8.8 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Force | 5/11 | https://en.wikipedia.org/wiki/Force | reference | science, encyclopedia | 2026-05-05T09:33:04.607426+00:00 | kb-cron |
For an object in free-fall, this force is unopposed and the net force on the object is its weight. For objects not in free-fall, the force of gravity is opposed by the reaction forces applied by their supports. For example, a person standing on the ground experiences zero net force, since a normal force (a reaction force) is exerted by the ground upward on the person that counterbalances his weight that is directed downward. Newton's contribution to gravitational theory was to unify the motions of heavenly bodies, which Aristotle had assumed were in a natural state of constant motion, with falling motion observed on the Earth. He proposed a law of gravity that could account for the celestial motions that had been described earlier using Kepler's laws of planetary motion. Newton came to realize that the effects of gravity might be observed in different ways at larger distances. In particular, Newton determined that the acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law. Further, Newton realized that the acceleration of a body due to gravity is proportional to the mass of the other attracting body. Combining these ideas gives a formula that relates the mass (
m
⊕
{\displaystyle m_{\oplus }}
) and the radius (
R
⊕
{\displaystyle R_{\oplus }}
) of the Earth to the gravitational acceleration:
g
=
−
G
m
⊕
R
⊕
2
r
^
,
{\displaystyle \mathbf {g} =-{\frac {Gm_{\oplus }}{{R_{\oplus }}^{2}}}{\hat {\mathbf {r} }},}
where the vector direction is given by
r
^
{\displaystyle {\hat {\mathbf {r} }}}
, is the unit vector directed outward from the center of the Earth. In this equation, a dimensional constant
G
{\displaystyle G}
is used to describe the relative strength of gravity. This constant has come to be known as the Newtonian constant of gravitation, though its value was unknown in Newton's lifetime. Not until 1798 was Henry Cavendish able to make the first measurement of
G
{\displaystyle G}
using a torsion balance; this was widely reported in the press as a measurement of the mass of the Earth since knowing
G
{\displaystyle G}
could allow one to solve for the Earth's mass given the above equation. Newton realized that since all celestial bodies followed the same laws of motion, his law of gravity had to be universal. Succinctly stated, Newton's law of gravitation states that the force on a spherical object of mass
m
1
{\displaystyle m_{1}}
due to the gravitational pull of mass
m
2
{\displaystyle m_{2}}
is
F
=
−
G
m
1
m
2
r
2
r
^
,
{\displaystyle \mathbf {F} =-{\frac {Gm_{1}m_{2}}{r^{2}}}{\hat {\mathbf {r} }},}
where
r
{\displaystyle r}
is the distance between the two objects' centers of mass and
r
^
{\displaystyle {\hat {\mathbf {r} }}}
is the unit vector pointed in the direction away from the center of the first object toward the center of the second object. This formula was powerful enough to stand as the basis for all subsequent descriptions of motion within the Solar System until the 20th century. During that time, sophisticated methods of perturbation analysis were invented to calculate the deviations of orbits due to the influence of multiple bodies on a planet, moon, comet, or asteroid. The formalism was exact enough to allow mathematicians to predict the existence of the planet Neptune before it was observed.
=== Electromagnetic ===
The electrostatic force was first described in 1784 by Coulomb as a force that existed intrinsically between two charges. The properties of the electrostatic force were that it varied as an inverse square law directed in the radial direction, was both attractive and repulsive (there was intrinsic polarity), was independent of the mass of the charged objects, and followed the superposition principle. Coulomb's law unifies all these observations into one succinct statement. Subsequent mathematicians and physicists found the construct of the electric field to be useful for determining the electrostatic force on an electric charge at any point in space. The electric field was based on using a hypothetical "test charge" anywhere in space and then using Coulomb's law to determine the electrostatic force. Thus the electric field anywhere in space is defined as
E
=
F
q
,
{\displaystyle \mathbf {E} ={\mathbf {F} \over {q}},}
where
q
{\displaystyle q}
is the magnitude of the hypothetical test charge. Similarly, the idea of the magnetic field was introduced to express how magnets can influence one another at a distance. The Lorentz force law gives the force upon a body with charge
q
{\displaystyle q}
due to electric and magnetic fields:
F
=
q
(
E
+
v
×
B
)
,
{\displaystyle \mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right),}
where
F
{\displaystyle \mathbf {F} }
is the electromagnetic force,
E
{\displaystyle \mathbf {E} }
is the electric field at the body's location,
B
{\displaystyle \mathbf {B} }
is the magnetic field, and
v
{\displaystyle \mathbf {v} }
is the velocity of the particle. The magnetic contribution to the Lorentz force is the cross product of the velocity vector with the magnetic field. The origin of electric and magnetic fields would not be fully explained until 1864 when James Clerk Maxwell unified a number of earlier theories into a set of 20 scalar equations, which were later reformulated into 4 vector equations by Oliver Heaviside and Josiah Willard Gibbs. These "Maxwell's equations" fully described the sources of the fields as being stationary and moving charges, and the interactions of the fields themselves. This led Maxwell to discover that electric and magnetic fields could be "self-generating" through a wave that traveled at a speed that he calculated to be the speed of light. This insight united the nascent fields of electromagnetic theory with optics and led directly to a complete description of the electromagnetic spectrum.
=== Normal ===