Difference between revisions of "Force" - New World Encyclopedia

From New World Encyclopedia
(imported latest version of article from Wikipedia)
 
 
(29 intermediate revisions by 7 users not shown)
Line 1: Line 1:
{{otheruses}}
+
{{Ebapproved}}{{Images OK}}{{Submitted}}{{Approved}}{{Paid}}{{Copyedited}}
  
In [[physics]], '''force''' is an [[influence]] that may cause an [[object]] to [[acceleration|accelerate]]. It may be experienced as a lift, a push, or a pull. The actual acceleration of the body is determined by the vector sum of all forces acting on it (known as [[net force]] or resultant force). In an extended body, force may also cause [[rotate|rotation]] or [[deformation]] of the body. Rotational effects and deformation are determined respectively by the [[torque]]s and [[Stress (physics)|stress]]es that the forces create.
+
[[Image:Weeghaak.JPG|thumb|100px|A [[spring scale]] measures the weight of an object, corresponding to the force of [[gravity]] exerted on the object.]]
  
Force is mathematically defined as the rate of change of the [[momentum]] of the body. Since [[momentum]] is a [[vector (spatial)|vector]] quantity (has both a magnitude and direction), force also is a vector quantity.
+
In [[physics]], '''force''' is defined as the rate of change of [[momentum]] of an object. This definition was given by [[Isaac Newton]] in the seventeenth century. In simpler terms, force may be thought of as an [[influence]] that may cause an [[object]] to [[acceleration|accelerate]]. Force and [[mass]] are fundamental to Newtonian [[physics]].
  
Force was first mentioned by [[Archimedes]] in the [[3rd century B.C.E.]] but only [[mathematics|mathematically]] defined by [[Isaac Newton]] in the [[17th century]]. Following the development of [[quantum mechanics]] it is now understood that particles influence each
+
In everyday life, a force may be experienced in various ways, such as a lift, a push, or a pull. A familiar example of force is the weight of an object, which is defined as the amount of gravitational force exerted on the object. In addition, a force (or combination of forces) may cause an object to [[rotate]] or become [[deformation|deformed]]. Rotational effects and deformation are determined respectively by the [[torque]]s and [[Stress (physics)|stress]]es that the forces create.
another through [[fundamental interaction]]s, making force a redundant concept.  Only four [[fundamental interactions]] are known: [[strong force|strong]], [[electromagnetic force|electromagnetic]], [[weak force|weak]] (unified into one [[electroweak]] interaction in 1970s), and [[gravitational force|gravitational]] (in order of decreasing strength).
+
 
 +
In the twentieth century, it was found that all known forces could be reduced to four fundamental forces: the strong force, weak force, [[electromagnetic force]], and [[gravity]]. However, contemporary physics such as [[quantum mechanics]] and [[general relativity]] no longer regard the concept of force as fundamental. In quantum mechanics, force is seen as derivative of the [[fundamental interaction|interactions]] between particles. In general relativity, gravitational force is a [[trajectory]] along curved space-time.
  
 
== History ==  
 
== History ==  
[[Aristotle]] and his followers believed that it was the ''natural state'' of objects on [[Earth]] to be motionless and that they tended towards that state if left alone. But this [[theory]], although based on the everyday experience of how objects move, was first shown to be unsatisfactory by [[Galileo]] as a result of his work on [[gravity]]. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the [[Aristotelian theory of gravity|Aristotelian theory of motion]] early in the [[17th century]]. He showed that the bodies were accelerated by gravity to an extent which was independent of their [[mass]] and argued that objects retain their [[velocity]] unless acted on by a force - usually [[friction]].
 
  
[[Isaac Newton]] is recognised as having given the mathematical definition as the rate of change ([[time derivative]]) of momentum.
+
[[Aristotle]] and his followers believed that it was the ''natural state'' of objects on [[Earth]] to be motionless and that they tended toward that state if left alone. But this [[theory]], although based on the everyday experience of how objects move, was first shown to be unsatisfactory by [[Galileo]] as a result of his work on [[gravity]]. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the [[Aristotelian theory of gravity|Aristotelian theory of motion]] early in the seventeenth century. He showed that the bodies were accelerated by [[gravity]] to an extent that was independent of their [[mass]] and argued that objects retain their [[velocity]] unless acted on by a force—usually [[friction]].
  
In [[1784]] [[Charles Coulomb]] discovered the [[Coulomb's law|inverse square law]] of interaction between [[electric charge]]s using a [[torsion balance]], which was the second fundamental force.  The weak and strong forces were discovered in the [[20th century]].
+
[[Isaac Newton]] is recognized as having given the mathematical definition of force as the rate of change ([[time derivative]]) of [[momentum]]. In 1784, [[Charles Coulomb]] discovered the [[Coulomb's law|inverse square law]] of interaction between [[electric charge]]s using a [[torsion balance]].
  
With the development of [[quantum field theory]] and [[general relativity]] it was realized that “force” is a redundant concept arising from conservation of momentum ([[4-momentum]] in relativity and momentum of [[virtual particle]]s in QED). Most fundamental theories - [[quantum mechanics]] and [[general relativity]] do not even have a concept of force. Thus currently known [[fundamental forces]] are not called forces but more accurately “[[fundamental interactions]].
+
With the development of [[quantum field theory]] and [[general relativity]] in the twentieth century, it was realized that particles influence one another through [[fundamental interaction]]s, and that "force" is a concept arising from the conservation of momentum. Only four fundamental interactions are known. They are called the [[strong interaction|strong]], [[electromagnetic force|electromagnetic]], [[weak interaction|weak]], and [[gravitation]]al interactions (in order of decreasing strength).<ref>The strong interaction (or strong force) represents the [[interaction]]s between [[quark]]s and [[gluon]]s, as explained by the theory of [[quantum chromodynamics]] (QCD). The weak interaction, affecting [[Chirality (physics)|left-handed]] [[lepton]]s, and [[quarks]], is attributed to exchange of the heavy [[W and Z bosons]]. The word "weak" derives from the fact that the field strength is some 10<sup>13</sup> times less than that of the [[strong interaction]].</ref> In the 1970s, the electromagnetic and weak interactions were unified into the "[[electroweak interaction]]."
  
== Types of force ==
+
== Definition ==
Although there are apparently many types of forces in the Universe, they are all based on four fundamental forces. The strong and weak forces only act at very short distances and are responsible for holding certain [[nucleons]] and compound [[nucleus|nuclei]]  together. The electromagnetic force acts between [[electric charge]]s and the gravitational force acts between [[mass]]es. The [[Pauli exclusion principle]] is responsible for the tendency of [[atom]]s not to overlap each other, and is thus responsible for the "stiffness" or "rigidness" of matter, but this also depends on the electromagnetic force which binds the constituents of every atom.
 
  
All other forces are based on these four. For example, [[friction]] is a manifestation of the [[electromagnetic]] force acting between the [[atom]]s of two [[surface]]s, and the Pauli exclusion principle, which does not allow atoms to pass through each other. The forces in [[spring (device)|spring]]s modeled by [[Hooke's law]] are also the result of electromagnetic forces and the exclusion principle acting together to return the object to its equilibrium position. [[Centrifugal force]]s are acceleration forces (inertia forces)which arise simply from the acceleration of rotating [[reference frame|frames of reference]].
+
Force is defined as the rate of change of [[momentum]] with time:
  
The modern quantum mechanical view of the first three fundamental forces (all except gravity) is that particles of matter ([[fermions]]) do not directly interact with each other but rather by exchange of [[virtual particles]] ([[bosons]]). This exchange results in what we call [[electromagnetic interaction]] ([[Coulomb force]] is one example of electromagnetic interaction).
+
: <math>\vec{F} = {\mathrm{d}\vec{p} \over \mathrm{d}t}</math>
  
In [[general relativity]], gravitation is not strictly viewed as a force. Rather, objects moving freely in gravitational fields  simply undergo [[inertial motion]] along a [[geodesic|straight line]] in the [[curved space-time]] - defined as the shortest space-time path between two points. This straight line in space-time is a curved line in space, and it is called the ''[[external ballistics|ballistic]] [[trajectory]]'' of the object. For example, a [[basketball]] thrown from the ground moves in a [[parabola]] shape as it is in a uniform gravitational field. Similarly, [[planet]]s move in [[ellipse]]s as they are in an [[inverse square]] gravitational field. The time derivative of the changing momentum of the body is what we label as "gravitational force".
+
The quantity <math>\vec{p} = m \vec{v}</math> (where <math>m\,</math> is the [[mass]] and <math>\vec{v}</math> is the [[velocity]]) is called the [[momentum]]. This is the only definition of force known in [[physics]].
  
== Examples ==
+
Momentum is a [[vector (spatial)|vector]] quantity—that is, it has both a magnitude and direction. Therefore force is also a vector quantity. The actual [[acceleration]] of the body is determined by the [[vector sum]] of all forces acting on it (known as [[net force]] or resultant force).
  
* A heavy object is in free fall. Its momentum changes as dp/dt = mdv/dt = ma =mg (if the mass m is constant), thus we call the quantity mg a "gravitational force" acting on the object. This is the [[definition]] of [[weight]] (w=mg) of an object. 
+
If the [[mass]] ''m'' is constant in time, then Newton's second law can be derived from this definition:
* A heavy object on a table is pulled (attracted) downward toward the floor by the force of gravity (i.e., its weight). At the same time, the table resists the downward force with equal upward force (called the [[normal force]]), resulting in zero net force, and no acceleration. (If the object is a person, he actually feels the normal force acting on him from below.)
 
* A heavy object on a table is gently pushed in a sideways direction by a finger. However, it doesn't move because the force of the finger on the object is now opposed by a ''new'' force of [[static friction]], generated between the object and the table surface. This newly generated force ''exactly'' balances the force exerted on the object by the finger, and ''again'' no acceleration occurs. The static friction increases or decreases automatically. If the force of the finger is increased (up to a point), the opposing sideways force of static friction '''increases''' exactly to the point of perfect opposition.
 
* A heavy object on a table is pushed by a finger hard enough that static friction cannot generate sufficient force to match the force exerted by the finger, and the object starts sliding across the surface. If the finger is moved with a constant velocity, it needs to apply a force that exactly cancels the force of [[kinetic friction]] from the surface of the table and then the object moves with the same constant velocity. Here it seems to the naive observer that application of a force produces a velocity (rather than an acceleration). However, the velocity is constant only because the force of the finger and the kinetic friction cancel each other. Without friction, the object would continually accelerate in response to a constant force.
 
* A heavy object reaches the edge of the table and falls. Now the object, subjected to the constant force of its weight, but freed of the normal force and friction forces from the table, gains in velocity in direct proportion to the time of fall, and thus (before it reaches velocities where air resistance forces becomes significant compared to gravity forces) its rate of ''gain'' in momentum and velocity is constant. These facts were first discovered by [[Galileo]].
 
 
 
== Definition ==
 
Force is defined as the rate of change of [[momentum]] with time:
 
 
 
: <math>\vec{F} = {\mathrm{d}\vec{p} \over \mathrm{d}t}</math>.
 
 
 
The quantity <math>\vec{p} = m \vec{v}</math> (where <math>m\,</math> is the [[mass]] and <math>\vec{v}</math> is the [[velocity]]) is called the [[momentum]]. This is the only definition of force known in physics (first proposed by Newton himself). If the mass ''m'' is constant in time, then Newton's second law can be derived from this definition:
 
  
 
: <math>\vec{F} = \frac{\mathrm{d}\vec{p}}{\mathrm{d}t}= \frac{\mathrm{d}(m\vec{v})}{\mathrm{d}t} = m\frac{\mathrm{d}(\vec{v})}{\mathrm{d}t} = m\vec{a} </math>
 
: <math>\vec{F} = \frac{\mathrm{d}\vec{p}}{\mathrm{d}t}= \frac{\mathrm{d}(m\vec{v})}{\mathrm{d}t} = m\frac{\mathrm{d}(\vec{v})}{\mathrm{d}t} = m\vec{a} </math>
  
where <math>\vec{a} = {\mathrm{d} \vec{v}} /{\mathrm{d}t}</math> is the [[acceleration]].  
+
where <math>\vec{a} = {\mathrm{d} \vec{v}} /{\mathrm{d}t}</math> (the rate of change of velocity) is the [[acceleration]].  
  
This is the form Newton's second law is usually taught in introductory physics courses in order to avoid calculus notation.  
+
This is the form Newton's second law is usually taught in introductory physics courses.  
  
All known forces of nature are defined via the above Newtonian definition of force. For example, [[weight]] (force of gravity) is defined as mass times acceleration of free fall: w = mg; spring balance force is defined as the force equilibrating certain gravitational force (say, the weight of 1 kg mass near Earth surface results in reaction force of spring equivalent to 9.8 N), etc. Calibration of spring balances (of various kinds) using either gravitational force or motion with known acceleration is important starting procedure in measuring many other forces (such as friction forces, reaction forces, electric forces, magnetic force, etc) in various physics labs.
+
All known forces of nature are defined via the above Newtonian definition of force. For example, [[weight]] (force of gravity) is defined as mass times acceleration of free fall: w = mg   
  
It is not always the case that ''m'' is independent of ''t''. For example, the mass of a [[rocket]] decreases as its propellant is ejected. Under such circumstances, the above equation (<math>\vec{F} = m\vec{a} </math>) is obviousely incorrect, and the original definition of force F=dp/dt must be used.
+
It is not always the case that ''m'', the mass of an object, is independent of time, ''t''. For example, the mass of a [[rocket]] decreases as its fuel is burned. Under such circumstances, the above equation <math>\vec{F} = m\vec{a} </math> is obviously incorrect, and the original definition of force: <math>\vec{F} = {\mathrm{d}\vec{p} \over \mathrm{d}t}</math> must be used.
  
Because momentum is a [[vector (physics)|vector]], then force, being its time derivative, is also a vector - it has [[magnitude (mathematics)|magnitude]] and [[Direction (geometry, geography)|direction]], and [[four-force]] is a [[four-vector]] in relativity. Vectors (and thus forces) are added together by their [[Spacial vector|component]]s. When two forces act on an object, the resulting force, the ''resultant'', is the [[vector addition|vector sum]] of the original forces.  This is called the principle of [[superposition]]. 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. As with all vector addition this results in a [[parallelogram rule]]: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector which is equal in magnitude and direction to the transversal of the parallelogram. If the two forces are equal in magnitude but opposite in direction, then the resultant is zero.  This condition is called [[static equilibrium]], with the result that the object remains at its constant velocity (which could be zero).  
+
Because momentum is a [[vector (physics)|vector]], then force is also a vector—it has [[magnitude (mathematics)|magnitude]] and [[Direction (geometry, geography)|direction]]. Vectors (and thus forces) are added together by their [[Spacial vector|component]]s. When two forces act on an object, the resulting force, often called the ''resultant'', is the [[vector addition|vector sum]] of the original forces.  This is called the principle of [[superposition]]. 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. As with all vector addition, this results in a [[parallelogram rule]]: the addition of two vectors represented by sides of a parallelogram gives an equivalent resultant vector, which is equal in magnitude and direction to the transversal of the parallelogram. If the two forces are equal in magnitude but opposite in direction, then the resultant is zero.  This condition is called [[static equilibrium]], with the result that the object remains at its constant velocity (which could be zero).  
  
As well as being added, forces can also be broken down (or 'resolved'). For example, a horizontal force pointing northeast can be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force.  Force vectors can also be three-dimensional, with the third (vertical) component at right-angles to the two horizontal components.
+
As well as being added, forces can also be broken down (or "resolved"). For example, a horizontal force pointing northeast can be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force.  Force vectors can also be [[three-dimensional space|three-dimensional]], with the third (vertical) component at right-angles to the two horizontal components.
  
In most explanations of [[mechanics]], force is usually defined only implicitly, in terms of the equations that work with it. Some physicists, philosophers and mathematicians, such as [[Ernst Mach]], [[Clifford Truesdell]] and [[Walter Noll]], have found this problematic and sought a more explicit definition of force.
+
== Examples ==
  
===Force in special relativity===
+
* An object is in free fall. Its [[momentum]] changes as dp/dt = mdv/dt = ma = mg (if the [[mass]], m, is constant), thus we call the quantity mg a "gravitational force" acting on the object. This is the [[definition]] of [[weight]] (w=mg) of an object. 
In the [[special theory of relativity]] mass and [[energy]] are equivalent (as can be seen by calculating the work required to accelerate a body). When an object's velocity increases so does its energy and hence its mass equivalent (inertia). It thus requires a greater force to accelerate it the same amount than it did at a lower velocity. The definition <math>\vec{F} = \mathrm{d}\vec{p}/\mathrm{d}t </math> remains valid, but the momentum must be redefined (in order to be conserved) as:
+
* An object on a table is pulled downward toward the floor by the force of [[gravity]]. At the same time, the table resists the downward force with equal upward force (called the [[normal force]]), resulting in zero net force, and no [[acceleration]]. (If the object is a person, he actually feels the normal force acting on him from below.)
 +
* An object on a table is gently pushed in a sideways direction by a finger. However, it doesn't move because the force of the finger on the object is now opposed by a force of [[static friction]], generated between the object and the table surface. This force ''exactly'' balances the force exerted on the object by the finger, and no acceleration occurs. The [[static friction]] increases or decreases automatically. If the force of the finger is increased (up to a point), the opposing sideways force of static friction ''increases'' exactly to the point of perfect opposition.
 +
* An object on a table is pushed by a finger hard enough that static friction cannot generate sufficient force to match the force exerted by the finger, and the object starts sliding across the surface. If the finger is moved with a constant velocity, it needs to apply a force that exactly cancels the force of [[kinetic friction]] from the surface of the table and then the object moves with the same constant velocity. Here it seems to the naive observer that application of a force produces a velocity (rather than an acceleration). However, the velocity is constant only because the force of the finger and the kinetic friction cancel each other. Without friction, the object would continually accelerate in response to a constant force.
 +
* An object reaches the edge of the table and falls. Now the object, subjected to the constant force of its weight, but freed of the normal force and friction forces from the table, gains in velocity in direct proportion to the time of fall, and thus (before it reaches velocities where air resistance forces becomes significant compared to gravity forces) its rate of ''gain'' in momentum and velocity is constant. These facts were first discovered by [[Galileo]].
  
:<math> \vec{p} = \frac{m\vec{v}}{\sqrt{1 - v^2/c^2}}</math>
+
== Types of Force ==
  
where
+
Although there are apparently many types of forces in the [[universe]], they are all based on four fundamental forces, mentioned above. The strong and weak forces only act at very short distances and are responsible for holding certain [[nucleons]] and compound [[nucleus|nuclei]] together. The [[electromagnetic force]] acts between [[electric charge]]s, and the [[gravitational force]] acts between [[mass]]es.
  
:<math>v</math> is the velocity and
+
All other forces are based on these four. For example, [[friction]] is a manifestation of the electromagnetic force (acting between the [[atom]]s of two [[surface]]s) and the Pauli exclusion principle, which does not allow atoms to pass through each other. The forces in [[spring (device)|spring]]s modeled by [[Hooke's law]] are also the result of electromagnetic forces and the exclusion principle acting together to return the object to its equilibrium position. [[Centrifugal force]]s are acceleration forces (inertia forces) that arise simply from the [[acceleration]] of rotating [[reference frame|frames of reference]].
  
:<math>c</math> is the [[speed of light]].
+
The modern quantum mechanical view of the first three fundamental forces (all except gravity) is that particles of matter ([[fermions]]) do not directly interact with each other but rather by the exchange of [[virtual particles]] ([[bosons]]). This exchange results in what we call [[electromagnetic interaction]]s. ([[Coulomb force]] is one example of electromagnetic interaction).
Note that this definition is consistent with classic definition of momentum mv at small speed.
 
  
The relativistic expression relating force and acceleration for a particle with non-zero [[rest mass]] <math>m\,</math> moving in the <math>x\,</math> direction is:
+
In [[general relativity]], gravitation is not strictly viewed as a force. Rather, objects moving freely in gravitational fields  simply undergo [[inertial motion]] along a [[geodesic|straight line]] in [[curved space-time]] — defined as the shortest space-time path between two points. This straight line in space-time is a curved line in space, and it is called the ''[[external ballistics|ballistic]] [[trajectory]]'' of the object. For example, a [[basketball]] thrown from the ground moves in a [[parabola]] shape, as it is in a uniform gravitational field. Similarly, [[planet]]s move in [[ellipse]]s, as they are in an [[inverse square]] gravitational field. The time derivative of the changing [[momentum]] of the body is what we label as "gravitational force."
  
:<math>F_x = \gamma^3 m a_x \,</math>
+
===Force in Special Relativity===
  
:<math>F_y = \gamma m a_y \,</math>
+
In the [[special theory of relativity]], [[mass]] and [[energy]] are equivalent (as can be seen by calculating the work required to accelerate a body). When an object's [[velocity]] increases, so does its energy and hence its mass equivalent (inertia). It thus requires a greater force to accelerate it the same amount than it did at a lower velocity. The definition <math>\vec{F} = \mathrm{d}\vec{p}/\mathrm{d}t </math> remains valid, but the [[momentum]] must be redefined (in order to be conserved) as:
  
:<math>F_z = \gamma m a_z \,</math>
+
:<math> \vec{p} = \frac{m\vec{v}}{\sqrt{1 - v^2/c^2}}</math>
  
where the [[Lorentz factor]]
+
where
  
:<math> \gamma = \frac{1}{\sqrt{1 - v^2/c^2}}</math>
+
:<math>v</math> is the velocity and
  
Here a constant force does not produce a constant acceleration, but an ever decreasing acceleration as the object approaches the speed of light.  Note that <math> \gamma</math> is [[Division by zero|undefined]] for an object with a non zero [[Invariant mass|rest mass]] at the speed of light, and the theory yields no prediction at that speed.
+
:<math>c</math> is the [[speed of light]].
 +
Note that this definition is consistent with the classic definition of momentum (mv) at low speeds.
  
One can however restore the form of  
+
Also, according to the theory of relativity, for objects moving at extremely high speeds, a constant force produces not a constant acceleration but an ever-decreasing acceleration as the object approaches the speed of light.
  
:<math>F^\mu = mA^\mu \,</math>
+
== Units of Measurement ==
  
for use in relativity through the use of [[four-vectors]]. This relation is correct in relativity when <math>F^\mu</math> is the [[four-force]], m is the [[invariant mass]], and <math>A^\mu</math> is the [[four-acceleration]].
+
The [[SI]] unit used to measure force is the [[newton]] (symbol N) where:
  
== Force and potential ==
+
<math>1\, \mathrm{N}=1\, \frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}^{2}}</math>.
Instead of a force, the mathematically equivalent concept of a [[potential energy]] field can be used for convenience. For instance, the gravitational force acting upon a body can be seen as the action of the [[gravitational field]] that is present at the body's location. Restating mathematically the definition of [[energy]] (via  definition of [[Mechanical work|work]]), a potential field <math>U(\vec{r})</math> is  defined as that field whose [[gradient]] is equal and opposite to the force produced at every point:
 
  
:<math>\vec{F}=-\vec{\nabla} U</math>
+
A ''[[newton]]'' is the amount of force required to [[accelerate]] a body with a [[mass]] of one [[kilogram]] at a rate of one [[meter per second squared]]. 
  
Forces can be classified as [[Conservative force|conservative ]] or nonconservative. Conservative forces are equivalent to the [[gradient]] of a [[potential]], and include [[gravity]], the [[Electromagnetism|electromagnetic]] force, and the [[Hooke's law|spring]] force. Nonconservative forces include [[friction]] and [[drag (physics)|drag]]. However, for any sufficiently detailed description, all forces are conservative.
+
A ''[[pound-force]]'' (''lb<sub>f</sub>'' or ''lbf'') is another common [[Units of measurement|unit]] of force. One pound-force is the force equivalent to that exerted on a mass of one [[pound (mass)|pound]] on the surface of [[Earth]]. When the standard [[gravity|''g'']] (an acceleration of 9.80665 m/s²) is used to define pounds force, the mass in pounds is numerically equal to the weight in pounds force. However, even at sea level on Earth, the actual acceleration of free fall is variable, over 0.53% more at the poles than at the equator.
  
 
+
The [[kilogram-force]] is a unit of force that was used in various fields of science and technology. In 1901, the [[CGPM]] improved the definition of the [[kilogram-force]], adopting a standard acceleration of gravity for the purpose, and making the kilogram-force equal to the force exerted by a mass of 1 kg when accelerated by 9.80665 m/s². The kilogram-force is not a part of the modern [[SI]] system, but is still used in applications such as:
== Units of measurement ==
+
*[[Thrust]] of [[jet engine|jet]] and [[rocket engine]]s
The [[SI]] unit used to measure force is the [[newton]] (symbol N), which is equivalent to kg·m·s<sup>&minus;2</sup>. The earlier [[CGS]] unit is the [[dyne]]. The relationship '''F'''=''m''·'''a''' can be used with either of these. In [[Imperial unit|Imperial]] engineering units, if ''F'' is measured in "[[Pound-force|pounds force]]" or "lbf", and ''a'' in feet per second squared, then ''m'' must be measured in [[slug (mass)|slug]]s. Similarly, if mass is measured in [[pound-mass|pounds mass]], and ''a'' in feet per second squared, the force must be measured in [[poundal]]s. The units of [[slugs]] and [[poundal]]s are specifically designed to avoid a constant of proportionality in this equation.
 
 
 
A more general form '''F'''=''k''·''m''·'''a''' is needed if consistent units are not used. Here, the constant ''k'' is a conversion factor dependent upon the units being used.
 
 
 
When the standard [[standard gravity|''g'']] (an acceleration of 9.80665 m/s²) is used to define pounds force, the mass in pounds is numerically equal to the weight in pounds force.  However, even at sea level on Earth, the actual acceleration of free fall is quite variable, over 0.53% more at the poles than at the equator.  Thus, a mass of 1.0000 lb at ''sea level'' at the equator exerts a force due to gravity of 0.9973 lbf, whereas a mass of 1.000 lb at ''sea level'' at the poles exerts a force due to gravity of 1.0026 lbf.  The normal average sea level acceleration on Earth (World Gravity Formula 1980) is 9.79764 m/s², so on average at ''sea level'' on Earth, 1.0000 lb will exerts a force of 0.9991 lbf.
 
 
 
The equivalence 1 lb = 0.453&nbsp;592&nbsp;37 kg is always true, by definition, anywhere in the universe.  If you use the standard [[standard gravity|''g'']] which is official for defining kilograms force to define pounds force as well, then the same relationship will hold between pounds-force and kilograms-force (an old non-SI unit is still used).  If a different value is used to define pounds force, then the relationship to kilograms force will be slightly different&mdash;but in any case, that relationship is also a constant anywhere in the universe.  What is not constant throughout the universe is the amount of force in terms of pounds-force (or any other force units) which 1 lb will exert due to gravity.
 
 
 
By analogy with the slug, there is a rarely used unit of mass called the "metric slug".  This is the mass that accelerates at one metre per second squared when pushed by a force of one [[Kilogram-force|kgf]]. An item with a mass of 10 kg has a mass of 1.01972661 metric slugs (= 10 kg divided by 9.80665 kg per metric slug).  This unit is also known by various other names such as the [[slug|hyl]], TME (from a German acronym), and mug (from metric slug).
 
 
 
Another unit of force called the [[poundal]] (pdl) is defined as the force that accelerates 1 lbm at 1 foot per second squared. Given that 1 lbf = 32.174 lb times one foot per second squared, we have 1 lbf = 32.174 pdl.
 
The [[kilogram-force]] is a unit of force that was used in various fields of science and technology. In 1901, the [[CGPM]] improved the definition of the kilogram-force, adopting a standard acceleration of gravity for the purpose, and making the kilogram-force equal to the force exerted by a mass of 1 kg when accelerated by 9.80665 m/s². The kilogram-force is not a part of the modern [[SI]] system, but is still used in applications such as:
 
*Thrust of [[jet engine|jet]] and [[rocket engine]]s
 
 
*Spoke tension of [[bicycle]]s
 
*Spoke tension of [[bicycle]]s
 
*Draw weight of [[Bow (weapon)|bows]]
 
*Draw weight of [[Bow (weapon)|bows]]
*[[Torque wrench]]es in units such as "meter kilograms" or "kilogram centimetres" (the kilograms are rarely identified as units of force)
+
*[[Torque wrench]]es in units such as "meter kilograms" or "kilogram centimeters" (the kilograms are rarely identified as units of force)
 
*Engine torque output (kgf·m expressed in various word orders, spellings, and symbols)
 
*Engine torque output (kgf·m expressed in various word orders, spellings, and symbols)
 
*Pressure gauges in "kg/cm²" or "kgf/cm²"
 
*Pressure gauges in "kg/cm²" or "kgf/cm²"
  
In colloquial, non-scientific usage, the "kilograms" used for "weight" are almost always the proper SI units for this purpose. They are units of mass, not units of force.  
+
Another unit of force called the [[poundal]] (pdl) is defined as the force that accelerates 1 lbm at 1 foot per second squared. Given that 1 lbf = 32.174 lb times one foot per second squared, we have 1 lbf = 32.174 pdl.
  
The symbol "kgm" for kilograms is also sometimes encountered. This might occasionally be an attempt to distinguish kilograms as units of mass from the "kgf" symbol for the units of force. It might also be used as a symbol for those obsolete torque units (kilogram-force metres) mentioned above, used without properly separating the units for kilogram and metre with either a space or a centered dot.
+
===Conversion Factors===
 +
 
 +
Below are several conversion factors for measuring force in various units:
  
===Conversions===
 
Below are several conversion factors between various measurements of force:
 
* 1 dyne = 10<sup>-5</sup> newtons
 
 
* 1 kgf (kilopond kp) = 9.80665 newtons
 
* 1 kgf (kilopond kp) = 9.80665 newtons
* 1 [[Slug (mass)|metric slug]] = 9.80665 kg
+
* 1 lbf = 4.448222 newtons
 
* 1 lbf = 32.174 poundals
 
* 1 lbf = 32.174 poundals
 +
* 1 kgf = 2.2046 lbf
 +
* 1 dyne = 10<sup>-5</sup> newtons
 
* 1 slug = 32.174 lb
 
* 1 slug = 32.174 lb
* 1 kgf = 2.2046 lbf
 
  
== See also ==
+
== See Also ==
 +
 
 
* [[Angular momentum]]
 
* [[Angular momentum]]
 
* [[Conservation law]]
 
* [[Conservation law]]
 
* [[Impulse]]
 
* [[Impulse]]
 
* [[Inertia]]
 
* [[Inertia]]
* [[Moment map]]
 
 
* [[Momentum]]
 
* [[Momentum]]
* [[Noether's theorem]]
 
 
* [[Physics]]
 
* [[Physics]]
 +
* [[Stress]]
 +
* [[Torque]]
 
* [[Velocity]]
 
* [[Velocity]]
 +
 +
== Notes ==
 +
<references/>
  
 
==References==
 
==References==
{{Citations missing|date=December 2006}}
+
   
<!-- ----------------------------------------------------------
+
*Parker, Sybil P. ''McGraw-Hill Encyclopedia of Physics.'' New York: McGraw-Hill, 1983. ISBN 0070452539
  See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for a
+
*Serway, Raymond A., John W. Jewett, and Robert J. Beichner''Physics for Scientists and Engineers with Modern Physics.'' Fort Worth, TX: Saunders College, 2000. ISBN 0030226570
  discussion of different citation methods and how to generate
+
*Tipler, Paul Allen. ''Physics for Scientists and Engineers.'' New York: W.H. Freeman/Worth Publishers, 1999. ISBN 978-1572598140
  footnotes using the <ref>, </ref> and <reference /> tags
+
*Young, Hugh D, and Roger A. Freedman. ''Physics for Scientists and Engineers'' 11th ed. San Fransisco, CA: Pearson, 2003. ISBN 080538684X
----------------------------------------------------------- —>
 
<div class="references-small">
 
<references />
 
 
 
* {{cite book
 
| last = Parker | first = Sybil
 
| title = Encyclopedia of Physics,  p 443,
 
| location = Ohio
 
| publisher = McGraw-Hill
 
| year = 1993
 
| id = ISBN 0-07-051400-3
 
}}
 
* {{cite book
 
| last = Corbell | first = H.C.
 
| coauthors = Philip Stehle
 
| title = Classical Mechanics  p 28,
 
| location = New York
 
| publisher = Dover publications
 
| year = 1994
 
| id = ISBN 0-486-68063-0
 
}}
 
* {{cite book
 
| last = Halliday | first = David
 
| coauthors = Robert Resnick; Kenneth S. Krane
 
| title = Physics v. 1
 
| location = New York
 
  | publisher = John Wiley & Sons
 
| year = 2001
 
| id = ISBN 0-471-32057-9
 
}}
 
* {{cite book
 
| last = Serway | first = Raymond A.
 
| title = Physics for Scientists and Engineers
 
| location = Philadelphia
 
| publisher = Saunders College Publishing
 
| year = 2003
 
| id = ISBN 0-534-40842-7
 
}}
 
* {{cite book
 
| last = Tipler | first = Paul
 
| title = Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics
 
| edition = 5th ed.
 
| publisher = W. H. Freeman
 
| year = 2004
 
| id = ISBN 0-7167-0809-4
 
}}
 
* {{cite book
 
| last = Verma | first = H.C.
 
| title = Concepts of Physics Vol 1.
 
| edition = 2004 Reprint
 
| publisher = Bharti Bhavan
 
| year = 2004
 
| id = ISBN 81-7709-187-5
 
}}
 
</div>
 
  
[[Category:Classical mechanics]]
+
[[Category:Physical sciences]]
[[Category:Fundamental physics concepts]]
+
[[Category:Physics]]
  
[[af:Krag]]
+
{{credits|Force|137962371|Newton|137643255|Pound-force|136625542}}
[[ar:قوة]]
 
[[zh-min-nan:La̍t]]
 
[[bs:Sila]]
 
[[ca:Força]]
 
[[cs:Síla]]
 
[[da:Kraft]]
 
[[de:Kraft]]
 
[[et:Jõud (füüsika)]]
 
[[el:Δύναμη]]
 
[[es:Fuerza]]
 
[[eo:Forto]]
 
[[eu:Indar]]
 
[[fa:نیرو]]
 
[[fr:Force (physique)]]
 
[[gu:બળ]]
 
[[hak:Li̍t]]
 
[[ko:힘 (물리)]]
 
[[hr:Sila]]
 
[[io:Forco]]
 
[[it:Forza (fisica)]]
 
[[he:כוח (פיזיקה)]]
 
[[lv:Spēks]]
 
[[hu:Erő]]
 
[[ms:Daya (fizik)]]
 
[[nl:Kracht]]
 
[[ja:力]]
 
[[no:Kraft]]
 
[[pl:Siła]]
 
[[pt:Força]]
 
[[ru:Сила]]
 
[[simple:Force (physics)]]
 
[[sk:Sila]]
 
[[sl:Sila]]
 
[[sr:Сила]]
 
[[fi:Voima (fysiikka)]]
 
[[sv:Kraft]]
 
[[ta:விசை]]
 
[[th:แรง]]
 
[[vi:Lực]]
 
[[uk:Сила]]
 
[[yi:קראפט]]
 
[[zh-yue:力]]
 
[[zh:力]]
 

Latest revision as of 01:41, 6 September 2022


A spring scale measures the weight of an object, corresponding to the force of gravity exerted on the object.

In physics, force is defined as the rate of change of momentum of an object. This definition was given by Isaac Newton in the seventeenth century. In simpler terms, force may be thought of as an influence that may cause an object to accelerate. Force and mass are fundamental to Newtonian physics.

In everyday life, a force may be experienced in various ways, such as a lift, a push, or a pull. A familiar example of force is the weight of an object, which is defined as the amount of gravitational force exerted on the object. In addition, a force (or combination of forces) may cause an object to rotate or become deformed. Rotational effects and deformation are determined respectively by the torques and stresses that the forces create.

In the twentieth century, it was found that all known forces could be reduced to four fundamental forces: the strong force, weak force, electromagnetic force, and gravity. However, contemporary physics such as quantum mechanics and general relativity no longer regard the concept of force as fundamental. In quantum mechanics, force is seen as derivative of the interactions between particles. In general relativity, gravitational force is a trajectory along curved space-time.

History

Aristotle and his followers believed that it was the natural state of objects on Earth to be motionless and that they tended toward that state if left alone. But this theory, although based on the everyday experience of how objects move, was first shown to be unsatisfactory by Galileo as a result of his work on gravity. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the Aristotelian theory of motion early in the seventeenth century. He showed that the bodies were accelerated by gravity to an extent that was independent of their mass and argued that objects retain their velocity unless acted on by a force—usually friction.

Isaac Newton is recognized as having given the mathematical definition of force as the rate of change (time derivative) of momentum. In 1784, Charles Coulomb discovered the inverse square law of interaction between electric charges using a torsion balance.

With the development of quantum field theory and general relativity in the twentieth century, it was realized that particles influence one another through fundamental interactions, and that "force" is a concept arising from the conservation of momentum. Only four fundamental interactions are known. They are called the strong, electromagnetic, weak, and gravitational interactions (in order of decreasing strength).[1] In the 1970s, the electromagnetic and weak interactions were unified into the "electroweak interaction."

Definition

Force is defined as the rate of change of momentum with time:

The quantity (where is the mass and is the velocity) is called the momentum. This is the only definition of force known in physics.

Momentum is a vector quantity—that is, it has both a magnitude and direction. Therefore force is also a vector quantity. The actual acceleration of the body is determined by the vector sum of all forces acting on it (known as net force or resultant force).

If the mass m is constant in time, then Newton's second law can be derived from this definition:

where (the rate of change of velocity) is the acceleration.

This is the form Newton's second law is usually taught in introductory physics courses.

All known forces of nature are defined via the above Newtonian definition of force. For example, weight (force of gravity) is defined as mass times acceleration of free fall: w = mg

It is not always the case that m, the mass of an object, is independent of time, t. For example, the mass of a rocket decreases as its fuel is burned. Under such circumstances, the above equation is obviously incorrect, and the original definition of force: must be used.

Because momentum is a vector, then force is also a vector—it has magnitude and direction. Vectors (and thus forces) are added together by their components. When two forces act on an object, the resulting force, often called the resultant, is the vector sum of the original forces. This is called the principle of superposition. 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. As with all vector addition, this results in a parallelogram rule: the addition of two vectors represented by sides of a parallelogram gives an equivalent resultant vector, which is equal in magnitude and direction to the transversal of the parallelogram. If the two forces are equal in magnitude but opposite in direction, then the resultant is zero. This condition is called static equilibrium, with the result that the object remains at its constant velocity (which could be zero).

As well as being added, forces can also be broken down (or "resolved"). For example, a horizontal force pointing northeast can be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Force vectors can also be three-dimensional, with the third (vertical) component at right-angles to the two horizontal components.

Examples

  • An object is in free fall. Its momentum changes as dp/dt = mdv/dt = ma = mg (if the mass, m, is constant), thus we call the quantity mg a "gravitational force" acting on the object. This is the definition of weight (w=mg) of an object.
  • An object on a table is pulled downward toward the floor by the force of gravity. At the same time, the table resists the downward force with equal upward force (called the normal force), resulting in zero net force, and no acceleration. (If the object is a person, he actually feels the normal force acting on him from below.)
  • An object on a table is gently pushed in a sideways direction by a finger. However, it doesn't move because the force of the finger on the object is now opposed by a force of static friction, generated between the object and the table surface. This force exactly balances the force exerted on the object by the finger, and no acceleration occurs. The static friction increases or decreases automatically. If the force of the finger is increased (up to a point), the opposing sideways force of static friction increases exactly to the point of perfect opposition.
  • An object on a table is pushed by a finger hard enough that static friction cannot generate sufficient force to match the force exerted by the finger, and the object starts sliding across the surface. If the finger is moved with a constant velocity, it needs to apply a force that exactly cancels the force of kinetic friction from the surface of the table and then the object moves with the same constant velocity. Here it seems to the naive observer that application of a force produces a velocity (rather than an acceleration). However, the velocity is constant only because the force of the finger and the kinetic friction cancel each other. Without friction, the object would continually accelerate in response to a constant force.
  • An object reaches the edge of the table and falls. Now the object, subjected to the constant force of its weight, but freed of the normal force and friction forces from the table, gains in velocity in direct proportion to the time of fall, and thus (before it reaches velocities where air resistance forces becomes significant compared to gravity forces) its rate of gain in momentum and velocity is constant. These facts were first discovered by Galileo.

Types of Force

Although there are apparently many types of forces in the universe, they are all based on four fundamental forces, mentioned above. The strong and weak forces only act at very short distances and are responsible for holding certain nucleons and compound nuclei together. The electromagnetic force acts between electric charges, and the gravitational force acts between masses.

All other forces are based on these four. For example, friction is a manifestation of the electromagnetic force (acting between the atoms of two surfaces) and the Pauli exclusion principle, which does not allow atoms to pass through each other. The forces in springs modeled by Hooke's law are also the result of electromagnetic forces and the exclusion principle acting together to return the object to its equilibrium position. Centrifugal forces are acceleration forces (inertia forces) that arise simply from the acceleration of rotating frames of reference.

The modern quantum mechanical view of the first three fundamental forces (all except gravity) is that particles of matter (fermions) do not directly interact with each other but rather by the exchange of virtual particles (bosons). This exchange results in what we call electromagnetic interactions. (Coulomb force is one example of electromagnetic interaction).

In general relativity, gravitation is not strictly viewed as a force. Rather, objects moving freely in gravitational fields simply undergo inertial motion along a straight line in curved space-time — defined as the shortest space-time path between two points. This straight line in space-time is a curved line in space, and it is called the ballistic trajectory of the object. For example, a basketball thrown from the ground moves in a parabola shape, as it is in a uniform gravitational field. Similarly, planets move in ellipses, as they are in an inverse square gravitational field. The time derivative of the changing momentum of the body is what we label as "gravitational force."

Force in Special Relativity

In the special theory of relativity, mass and energy are equivalent (as can be seen by calculating the work required to accelerate a body). When an object's velocity increases, so does its energy and hence its mass equivalent (inertia). It thus requires a greater force to accelerate it the same amount than it did at a lower velocity. The definition remains valid, but the momentum must be redefined (in order to be conserved) as:

where

is the velocity and
is the speed of light.

Note that this definition is consistent with the classic definition of momentum (mv) at low speeds.

Also, according to the theory of relativity, for objects moving at extremely high speeds, a constant force produces not a constant acceleration but an ever-decreasing acceleration as the object approaches the speed of light.

Units of Measurement

The SI unit used to measure force is the newton (symbol N) where:

.

A newton is the amount of force required to accelerate a body with a mass of one kilogram at a rate of one meter per second squared.

A pound-force (lbf or lbf) is another common unit of force. One pound-force is the force equivalent to that exerted on a mass of one pound on the surface of Earth. When the standard g (an acceleration of 9.80665 m/s²) is used to define pounds force, the mass in pounds is numerically equal to the weight in pounds force. However, even at sea level on Earth, the actual acceleration of free fall is variable, over 0.53% more at the poles than at the equator.

The kilogram-force is a unit of force that was used in various fields of science and technology. In 1901, the CGPM improved the definition of the kilogram-force, adopting a standard acceleration of gravity for the purpose, and making the kilogram-force equal to the force exerted by a mass of 1 kg when accelerated by 9.80665 m/s². The kilogram-force is not a part of the modern SI system, but is still used in applications such as:

  • Thrust of jet and rocket engines
  • Spoke tension of bicycles
  • Draw weight of bows
  • Torque wrenches in units such as "meter kilograms" or "kilogram centimeters" (the kilograms are rarely identified as units of force)
  • Engine torque output (kgf·m expressed in various word orders, spellings, and symbols)
  • Pressure gauges in "kg/cm²" or "kgf/cm²"

Another unit of force called the poundal (pdl) is defined as the force that accelerates 1 lbm at 1 foot per second squared. Given that 1 lbf = 32.174 lb times one foot per second squared, we have 1 lbf = 32.174 pdl.

Conversion Factors

Below are several conversion factors for measuring force in various units:

  • 1 kgf (kilopond kp) = 9.80665 newtons
  • 1 lbf = 4.448222 newtons
  • 1 lbf = 32.174 poundals
  • 1 kgf = 2.2046 lbf
  • 1 dyne = 10-5 newtons
  • 1 slug = 32.174 lb

See Also

Notes

  1. The strong interaction (or strong force) represents the interactions between quarks and gluons, as explained by the theory of quantum chromodynamics (QCD). The weak interaction, affecting left-handed leptons, and quarks, is attributed to exchange of the heavy W and Z bosons. The word "weak" derives from the fact that the field strength is some 1013 times less than that of the strong interaction.

References
ISBN links support NWE through referral fees

  • Parker, Sybil P. McGraw-Hill Encyclopedia of Physics. New York: McGraw-Hill, 1983. ISBN 0070452539
  • Serway, Raymond A., John W. Jewett, and Robert J. Beichner. Physics for Scientists and Engineers with Modern Physics. Fort Worth, TX: Saunders College, 2000. ISBN 0030226570
  • Tipler, Paul Allen. Physics for Scientists and Engineers. New York: W.H. Freeman/Worth Publishers, 1999. ISBN 978-1572598140
  • Young, Hugh D, and Roger A. Freedman. Physics for Scientists and Engineers 11th ed. San Fransisco, CA: Pearson, 2003. ISBN 080538684X

Credits

New World Encyclopedia writers and editors rewrote and completed the Wikipedia article in accordance with New World Encyclopedia standards. This article abides by terms of the Creative Commons CC-by-sa 3.0 License (CC-by-sa), which may be used and disseminated with proper attribution. Credit is due under the terms of this license that can reference both the New World Encyclopedia contributors and the selfless volunteer contributors of the Wikimedia Foundation. To cite this article click here for a list of acceptable citing formats.The history of earlier contributions by wikipedians is accessible to researchers here:

The history of this article since it was imported to New World Encyclopedia:

Note: Some restrictions may apply to use of individual images which are separately licensed.