Force

===Equilibrium===
When all the forces that act upon an object are balanced, then the object is said to be in a state of [[Mechanical equilibrium|equilibrium]].<ref name="openstax-university-physics">{{cite book|title=University Physics, Volume 1 |last1=Ling |first1=Samuel J. |last2=Sanny |first2=Jeff |last3=Moebs |first3=William |display-authors=etal |publisher=[[OpenStax]] |url=https://openstax.org/details/books/university-physics-volume-1 |year=2021 |isbn=978-1-947-17220-3}}</ref>{{rp|566}} Hence, equilibrium occurs when the resultant force acting on a point particle is zero (that is, the vector sum of all forces is zero). When dealing with an extended body, it is also necessary that the net torque be zero. A body is in ''static equilibrium'' with respect to a frame of reference if it at rest and not accelerating, whereas a body in ''dynamic equilibrium'' is moving at a constant speed in a straight line, i.e., moving but not accelerating. What one observer sees as static equilibrium, another can see as dynamic equilibrium and vice versa.<ref name="openstax-university-physics"/>{{rp|566}}

==== Static <span class="anchor" id="Static equilibrium"></span> ====
{{main|Statics|Static equilibrium}}
Static equilibrium was understood well before the invention of classical mechanics. Objects that are at rest have zero net force acting on them.<ref>{{cite web
|title=Static Equilibrium
|work=Physics Static Equilibrium (forces and torques)
|publisher=[[University of the Virgin Islands]]
|url=http://www.uvi.edu/Physics/SCI3xxWeb/Structure/StaticEq.html
|access-date=2008-01-02 |archive-url=https://web.archive.org/web/20071019054156/http://www.uvi.edu/Physics/SCI3xxWeb/Structure/StaticEq.html |archive-date=October 19, 2007}}</ref>

The simplest case of static equilibrium occurs when two forces are equal in magnitude but opposite in direction. For example, an object on a level surface is pulled (attracted) downward toward the center of the Earth by the force of gravity. At the same time, a force is applied by the surface that resists the downward force with equal upward force (called a [[normal force]]). The situation produces zero net force and hence no acceleration.<ref name=uniphysics_ch2/>

Pushing against an object that rests on a frictional surface can result in a situation where the object does not move because the applied force is opposed by [[static friction]], generated between the object and the table surface. For a situation with no movement, the static friction force ''exactly'' balances the applied force resulting in no acceleration. The static friction increases or decreases in response to the applied force up to an upper limit determined by the characteristics of the contact between the surface and the object.<ref name=uniphysics_ch2/>

A static equilibrium between two forces is the most usual way of measuring forces, using simple devices such as [[weighing scale]]s and [[spring balance]]s. For example, an object suspended on a vertical [[spring scale]] experiences the force of gravity acting on the object balanced by a force applied by the "spring reaction force", which equals the object's weight. Using such tools, some quantitative force laws were discovered: that the force of gravity is proportional to volume for objects of constant [[density]] (widely exploited for millennia to define standard weights); [[Archimedes' principle]] for buoyancy; Archimedes' analysis of the [[lever]]; [[Boyle's law]] for gas pressure; and [[Hooke's law]] for springs. These were all formulated and experimentally verified before Isaac Newton expounded his [[Newton's Laws of Motion|Three Laws of Motion]].<ref name=uniphysics_ch2/><ref name=FeynmanVol1 />{{rp|at=ch.12}}<ref name=Kleppner />

==== Dynamic <span class="anchor" id="Dynamical equilibrium"></span><span class="anchor" id="Dynamic equilibrium"></span> ====
{{main|Dynamics (physics)}}
[[File:Galileo.arp.300pix.jpg|thumb|upright|[[Galileo Galilei]] was the first to point out the inherent contradictions contained in Aristotle's description of forces.]]
Dynamic equilibrium was first described by [[Galileo]] who noticed that certain assumptions of Aristotelian physics were contradicted by observations and [[logic]]. Galileo realized that [[Galilean relativity|simple velocity addition]] demands that the concept of an "absolute [[rest frame]]" did not exist. Galileo concluded that motion in a constant [[velocity]] was completely equivalent to rest. This was contrary to Aristotle's notion of a "natural state" of rest that objects with mass naturally approached. Simple experiments showed that Galileo's understanding of the equivalence of constant velocity and rest were correct. For example, if a mariner dropped a cannonball from the crow's nest of a ship moving at a constant velocity, Aristotelian physics would have the cannonball fall straight down while the ship moved beneath it. Thus, in an Aristotelian universe, the falling cannonball would land behind the foot of the mast of a moving ship. When this experiment is actually conducted, the cannonball always falls at the foot of the mast, as if the cannonball knows to travel with the ship despite being separated from it. Since there is no forward horizontal force being applied on the cannonball as it falls, the only conclusion left is that the cannonball continues to move with the same velocity as the boat as it falls. Thus, no force is required to keep the cannonball moving at the constant forward velocity.<ref name="Galileo"/>

Moreover, any object traveling at a constant velocity must be subject to zero net force (resultant force). This is the definition of dynamic equilibrium: when all the forces on an object balance but it still moves at a constant velocity. A simple case of dynamic equilibrium occurs in constant velocity motion across a surface with [[kinetic friction]]. In such a situation, a force is applied in the direction of motion while the kinetic friction force exactly opposes the applied force. This results in zero net force, but since the object started with a non-zero velocity, it continues to move with a non-zero velocity. Aristotle misinterpreted this motion as being caused by the applied force. When kinetic friction is taken into consideration it is clear that there is no net force causing constant velocity motion.<ref name=FeynmanVol1 />{{rp|at=ch.12}}<ref name=Kleppner />
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