# Force

*see Force at Schools Wikipedia*

*This article is about the concept of force in physics. For all other uses see Force (disambiguation).*

In physics, a net **force** acting on a body causes that body to accelerate: to change its velocity. 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.

Force, usually represented with the symbol **F**, is a vector quantity. The SI unit used to measure force is the newton (symbol *N*), which is equivalent to kg·m·s^{-2}

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.

*m*is the inertial mass of the particle in kilograms,

*v*is its initial velocity in meters per second,

_{o}*v*is its final velocity, and

*T*is the time in seconds from the initial state to the final state; the expression on the right of the equation being the limit as

*T*goes to 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.

Since force is a vector it can 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 vector sum of these component forces is equal to the original force.

## More depth

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:

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.

## Relationships between force units and mass units

which is derived from Newton's second law of motion,*F*is the force in newtons,

*m*the mass in kilograms and

*a*the acceleration in meters per second squared. To a physicist, the kilogram is a unit of mass, but in common usage "kilogram" is 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 9.807 meters per second squared, so the weight of one kilogram is 1 kg × 9.807 m/s² = 9.807 N.

To distinguish these two meanings of "kilogram", the abbreviations "kgm" for kilogram mass (i.e. 1 kg) and "kgf" for kilogram force, also called kilopond (kp), equal to 9.807 N, are sometimes used. These are only informal terms and are not recognized in the SI system of units.

## Imperial units of force

The relationship F = m×a mentioned above may also be used with non-metric units.

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.

## Conversion between SI and imperial units of force

- 1 kgf = 9.807 newton
- 1 metric slug = 9.807 kgm
- 1 lbf = 32.174 imperial newtons
- 1 slug = 32.174 lbm
- 1 kgf = 2.2046 lbf

## Combining forces

When two forces act on a single point, 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 equilibrium.

## See also

## External link