Force
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.
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.
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:
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.
In the relationship
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.
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 1.0197 metric slugs (= 10 kgm divided by 9.807 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.
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.Imperial units of force
Conversion between SI and imperial units of force
Combining forces