8.3 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Force | 6/11 | https://en.wikipedia.org/wiki/Force | reference | science, encyclopedia | 2026-05-05T09:33:04.607426+00:00 | kb-cron |
When objects are in contact, the force directly between them is called the normal force, the component of the total force in the system exerted normal to the interface between the objects. The normal force is closely related to Newton's third law. The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever an external force pushes on a solid object. An example of the normal force in action is the impact force on an object crashing into an immobile surface.
=== Friction ===
Friction is a force that opposes relative motion of two bodies. At the macroscopic scale, the frictional force is directly related to the normal force at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction. The static friction force (
F
s
f
{\displaystyle \mathbf {F} _{\mathrm {sf} }}
) will exactly oppose forces applied to an object parallel to a surface up to the limit specified by the coefficient of static friction (
μ
s
f
{\displaystyle \mu _{\mathrm {sf} }}
) multiplied by the normal force (
F
N
{\displaystyle \mathbf {F} _{\text{N}}}
). In other words, the magnitude of the static friction force satisfies the inequality:
0
≤
F
s
f
≤
μ
s
f
F
N
.
{\displaystyle 0\leq \mathbf {F} _{\mathrm {sf} }\leq \mu _{\mathrm {sf} }\mathbf {F} _{\mathrm {N} }.}
The kinetic friction force (
F
k
f
{\displaystyle F_{\mathrm {kf} }}
) is typically independent of both the forces applied and the movement of the object. Thus, the magnitude of the force equals:
F
k
f
=
μ
k
f
F
N
,
{\displaystyle \mathbf {F} _{\mathrm {kf} }=\mu _{\mathrm {kf} }\mathbf {F} _{\mathrm {N} },}
where
μ
k
f
{\displaystyle \mu _{\mathrm {kf} }}
is the coefficient of kinetic friction. The coefficient of kinetic friction is normally less than the coefficient of static friction.
=== Tension ===
Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and do not stretch. They can be combined with ideal pulleys, which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action–reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by the second object. By connecting the same string multiple times to the same object through the use of a configuration that uses movable pulleys, the tension force on a load can be multiplied. For every string that acts on a load, another factor of the tension force in the string acts on the load. Such machines allow a mechanical advantage for a corresponding increase in the length of displaced string needed to move the load. These tandem effects result ultimately in the conservation of mechanical energy since the work done on the load is the same no matter how complicated the machine.
=== Spring ===
A simple elastic force acts to return a spring to its natural length. An ideal spring is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring from its equilibrium position. This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named. If
Δ
x
{\displaystyle \Delta x}
is the displacement, the force exerted by an ideal spring equals:
F
=
−
k
Δ
x
,
{\displaystyle \mathbf {F} =-k\Delta \mathbf {x} ,}
where
k
{\displaystyle k}
is the spring constant (or force constant), which is particular to the spring. The minus sign accounts for the tendency of the force to act in opposition to the applied load.
=== Centripetal ===
For an object in uniform circular motion, the net force acting on the object equals:
F
=
−
m
v
2
r
r
^
,
{\displaystyle \mathbf {F} =-{\frac {mv^{2}}{r}}{\hat {\mathbf {r} }},}
where
m
{\displaystyle m}
is the mass of the object,
v
{\displaystyle v}
is the velocity of the object and
r
{\displaystyle r}
is the distance to the center of the circular path and
r
^
{\displaystyle {\hat {\mathbf {r} }}}
is the unit vector pointing in the radial direction outwards from the center. This means that the net force felt by the object is always directed toward the center of the curving path. Such forces act perpendicular to the velocity vector associated with the motion of an object, and therefore do not change the speed of the object (magnitude of the velocity), but only the direction of the velocity vector. More generally, the net force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates the object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction.
=== Continuum mechanics ===
Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. In real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together the atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids, differences in pressure result in forces being directed along the pressure gradients as follows:
F
V
=
−
∇
P
,
{\displaystyle {\frac {\mathbf {F} }{V}}=-\mathbf {\nabla } P,}