Other objects can cause object to tend to change motion {force, physics}|. Force requires interaction between two objects. All forces are pushes or pulls, such as when two objects collide. Gravity and electric forces are interactions of objects with second-object fields. Force F that object receives equals object mass m times object acceleration a: F = m*a. Force has direction and amount and so is vector. Mechanical force can be interaction between two colliding masses, but repulsions between electrons around molecules mediate contact between objects.
Gravity and electric force can act between two objects over distance {force field}.
exchange
All forces transmit bosons. In all field interactions, two objects exchange bosons. Gravity exchanges graviton bosons. Electromagnetism exchanges photon bosons. Strong nuclear force exchanges gluon bosons. Weak nuclear force exchanges W-particle and Z-particle bosons.
field
All forces are metric gauge fields. Bosons form field around object. Field changes space curvature, from flat to curved. When two objects interact, they go through curved space and change motion accordingly, just as cars turn on banked curves. Acceleration involves boson exchange. Boson exchange and curved spaced have identical effects, because bosons curve space, and space-curvature acceleration releases bosons to interact.
mass and distance
Bosons with no mass, such as gravitons and photons, can exchange to infinite distances. Bosons with mass, such as gluons, W particles, and Z particles, have short action distances.
time
Particles exchanged by forces take time to act, based on force strength. Strong force takes 10^-23 seconds. Electric force takes 10^-21 seconds. Weak force takes 10^-18 seconds to 1000 seconds. Gravitational force takes much longer.
electromagnetism
Electrical force is interaction between two charges. Magnetic force is interaction between two relativistic charges.
weak force
Electric force is 1000 times stronger than weak force.
gravity
Gravitation and electromagnetism are similar, because interactions cause both forces and both forces radiate in all directions. Because masses are positive, gravitational force is attractive. Because charges are positive and negative, electromagnetic force is attractive or repulsive. Electric-force to gravitational-force ratio is 10^36. If gravity is stronger, universe is smaller, and stars are smaller and exist shorter. If gravity is weaker, universe is larger, and stars are larger and exist longer.
Electromagnetic and weak forces unify {electroweak force}| {electric-weak unification theory} under SU(2) x U(1) Lie symmetry group, with gauge symmetry. An adjoint representation uses U(1) subgroup of SU(2), making electroweak Higgs field. W+, W-, and Z bosons and photons are equivalent at proton-diameter distances and high energies. Spontaneous symmetry breaking in current universe causes W+, W-, and Z bosons to have mass and photons to have zero rest mass.
All forces are metric fields {gauge invariant field} {gauge field}| that transmit bosons.
Gravitational force {gravity, mass} is interaction between two masses. Gravitons mediate gravity, by exchange at light speed. Gravity curves space. If only gravity shapes space-time, why does light speed, which depends on electromagnetic force, determine space-time boundaries?
Mass is always positive, and gravity is always attractive. Negative energy is repulsive {antigravity} {anti-gravity}. Negative internal pressure is also repulsive.
Atomic particles that have quarks and gluons interact {strong nuclear force}|. Strong nuclear force is positive and constant over distances more than 10^-14 centimeters, is repulsive over shorter distances, depends on quark number, and is 100 to 1000 times stronger than electric force.
Perhaps, nuclear forces {superweak force}| can mediate between strong and weak nuclear forces.
Leptons and quarks interact {weak nuclear force}|. Quarks and leptons have left-handed and right-handed spin states. Weak forces act on one or the other. For example, left-handed down quark can become up quark, making neutron into proton, electron, and neutrino {radioactive beta decay}. Right-handed down quarks have no change.
antiparticles
Particles that are right-handed or left-handed have weak nuclear force, but their antiparticles do not have weak force.
bosons
Weak-force W-particle and Z-particle bosons can come from vacuum with no conservation, except at very high energy.
distance
Weak nuclear force acts over less than 10^-16 centimeters.
strength
Weak nuclear force is 10^34 times stronger than gravity.
Relation between weak and electromagnetic forces became constant at 10^-12 seconds after universe origin, when U(2) symmetry broke at a rotation angle {electroweak mixing angle} {Weinberg angle}.
Motions {simple harmonic motion}| can oscillate along lines, with acceleration proportional to distance from center point. Molecule-bond vibrations, springs, pendulums, rigid-bar vibrations, rotations, guitar-string vibrations, bridge vibrations, and tall-building sway have simple harmonic motion.
force
Restoring-force strength depends on material type and distance from center. For molecule bonds, spring constant depends on electrical forces between atoms. Restoring force F equals negative of spring constant k expressing restoring force strength times displacement x: F = -k*x. Restoring force is negative because it opposes displacement.
amplitude
Amplitude depends on input energy, which causes more or less displacement.
period
One oscillation takes one time period. Period depends on material restoring force. Period and amplitude are independent. Spring period T is 360 degrees expressed in radians 2*pi times square root of mass m divided by spring constant k: T = 2 * pi * (m/k)^0.5. Higher mass makes longer period. Higher spring constant makes shorter period.
energy
Potential energy PE equals half spring constant k times displacement x squared, which is average force, k*x/2, times distance x: PE = 0.5 * k * x^2. At center, force equals zero, and potential energy equals zero. At maximum displacement amplitude, force and potential energy are highest. At maximum displacement, kinetic energy equals zero, because motion stops as direction reverses. At center, velocity and kinetic energy maximize, because potential energy is zero.
velocity
Maximum velocity v is maximum displacement A times square root of spring constant k divided by object mass m: v = A * (k/m)^0.5. Average velocity is 4*A/T, where A is amplitude and T is period. Average velocity is 2 * v / pi, where v is maximum velocity.
friction
If friction damps simple harmonic motion, amplitude decreases, but frequency stays the same, because material is the same.
When pulled sideways and released, weight {pendulum} hanging by string or wire from point starts oscillating motion.
force
Pendulum restoring force is gravity. Gravity g pulls pendulum-bob mass m back toward center with force F from distance x, depending on displacement angle A: F = m * g * sin(A) = m * k * x.
distance
If pendulum displacement is small, displacement-angle sine equals displacement angle: sin(A) = A. For small displacement, displacement x is displacement angle, expressed in radians, times pendulum length L: x = A*L. For small displacement, constant k is gravity acceleration g divided by pendulum length L: k = g/L.
period
Pendulum period T is 360 degrees, expressed in radians 2*pi, times square root of gravitational-constant reciprocal 1/g: T = 2 * pi * (1/g)^0.5. Longer pendulums have longer periods. Weaker gravity makes longer period. Pendulum mass does not affect period.
Spring oscillation time T {period, oscillation}| is 360 degrees, expressed in radians 2*pi, times square root of mass m divided by spring constant k: T = 2 * pi * (m/k)^0.5. Higher mass makes longer period. Higher spring constant makes shorter period.
Springiness {spring constant, force} depends on length, cross-sectional area, and force strength between molecules. Stiff springs {spring, metal}| have high spring constant.
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Date Modified: 2022.0225