Force
From open-encyclopedia.com - the free encyclopedia.
- For other uses, see Force (disambiguation).
In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. The concept appeared first in the second law of motion of classical mechanics. It is usually expressed by the equation
F = m · a
where
F is the force, measured in newtons
m is the mass, measured in kilograms
a is the acceleration, measured in metre per second squared
The concept is much used in engineering, although scientists have developed more accurate concepts. Force is not a fundamental quantity in physics, despite the tendency to introduce students to physics via this concept. More fundamental are momentum, energy and stress. Force is rarely measured directly and is often confused with related concepts such as tension and stress.
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Forces in applications
Types of forces
Engineers uses many types of force: Coulomb's force between 2 electrical charges, gravity between 2 masses, magnetic force, friction, spring force, ...
Yet, scientists consider that there are only 3 fundamental forces of nature, with which every observed phenomenon can be explained: the strong nuclear force, the electromagnetic force, and the weak nuclear force. Gravity is not really a force, in the sense that it cannot be adequately modelled using advanced versions of Newton's laws: general relativity is used instead.
Pressure is a force applied over a surface. Some forces are conservative, others not.
Properties of force
Forces have an intensity and direction.
Forces can be added together using parallelogram of force. When two forces act on an object, the resulting force (called the resultant) is the vector sum of the original forces. The magnitude of the resultant varies from zero to the sum of the magitudes of the two forces, depending on the angle between their lines of action. If the two forces are equal but opposite, the resultant is zero. This condition is called static equilibrium, and the object moves at a constant speed (possibly, but not necessarily zero).
While forces can be added together, they can also be resolved into components. For example, an horizontal force acting in the direction of northeast can be split into two forces along the north and east directions respectively. The sum of these component forces is equal to the original force.
Units of measure
The SI unit used to measure force is the newton (symbol N), which is equivalent to kg·m·s−2
Imperial units of force and mass
The relationship F=m·a mentioned above may also be used with non-metric units.
For example, in imperial engineering units, F is in "pounds force" or "lbf", m is in "pounds mass" or "lbm", and a is in feet per second squared.
As with the kilogram, the pound is colloquially used as both a unit of mass and a unit of force or weight. 1 lbf is the force required to accelerate 1 lbm at 32.174 ft per second squared, since 32.174 ft per second squared is the acceleration due to terrestrial gravity at sea level.
Another imperial unit of mass is the slug, defined as 32.174 lbm. It is the mass that accelerates by one foot per second squared when a force of one lbf is exerted on it.
At sea level on earth, the magnitude of lbm exactly equals the magnitude of lbf, and the magnitude of kgm exactly equals the magnitude of kgf. This equivalency is only true at the surface of the earth, and does not hold up when acceleration other than that of the standard acceleration of gravity (that at the sea level of Earth) is used.
In other words, your mass and force exerted on the ground equal the same number in pounds (that is, lbm and lbf) on Earth at sea level. Since kgf and lbf are units of force, they are invariant, and the equivalence 1 kgf = 2.2046 lbf is always true. However, the conversion 1 kgm = 2.2046 lbm is true only on Earth at sea level.
The concept of weight, unlike force and mass, depends on the environment in which the weighing is done. It can be assumed that this is at sea level on Earth, unless other conditions are stated. Thus one pound mass (lbm) weighs one pound (lbf), and one kilogram mass (kgm) weighs one kilogram force (kgf). Further, an item with a weight of 10 lbf has a mass of 10 lbm and also a mass of 0.3108 slugs (= 10 lbm divided by 31.174 lbm per slug).
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 kgf. An item with a weight (on Earth at sea level) of 10 kgf has a mass of 10 kgm and also a mass of 1.01972661 metric slugs (= 10 kgm divided by 9.80655 kgm per metric slug).
An even rarer unit of force called the "imperial newton" is defined as the force that accelerates 1 lbm at 1 foot per second squared. Given that 1 lbf = 32.174 lbm times one foot per square second, we have (1/32.174 =) 0.0311 lbf = 1 lbm times 1 foot per square second = 1 imperial newton. Thus 1 lbf = 32.174 imperial newtons.
In conclusion, we have the following conversions, with "metric slugs" used very infrequently, and "imperial newtons" virtually never used.
- 1 kgf (Kilopond kp) = 9.80665 newton
- 1 metric slug = 9.80665 kgm
- 1 lbf = 32.174 imperial newtons
- 1 slug = 32.174 lbm
- 1 kgf = 2.2046 lbf
Forces in everyday life
Forces are part of everyday life:
- gravity: objects fall, even after being thrown upwards, objects slide and roll down
- friction: floors and objects are not extremely slippery
- spring force, objects resist tensile stress, compressive stress and/or shear stress, objects bounce back.
- electromagnetic force: attraction of magnets
Forces in industry
<to be completed>
Forces in the laboratory
Founding experiments
- Galileo Galilei uses rolling balls to disprove the Aristotelian theory of motion (1602 - 1607)
- Henry Cavendish's torsion bar experiment measured the force of gravity between 2 masses (1798)
Instruments to measure forces
<to be completed>
Forces in theory
Force, usually represented with the symbol F, is a vector quantity.
Forces in theoretical physics
It is very important to mention that it is impossible to define force. All attempts in history failed because of definitions in circles. This is a reason why modern physics theories don't operate with the forces as the source or symptom of interaction. General relativity uses a conception of curved spacetime and Quantum field theory talks about exchanging of intermediate particles like photons, W and Z bosons or gluons. Both theories don't need force. However, because it is easy to imagine forces, one can compute them from these theories. But we must not forget, that correct definition of this concept does not exist.
Fields of study
See also engineering mechanics:
- Statics Where the sum of the forces acting on a body in static equilibrium (motionless) is zero. F=m·a=0
- Dynamics The sum of the forces acting on a body or system over time is non-zero with a resulting set of accelerations defined by detailed analysis of equations derived from F=m·a=0.
Formula
Newton's second law of motion can be formulated as follows:
- F = m · a
where
F is the force, measured in newtons
m is the mass, measured in kilograms
a is the acceleration, measured in metre per second squared
The total (Newtonian) force, in newtons, on an object at any given time is defined as the rate of change of the object's velocity multiplied by the object's mass:
- <math>\mathbf{F} = \lim_{T \rightarrow 0 } \frac{m\mathbf{v} - m\mathbf{v}_0}{T}<math>
where
m is the inertial mass of the particle (measured in kilograms)
vo is its initial velocity (measured in metres per second)
v is its final velocity (measured in metres per second)
T is the time from the initial state to the final state (measured in seconds);
Lim T→0 is the limit as T tends towards zero.
Force was so defined in order that its reification would explain the effects of superimposing situations: If in one situation, a force is experienced by a particle, and if in another situation another force is experienced by that particle, then in a third situation, which (according to standard physical practice) is taken to be a combination of the two individual situations, the force experienced by the particle will be the vector sum of the individual forces experienced in the first two situations. This superposition of forces, and the definition of inertial frames and inertial mass, are the empirical content of Newton's laws of motion.
The content of above definition of force can be further explicated. First, the mass of a body times its velocity is designated its momentum (labeled p). So the above definition can be written:
- <math>\textbf{F}={\Delta \textbf{p} \over \Delta t}<math>
If F is not constant over Δt, then this is the definition of average force over the time interval. To apply it at an instant we apply an idea from Calculus. Graphing p as a function of time, the average force will be the slope of the line connecting the momentum at two times. Taking the limit as the two times get closer together gives the slope at an instant, which is called the derivative:
- <math>\textbf{F}={d\textbf{p}\over dt}<math>
With many forces a potential energy field is associated. 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. The potential field is defined as that field whose gradient is minus the force produced at every point:
- <math>\textbf{F}=-\nabla U<math>
While force is the name of the derivative of momentum with respect to time, the derivative of force with respect to time is sometimes called yank. Higher order derivates can be considered, but they lack names, because they are not commonly used.
In most expositions 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.
Non-SI usage of force and mass units
To a physicist, the kilogram is precisely the SI unit of mass, but in colloquial, non-scientific, usage "kilogram" can be a shorthand for "the weight of a one kilogram mass at sea level on earth". At sea level on earth, the acceleration due to gravity (a in the above equation) is approximately 9.807 metres per second squared, so the weight of one kilogram is 1 kg × 9.80665 m/s² = 9.80665 N.
To distinguish these two meanings of "kilogram", the abbreviations "kgm" for kilogram mass (or kilogram metre) (i.e. 1 kg) and "kgf" for kilogram force, also called kilopond (kp), equal to 9.80665 N, are sometimes used. These are only informal terms, not recognized in the SI system of units, and their usage is deprecated.
History
Force was first described by Archimedes.
See also
External link
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