Force

In physics, a force is an external cause responsible for any change of a physical system. For instance, a person holding a dog by a rope is experiencing the force applied by the rope on his hand, and the cause for its pulling forward is the force exercised by the rope. The kinetic expression of this change is, according to Newton's second law, acceleration, non kinetic expressions such as deformation can also occur. The SI unit for force is the newton.

Quantitative definition

If the system is a point-like system, which is one that cannot rotate nor be deformed (like an idealised cannon ball), the only change it can experience is a change of its movement (more precisely of its center of mass); that is, its speed, or more generally its momentum. Since the rise of the atomic theory, any physical system has been considered in classical physics as composed of point-like systems called atoms or molecules. Therefore, all forces can be defined by their effect; that is, by the change of movement they induce on point-like systems. This change of movement can be quantified by the acceleration (the derivative of velocity), but a given force will induce different effects on different point-like systems depending on the system. The discovery by Isaac Newton that a given force will induce an acceleration in inverse proportion to a quantity called the mass of inertia or inertial mass which is independent of the speed of the system is Newton's second law. This law allows us to predict the effect of a force on any point-like system whose mass is known. It is usually written as:

Related Topics:
Movement - Center of mass - Speed - Momentum - Atomic theory - Classical physics - Atom - Molecule - Effect - Acceleration - Derivative - Velocity - Isaac Newton - Inverse proportion - Mass - Inertia - Inertial mass - Newton's second law

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:F = dp/dt = d(m·v)/dt = m·a (in the case where m does not depend on t)

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where

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:F is the force (a vector quantity),

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:p is the momentum,

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:t is the time,

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:v is the velocity,

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:m is the mass, and

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:a=d²x/dt² is the acceleration, the second derivative with respect to t of the position vector x.

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If the mass m is measured in kilograms and the acceleration a is measured in metres per second squared, then the unit of force is kilogram x metre/second squared. This unit is called the newton: 1 N = 1 kg x 1 m/s².

Related Topics:
Kilogram - Acceleration - Metres per second squared - Newton

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This equation is a system of three second-order differential equations with respect to the three-dimensional position vector which is an unknown function of time. This equation can be solved if F is a known function of x and some of its derivatives and if the mass m is known. Morevover the boundary conditions are required; for example, the values of the position vector and x and the velocity v at the starting time, say t=0.

Related Topics:
Differential equation - Dimension - Function - Boundary condition

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Of course, this formula is only useful if one knows the numerical values of F and m. The definition above is an implicit definition, arrived at as follows. One defines a reference system (one litre of water) and a reference force (the gravitational force applied by the Earth on it at the altitude of Paris). One takes Newton's second law for granted (one postulates that it is true) and measures the acceleration induced by the reference force on the reference system. This gives us a mass unit (1 kg) and a force unit (the older unit of 1 kilogram-force = 9.81 N). Once this is done, one can measure any force by the acceleration it induces on the reference system and measure the inertial mass of any system by measuring the acceleration induced on this system by the reference force.

Related Topics:
Implicit - Litre - Water - Gravitational - Earth - Paris - Postulate - Kilogram-force

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Force is often considered a fundamental quantity in physics, but there are more fundamental quantities, such as momentum (p = mass m x velocity v). Energy, measured in joules, is still less fundamental than force and momentum, because it is defined as work, and work is defined in terms of force. The two most fundamental theories of nature - quantum electrodynamics and general relativity - do not contain the concept of force at all.

Related Topics:
Momentum - Velocity - Joule - Quantum electrodynamics - General relativity

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Although not the most fundamental quantity in physics, force is an important basic mathematical concept from which other concepts, such work and pressure (measured in pascals), are derived. Force is sometimes confused with stress.

Related Topics:
Pascal - Stress

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