule).

Forces associated with fluids (include liquids and gases)

  • Buoyancy (B, Fb) – The force exerted on an object immersed in a fluid. Buoyancy is usually directed up (although there are exceptions to this rule).
  • Drag (R, D, Fd) – The force that resists the motion of an object through a fluid. Drag is directed opposite the direction of motion of the object relative to the fluid.
  • Lift (L, F) – The force that a moving fluid exerts as it flows around an object; typically a wing or wing-like structure, but also golf balls and baseballs. Lift is generally directed perpendicular to the direction of fluid flow (although there are exceptions to this rule).
  • Thrust (T, Ft) – The force that a fluid exerts when expelled by a propeller, turbine, rocket, squid, clam, etc. Thrust is directed opposite the direction the fluid is expelled.

Forces associated with physical phenomena

  • Electrostatic Force (FE) – The attraction or repulsion between charged bodies. Experienced in everyday life through static cling and in school as the explanation behind much of elementary chemistry.
  • Magnetic Force (FB) – The attraction or repulsion between charged bodies in motion. Experienced in everyday life through magnets and in school as the explanation behind why a compass needle points north.

Fundamental forces

The fundamental forces, also known as fundamental interactions, are a type of interaction between physical particles that do not appear to be reducible to more basic interactions. Four fundamental forces or fundamental interactions have been identified:

  1. gravitational interaction (gravity): the interaction between objects due to their mass. Weight is a synonym for the force of gravity;
  2. electromagnetic interaction (electromagnetism): the interaction between objects due to their charge. All the forces discussed above are electromagnetic in origin except weight;
  3. the weak nuclear interaction: the interaction between subatomic particles with “flavor” (an abstract quantity that has nothing to do with human taste). This force, which is many times weaker than the strong nuclear interaction, is involved in certain forms of radioactive decay;
  4. strong nuclear interaction: the interaction between subatomic particles with “color” (an abstract quantity that has nothing to do with human vision). This is the force that holds protons and neutrons together in the nucleus and holds quarks together in the protons and neutrons. It cannot be felt outside of the nucleus.

Weak nuclear interaction

The weak interaction, which is also often called the weak force or weak nuclear force, is responsible for some nuclear phenomena such as beta decay of the atomic nuclei associated with radioactivity and acts between leptons and quarks (semileptonic interactions), between only leptons (leptonic interactions) and between only quarks (non-leptonic interactions) through the exchange of massive vector bosons called the W+, W, and Z bosons. It is the only force that in experiments acts on neutrinos, for which gravity is negligible. A vector boson is a boson with the spin equal to 1.

The masses of W+, W, and Z bosons are far greater than the mass of a proton or neutron, which is consistent with the short range of the weak force. In fact, the force is termed weak because its field strength over a given distance is typically several orders of magnitude less than that of the strong nuclear force or electromagnetic force.

The weak interaction has a finite range of action comparable to the subatomic length scale, therefore particularly small, when compared with human scales. The weak interaction is the only known fundamental interaction that does not conserve parity-symmetry, and similarly, the only one to break charge parity symmetry; it is left-right asymmetric. The weak interaction even violates CP symmetry but does conserve CPT.

According to the electroweak theory, at certain levels of energy, the weak interaction is unified to the electromagnetic interaction into a single interaction called electroweak. Electromagnetism and the weak force are now understood to be two aspects of a unified electroweak interaction — this discovery was the first step toward the unified theory known as the Standard Model. The Standard Model provides a uniform framework for understanding the electromagnetic, weak, and strong interactions.

For energies of the order of 100 GeV, the electromagnetic force and the weak force appear as unified in the electroweak interaction. The range and intensity of a force are the two most important characteristics of fundamental interactions. Intensity provides a measure of the power relationships between the interactions of different nature. Simplifying, the range can be thought of as the maximum distance at which interaction is influential. For example, gravitational interaction has an infinite range of action; for this reason, the Sun exerts its gravitational force even on very distant objects such as Pluto.

Strong nuclear interaction

Strong nuclear interaction, has a property called color charge, holds quarks together, elementary constituents of protons and neutrons, and also the latter within the nucleus. It is absolutely the most intense force among those known so far, to the point that it is not possible at low energy to isolate and separate a single quark from a proton. Such isolation of the color charge theoretically allows long-range strong interactions only through globally neutral composite bosons by color, formed by a quark and an antiquark, in turn, linked by strong force (mesons).

However, since these are all unstable, and decaying in a short time, the strong nuclear force acts in fact only at a short distance in the nuclei. For example, the strong interaction between two nucleons can be described at low energy as the result of the exchange of Pi mesons, or pions.

Fictitious forces

These are apparent forces that object experience in an accelerating coordinate system like an accelerating car, airplane, spaceship, elevator, or amusement park ride. Fictitious forces do not arise from an external object like genuine forces do, but rather as a consequence of trying to keep up with an accelerating environment.

  • Centrifugal force – The force experienced by all objects in a rotating coordinate system that seems to pull them away from the center of rotation.
  • Coriolis force – The force experienced by moving objects in a rotating coordinate system that seems to deflect them at right angles to their direction of motion.
  • G-Force” – Not really a force (or even a fictitious force) but rather an apparent gravity-like sensation experienced by objects in an accelerating coordinate system.
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