Sandra Bullock

See also: Force

This article relates to the use of this concept in Physique, old use, still current, and which allows, since Isaac Newton, a precise definition: the force is an action Mécanique able to create a Accélération, i.e. a modification the speed of an object or part of an object, which induces a displacement or either or either,… or… --> a deformation of the object.

A little history

The concept of force is old, but it took a long time to obtain a definition usable. Indeed, unlike physical sizes such as the length or the mass, a force is an abstracted concept, which cannot be apprehended by the direct experiment, and which represents already a modeling world. The forces are not seen, they are not even real , they are only one explanation of visible effects.

Archimedes, at the time of the study of the problem of the arm of lever, evoked the weight of the bodies without explaining more explicitly than he understood by there. At the time of the studies on the pulleys, the concept of force is used confusedly as being the tension in wire. Even the problem of the tilted plan or that of the fall of the bodies is solved by Galileo without explicitly calling upon the concept of force.

In parallel, the composition of the forces appears implicitly in work of Stevin ( De Beghinselen der Weeghconst , 1586). However, the distinction between the concept of force and Speed is not done yet, and it will be necessary to await work of Isaac Newton to have a precise formalization of the concept of force. The definition given in famous the Philosophiae Naturalis Principia Mathematica (1687) is that which is still accepted nowadays.

The definition of the concept of force allowed a simple presentation of the traditional Mécanique by Isaac Newton (Lois of the movement of Newton).

Today, the concept of force remains very much used in the Enseignement and the Ingénierie. However, whereas the moments, the energy and the impulses are fundamental sizes of physics in the direction where they all obey a Loi of conservation, the force is only one artifice of calculation, sometimes convenient but which one can do perfectly. This is why there exists in Analytical mechanics, of the formulations of traditional mechanics which do not use the concept of force. These formulations, appeared after Newtonian mechanics, call however upon concepts even more abstract than the vector forces, and it is considered consequently that it is to better introduce them only into higher education.

The forces in addition are often confused with the concept of Contrainte and in particular with the tensions.

A very useful concept

The concept of force is very useful “to imagine” the movement of an object. Whatever the causes of the movement (braking by friction, acceleration by engine, bearing pressure on a wing by the air flow, attraction by the ground, attraction by a magnet etc), all occurs as if one attached to this object of the small rubber bands tended with the same tension as the force which applies to the object.

Who more is, it is possible to combine the forces applying to the same point, but coming from various causes, in only one force. For that, it is enough to summon the vectors forces (this operation amounts replacing two rubber bands attached to the same point, but perhaps drawing in different directions, by only one rubber band producing the same tension).

It is this capacity to be joined together and combine in the same tool of the so varied phenomena which confers all its power on the concept of force.

Thus, once comparable the Laws of the movement of Newton, one can include/understand the effect of any interaction on an object. Provided however that one remains under the conditions for application of traditional mechanics:

• the objects must be sufficiently large compared to an atom, so that the matter appears continuous (if not, it is necessary to use the quantum Mécanique)
• speeds must be relatively weak compared to speed of light (if not, it is necessary to use the General relativity or the restricted Relativité)
• the field of Gravitation must be not very variable and of limited intensity, so that one can neglect his effects on the geometry of space (if not, general relativity should be used).

In our daily life the land human ones, the conditions for application of traditional mechanics are always satisfied on the objects which we can see on ground with the naked eye. But the properties of these objects (colors, hardness, operation of an electronic device etc) are explained in general by interactions at the molecular level, and require sometimes to be explained, to have recourse to quantum mechanics.

The vector forces

A representative of the vector force is characterized by 4 elements:

1. direction: orientation of the force
2. the direction: towards where the force
3. the intensity acts: size of the force, it is measured in " Newton" (NR)
4. the point of application: place where the force is exerted

The force parallelogram

The Théorème of the force parallelogram comes from the observation owing to the fact that movements can be combined between them without the order of this combination having any influences on the final movement.

In the parallelogram opposite, one can distinguish two types of movement:

• a displacement parallel with AB and cd. (blue sides of the parallelogram)
• a displacement parallel with AD and BC (green sides of the parallelogram)

When a solid is located initially at the point has, the order of course AB then BC or AD then cd. does not have any influence on the end result: whatever the order of the movements, the solid is moved at the point C.

Forts of this observation, when the distinction between the forces (causes) and the movements (effects) was made, Simon Stevin then Isaac Newton could state the theorem of the force parallelogram:

Considérons a solid at the point has . Let us apply to him a force F ₁ proportional and parallel with the segment AB and which moves the balance of the solid at the point B , then a force F ₂ proportional and parallel with the segment BC and which moves the balance of the solid of the point B at the point C . Then the force F ₃ parallel with the segment AC and which moves the balance of the solid of the point has at the point C is such as:

$\backslash \; frac\; \{F\_3\}\; \{AC\}\; =\; \backslash \; frac\; \{F\_1\}\; \{AB\}\; =\; \backslash \; frac\; \{F\_2\}\; \{BC\}$

The force F ₃ is called the force “resulting” from the two forces F ₁ and F ₂.

Conversely, is an unspecified point B and the force F ₃ proportional and parallel with the segment AC and which moves the balance of the solid of the point has at the point C . Let us consider the forces F ₁ and F ₂ parallel respectively with the segments AB and BC and such as:

$\backslash \; frac\; \{F\_1\}\; \{AB\}\; =\; \backslash \; frac\; \{F\_2\}\; \{BC\}\; =\; \backslash \; frac\; \{F\_3\}\; \{AC\}$

Then the application of the forces F ₁ and F ₂ to the solid will move the balance of this last of the point has at the point C .

This last property of the forces makes it possible to separate a force in several components and is used for example to break up a force of reaction R into its components normal (effort of support NR ) and tangential (effort of friction T ).

Lastly, either a point D such as ABCD or a parallelogram, then the force F ₂, which moves the balance of the solid of the point B at the point C , can also move the balance of the point has at the point D . It is the same for the force F ₁ which can indifferently move the solid of the point has at the point B or of the point D at the point C .

The force parallelogram naturally brings to model those by a Vecteur often noted $\backslash \; vec\; \{F\}$. The direction and the direction of the vector respectively indicate the direction and the direction of the action, the length of the vector indicating the intensity of this same action.

With this notation, the force parallelogram is summarized simply with the following vectorial relation:

$\backslash \; vec\; \{F\_3\}\; =\; \backslash \; vec\; \{F\_1\}\; +\; \backslash \; vec\; \{F\_2\}$

The point of application

A force exerts its action in a point called not of application. The knowledge of this point is important to determine the moment force.

The action of a force can be transmitted to the other points of the object by elastic strain, for example, if a car is pushed, the force exerted by the palm of the hand is transmitted to the remainder of the vehicle.

The concept of point of application is obvious in the case of a “specific” cause: if one pushes an object with the hand, the point of application is the contact point between the object and the hand, and if one draws it with a cord, it is the point of fastener of the cord. However, to look at there more closely, the palm of the hand makes a certain surface, and the cord has a nonnull section. The force is thus exerted on a surface, and not in a point. The point of application is in fact the Barycentre surface, by supposing that the force is distributed uniformly on surface; if not, that brings back to a problem Pression.

The concept can extend if the surface of contact is important, as for example in the case from the reaction from a support on which an object is posed, or the Poussée of Archimedes. One also extends it to the case of the voluminal forces, i.e. remote forces which are exerted in each point of the object, like the weight or the electrostatic attraction; the point of application is then also a barycentre (the Center of inertia of the object in the case of the weight).

Measuring unit

The measuring unit IF of a force is the newton, symbol NR, in homage to the scientist.

The newton is equivalent to 1 kg.m.s^-2, i.e. a newton is the force colinéaire with the movement which, applied during one second to an object of one kg, is able to add (or to cut off) one meter a second at its speed.

One also used to it kg-force, force exerted by a mass of 1 kg in the fields of terrestrial pesentor (to the sea level, etc), and which is worth thus 9,81 NR. the Aéronautique and the Astronautique made a great use of a multiple of the kg-force: the ton of push.

Some examples of forces

The phenomena which cause the Accélération or the Déformation of a body are very diverse, one thus distinguishes several types of forces, but which all are modelled by the same object: the vector forces. For example, one can classify the forces according to their distance from action:

• forces of contact: Pressure of a gas, action of contact of an object on another (to support, draw), Friction.
• remote forces: Weight (gravitational attraction), electromagnetic Force.

Elastic forces

In the simplest case of the elastic strain, the lengthening or the moderate compression of a Ressort in its axis generates a force proportional to relative lengthening, that is to say:

$F=k\; \backslash \; cdot\; \backslash \; Delta\; l$

where K is the constant of stiffness of the spring and Δ L is its lengthening (final length minus initial length). The deformation of the solids is studied by the Mécanique continuous mediums (MMC).

Pressures

When a force is exerted on a surface, it is sometimes interesting to consider the distribution of the force according to surface. For example, if one inserts a bug in Bois, the bug is inserted because the force is distributed on a very small surface (the end of the point); if one supports simply with the finger, the finger will not be inserted in wood because the force is distributed on a large surface (the end of the finger). For this type of studies, one divides the intensity of the force by the surface on which she is exerted, it is the Pression. Within a solid Material, this pressure is called Contrainte ( stress ).

By definition, p: F/S . That means that the pressure is the force exerted per unit of area. In the system MKSA ,

F: in Newtons S: in m ² p: in N/m ²

There exist many measuring units of Pressure (Pa (Pascals), mmHg (Millimètres of mercury), Atm (Atmosphères), bar…).

In hydraulics as in tire, the pressure is expressed in bars. (1 bar = 100.000 Pa).

Pascal Pa (derived unit MKSA) is the report/ratio of a force of 1N on a surface of 1m ².

1 bar = 100.000 Pa = 750.0638 mmHg = 0.9869 Atm = 750.O638 Torr

1 bar = 100.000 Pa = 100.000 NR /m ² = 10 NR/cm ²

Finally 10 N/cm ² it is roughly 1Kg/cm ². (F = m G) if G = 10m/s ² F = 10N. However g= 9.81 m/s ² gravific acceleration.

Conservative forces

See also: conservative Force

Certain forces can derive from a Potentiel, in this case, it exists a homogeneous field U with a energy such as the resulting force can be written in the following form:

$\backslash \; vec\; \{F\}\; =\; \backslash \; vec\; \{\backslash \; nabla\}\; \backslash ,\; U$

Such forces are conservative.

Voluminal forces

There exist forces which are exerted on the totality of the object, like the weight, these forces are known as voluminal. One shows, in the case of the indeformable solids, that the action of such forces is equivalent to the application of only one force to the Barycentre of the body, still called “center of mass”, “center of gravity” or “center of inertia”.

Force and Lagrangian

In Lagrangian Mécanique, if one notes L ( Q , q' ) the Lagrangian one of the system with Q the position and q' the speed of the system, one a:

$F\; =\; \backslash \; frac\; \{DLL\}\; \{dq\}$

Force, work and energy

The energy provided by the action of a force at a given distance is called work.

In physics, force and energy are two different manners to model the phenomena. According to the cases, one prefers one or the other expression. For example, one will be able to treat the fall of an object with the forces while making use of the laws of Newton, particularly the second (the Accélération is proportional to the force and inversely proportional to the Masse), or with energies (the reduction in the potential energy of gravity is equal to the increase in the kinetic energy).

A force works (or a work carries out) when its point of application moves. In the case of a constant force, the value of the work of a force noted W (F), is equal to the scalar product of the vector forces by the vector displacement.

Measure of a force

All the apparatuses being used to measure a force rest in their principle of operation on the third law of Newton: the idea is to determine the required effort which it is necessary to oppose to the force to be measured to reach balance.

In the particular case, Weight, one can use a balances which compares the weight to be measured with the weight of a known mass.

For the other cases, one generally uses a Dynamomètre which in general consists of a Ressort which one knows the stiffness K and whose end is attached to a fixed point. One applies the force to be measured to the other end of the spring and one measures the variation length Δ L of the spring. One from of deduced the force F by the relation which we saw higher:

F = K ⋅Δ L

The measure of length Δ L is generally made by a comparator. The force F being directly proportional to Δ L , it is enough to rather graduate the dial of the comparator in newtons than in Mètre S.

When the force to be measured is important, one can use a massive bar as “arises” (cf the Loi of Hooke). The Elastic strain of the bar is then measured with a extensometer (or Strain gauge); it is in general about a wire in zigzag stuck on the bar, and whose Electrical resistance varies with relative lengthening.

The concept of force and modern theories of physics

In Mechanical Newtonian, the relation between the force and the movement is given by the 2nd law of Newton or “basic principle of dynamics”:

$\backslash \; vec\; \{F\}\; =\; \backslash \; frac\; \{D\; \backslash \; vec\; \{p\}\}\; \{dt\}$

where $\backslash \; vec\; \{p\}$ is the Quantité of movement of the object, i.e. the bulk product by speed (while the impulse is the change of the momentum produced in a short given amount of time), and T is the Temps. If the mass is constant, then there is

$\backslash \; vec\; \{F\}\; =\; m\; \backslash \; cdot\; \backslash \; vec\; \{has\}$

where $\backslash \; vec\; \{has\}$ is the Accélération.

Ernst Mach pointed out in its work mechanics: Exposed historical and critical of its development (1883) that the second law of Newton contains the definition of the force given by Isaac Newton itself. Indeed, to define a force as being what creates the Accélération does not learn anything more than what is in F = m ⋅ has and is finally only one reformulation (incomplete) of this last equation.

This impotence to differently define a force than by circular definitions was problematic for many physicists among whom Ernst Mach, Clifford Truesdell and Walter Noll. The latter thus sought, in vain, to establish an explicit definition of the concept of force.

The modern Théorie S of the Physique do not make call to the forces as sources or symptoms of an interaction. The General relativity uses the concept of curve of the Espace-temps. The quantum Mécanique describes the exchanges between elementary particles in the form of Photon S, Boson S and Gluon S. None of these two theories has recourse to the forces. However, as the concept of force is a practical support for the intuition, it is always possible, as well for general relativity as for quantum mechanics, to calculate forces. But, as in the case of the 2nd law of Newton, the equations used do not bring extra informations on what is the intrinsic nature of a force.

Four forces of nature

The whole of the interactions of the matter is explained by only four types of forces:

• the electromagnetic force

• the force nelle Gravitation
• the strong Interaction
• the weak Interaction

On our scale, the majority of the interactions come from the gravitational force (primarily, in what concerns us, fact that one is attracted by Ground, that it does not disaggregate in dust, movements of stars and efforts which it creates on the earth's crust, participant in his geological evolution, the tides), and from the electromagnetic force, which is the cause of practically all that one can observe (hardness of certain matters, chemical reactions, fire, state liquid, solid or gas of the matter, frictions, behavior of the light, electricity, microprocessors, storage of this article on any type of known media etc). These phenomena are governed by the electromagnetic interactions between the molecules which compose the matter.

The weak interaction is responsible for the stability of the Atome S, which is much, since it is one of the conditions of our existence. Apart from that, one sees the demonstration in the nuclear reactions of it and the fact that the sun, also helped in that by a beautiful joint effort of the gravitational force (to create the conditions of the nuclear reactions in its center, and also to prevent with our ground too much moving away from him) and electromagnetic force (to transport its luminous rays to us) heats us and floods us of his vital energy.

The strong interaction, much more discrete our scale, allows the particles made up of Quark S, like the Proton S and the Neutron S, not to disaggregate. Apart from the particle accelerator of the physicists, it is held sufficiently quiet never not to intervene in our daily life, at least since the Big Bang.

See also: elementary Interaction

See too

Related articles

• Mechanical statics;

• Moment (mechanical);
• Balance;
• Work of a force

External bonds

• dynamics, Martin Pohl (CERN)

Simple: Force (physics) Zh-min-nan: La̍t Zh-yue: 力

Random links:

Fouchères (Paddle) | Magneux-High-bank | Oenopia | Octafluorocyclobutane | Brad Paisley | Sandra_Bullock

© 2007-2008 speedlook.com; article text available under the terms of GFDL, from fr.wikipedia.org