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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Force | 8/11 | https://en.wikipedia.org/wiki/Force | reference | science, encyclopedia | 2026-05-05T09:33:04.607426+00:00 | kb-cron |
with
v
=
d
x
/
d
t
{\displaystyle \mathbf {v} =\mathrm {d} \mathbf {x} /\mathrm {d} t}
the velocity.
=== Potential energy ===
Instead of a force, often the mathematically related concept of a potential energy field is used. For instance, the gravitational force acting upon an object can be seen as the action of the gravitational field that is present at the object's location. Restating mathematically the definition of energy (via the definition of work), a potential scalar field
U
(
r
)
{\displaystyle U(\mathbf {r} )}
is defined as that field whose gradient is equal and opposite to the force produced at every point:
F
=
−
∇
U
.
{\displaystyle \mathbf {F} =-\mathbf {\nabla } U.}
Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential while nonconservative forces are not.
=== Conservation ===
A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms. This means that for a closed system, the net mechanical energy is conserved whenever a conservative force acts on the system. The force, therefore, is related directly to the difference in potential energy between two different locations in space, and can be considered to be an artifact of the potential field in the same way that the direction and amount of a flow of water can be considered to be an artifact of the contour map of the elevation of an area. Conservative forces include gravity, the electromagnetic force, and the spring force. Each of these forces has models that are dependent on a position often given as a radial vector
r
{\displaystyle \mathbf {r} }
emanating from spherically symmetric potentials. Examples of this follow: For gravity:
F
g
=
−
G
m
1
m
2
r
2
r
^
,
{\displaystyle \mathbf {F} _{\text{g}}=-{\frac {Gm_{1}m_{2}}{r^{2}}}{\hat {\mathbf {r} }},}
where
G
{\displaystyle G}
is the gravitational constant, and
m
n
{\displaystyle m_{n}}
is the mass of object n. For electrostatic forces:
F
e
=
q
1
q
2
4
π
ε
0
r
2
r
^
,
{\displaystyle \mathbf {F} _{\text{e}}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r^{2}}}{\hat {\mathbf {r} }},}
where
ε
0
{\displaystyle \varepsilon _{0}}
is electric permittivity of free space, and
q
n
{\displaystyle q_{n}}
is the electric charge of object n. For spring forces:
F
s
=
−
k
r
r
^
,
{\displaystyle \mathbf {F} _{\text{s}}=-kr{\hat {\mathbf {r} }},}
where
k
{\displaystyle k}
is the spring constant. For certain physical scenarios, it is impossible to model forces as being due to a simple gradient of potentials. This is often due a macroscopic statistical average of microstates. For example, static friction is caused by the gradients of numerous electrostatic potentials between the atoms, but manifests as a force model that is independent of any macroscale position vector. Nonconservative forces other than friction include other contact forces, tension, compression, and drag. For any sufficiently detailed description, all these forces are the results of conservative ones since each of these macroscopic forces are the net results of the gradients of microscopic potentials. The connection between macroscopic nonconservative forces and microscopic conservative forces is described by detailed treatment with statistical mechanics. In macroscopic closed systems, nonconservative forces act to change the internal energies of the system, and are often associated with the transfer of heat. According to the Second law of thermodynamics, nonconservative forces necessarily result in energy transformations within closed systems from ordered to more random conditions as entropy increases.
== Units == The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or kg·m·s−2.The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or g·cm·s−2. A newton is thus equal to 100,000 dynes. The gravitational foot-pound-second English unit of force is the pound-force (lbf), defined as the force exerted by gravity on a pound-mass in the standard gravitational field of 9.80665 m·s−2. The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force. An alternative unit of force in a different foot–pound–second system, the absolute fps system, is the poundal, defined as the force required to accelerate a one-pound mass at a rate of one foot per second squared. The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass. The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass that accelerates at 1 m·s−2 when subjected to a force of 1 kgf. The kilogram-force is not a part of the modern SI system, and is generally deprecated, sometimes used for expressing aircraft weight, jet thrust, bicycle spoke tension, torque wrench settings and engine output torque.
See also Ton-force.
== Revisions of the force concept == At the beginning of the 20th century, new physical ideas emerged to explain experimental results in astronomical and submicroscopic realms. As discussed below, relativity alters the definition of momentum and quantum mechanics reuses the concept of "force" in microscopic contexts where Newton's laws do not apply directly.
=== Special theory of relativity ===
In the special theory of relativity, mass and energy are equivalent (as can be seen by calculating the work required to accelerate an object). When an object's velocity increases, so does its energy and hence its mass equivalent (inertia). It thus requires more force to accelerate it the same amount than it did at a lower velocity. Newton's second law,
F
=
d
p
d
t
,
{\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},}