Force Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! == Combining forces == [[File:Addition av vektorer 003.jpg|thumb|Addition of vectors <math>v_1</math> and <math>v_2</math> results in <math>v</math>]] Forces act in a particular [[direction (geometry)|direction]] and have [[Magnitude (mathematics)|sizes]] dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as "[[Euclidean vector|vector quantities]]". This means that forces follow a different set of mathematical rules than physical quantities that do not have direction (denoted [[scalar (physics)|scalar]] quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the [[resultant vector|result]]. If both of these pieces of information are not known for each force, the situation is ambiguous.<ref name="openstax-university-physics"/>{{rp|197}} Historically, forces were first quantitatively investigated in conditions of [[static equilibrium]] where several forces canceled each other out. Such experiments demonstrate the crucial properties that forces are additive [[Vector (geometric)|vector quantities]]: they have [[magnitude (mathematics)|magnitude]] and direction.<ref name=uniphysics_ch2/> When two forces act on a [[point particle]], the resulting force, the ''resultant'' (also called the ''[[net force]]''), can be determined by following the [[parallelogram rule]] of [[vector addition]]: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action.<ref name=FeynmanVol1 />{{rp|at=ch.12}}<ref name=Kleppner /> [[File:Freebodydiagram3 pn.svg|thumb|[[Free body diagram]]s of a block on a flat surface and an [[inclined plane]]. Forces are resolved and added together to determine their magnitudes and the net force.]] [[Free-body diagram]]s can be used as a convenient way to keep track of forces acting on a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of the force vectors preserved so that [[Vector (geometric)|graphical vector addition]] can be done to determine the net force.<ref>{{cite web |title=Introduction to Free Body Diagrams |work=Physics Tutorial Menu |publisher=[[University of Guelph]] |url=http://eta.physics.uoguelph.ca/tutorials/fbd/intro.html |access-date=2008-01-02 |url-status=dead |archive-url=https://web.archive.org/web/20080116042455/http://eta.physics.uoguelph.ca/tutorials/fbd/intro.html |archive-date=2008-01-16 }}</ref> As well as being added, forces can also be resolved into independent components at [[right angle]]s to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Resolving force vectors into components of a set of [[basis vector]]s is often a more mathematically clean way to describe forces than using magnitudes and directions.<ref>{{cite web |first=Tom |last=Henderson |title=The Physics Classroom |work=The Physics Classroom and Mathsoft Engineering & Education, Inc. |year=2004 |url=http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/vectors/u3l1b.html |access-date=2008-01-02 |url-status=dead |archive-url=https://web.archive.org/web/20080101141103/http://www.glenbrook.k12.il.us/gbssci/Phys/Class/vectors/u3l1b.html |archive-date=2008-01-01 }}</ref> This is because, for [[orthogonal]] components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on the magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right angles to the other two.<ref name=FeynmanVol1 />{{rp|at=ch.12}}<ref name=Kleppner /> ===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 /> Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! Cancel Editing help (opens in new window) Discuss this page