An influence applied to an unrestrained object which results in a change in its motion, causing it to accelerate in some way; symbol F, units N (newton); a vector quantity. Force equals mass of object multiplied by acceleration (Newton's second law).
A force is a lift, a push, or a pull that has a size and a direction. 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).
Force is a vector quantity defined as the rate of change of the momentum of the body that would be induced by that force acting alone. Henry Cavendish's in 1798 measured the force of gravity between two masses (in torsion balance experiment) With the development of quantum electrodynamics in mid 20 century it was realised that "force" is strictly a macroscopic concept which arises from conservation of momentum of interacting elementary particles. Thus currently known fundamental forces are not called forces but "fundamental interactions". This was a common experience of humans with ordinary conditions in which friction was involved, so Newton's idea that force naturally produces a constant increase in velocity was not an obvious one. Frictional forces, acting in opposition to other kinds of forces, historically tended to hide the correct mathematical relationship between simple unopposed force and motion.
The correct behavior of objects accelerated by constant force was first discovered by Galileo in working with gravity (dropping stones and rolling cannonballs on an incline), although it was not until Newton that gravity was seen as a force. Newton generalized the behavior of constant acceleration, or constant momentum gain, to forces other than gravity. He asserted in his second law of motion that this behavior of constant momentum increase was characteristic of all forces-- including the "forces" of ordinary experience, such as tension or the stress produced by pushing on an object with a finger. In fact, he defined force as mass times acceleration, or more accurately, as a rate of change of momentum.
Examples
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 fails to accelerate sideways, 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. 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. 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.Quantitative definition
Force is defined as the rate of change of momentum with time:
.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.
Because momentum is a vector, then force, being its time derivative, is also a vector - it has magnitude and direction, and four-force is a four-vector in relativity. When two forces act on an object, the resulting force, the resultant, is the vector sum of the original forces.
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.
In most explanations of mechanics, force is usually defined only implicitly, in terms of the equations that work with it.
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).
The relativistic expression relating force and acceleration for a particle with non-zero rest mass moving in the direction is:
where the Lorentz factor
Here a constant force does not produce a constant acceleration, but an ever decreasing acceleration as the object approaches the speed of light.
Force and potential
Instead of a force, the mathematically equivalent concept of a potential energy field can be used for convenience. Restating mathematically the definition of energy (via definition of work), a potential field U(r) is defined as that field whose gradient is equal and opposite to the force produced at every point:
Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential, and include gravity, electromagnetic force, and spring force.
Types of force
Many forces exist: the Coulomb force (between electrical charges), gravitational force (between masses), magnetic force, frictional forces, centrifugal forces (in rotating reference frames), spring force, magnetic forces, tension, chemical bonding and contact forces to name a few.
Only four fundamental forces of nature are known: the strong force, the electromagnetic force, the weak force, and the gravitational force.
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) (as, for example, virtual photons in case of interaction of electric charges).
In general relativity, gravitation is not strictly viewed as a force.
Units of measurement
The SI unit used to measure force is the newton (symbol N), which is equivalent to kg·m·s−2. In Imperial engineering units, if F is measured in "pounds force" or "lbf", and a in feet per second squared, then m must be measured in slugs. Similarly, if mass is measured in pounds mass, and a in feet per second squared, the force must be measured in poundals.
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. 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. If you use the standard '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—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. This is the mass that accelerates at one metre per second squared when pushed by a force of one kgf.
Another unit of force called the poundal (pdl) is defined as the force that accelerates 1 lbm at 1 foot per second squared. 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 centimetres" (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"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. This might occasionally be an attempt to disintinguish kilograms as units of mass from the "kgf" symbol for the units of force.
Conversions
Below are several conversion factors between various measurements of force:
1 dyne = 10-5 newtons 1 kgf (kilopond kp) = 9.80665 newtons 1 metric slug = 9.80665 kg 1 lbf = 32.174 poundals 1 slug = 32.174 lb 1 kgf = 2.2046 lbf
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