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.

Forces in theory

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:

Related Topics:
Newtonian - Newton - Velocity - Mass

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:mathbf{F} = lim_{T ightarrow 0 } rac{mmathbf{v} - mmathbf{v}_0}{T}

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where

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:m is the inertial mass of the particle (measured in kilograms)

Related Topics:
Inertial mass - Kilograms

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:vo is its initial velocity (measured in metres per second)

Related Topics:
Velocity - Metres per second

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:v is its final velocity (measured in metres per second)

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:T is the time from the initial state to the final state (measured in seconds);

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:Lim T→0 is the limit as T tends towards zero.

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Force was so defined to 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.

Related Topics:
Vector - Inertial frame - Inertial mass - Newton's laws of motion

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There are other ways to look at the above definition of force. First, the mass of a body multiplied by its velocity is called its momentum, p, so the above definition is equivalent to:

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: extbf{F}={Delta extbf{p} over Delta t}

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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. If we graph 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:

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: extbf{F}={d extbf{p}over dt}

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Many forces are associated with a potential energy field. 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 equal and opposite to the force produced at every point:

Related Topics:
Potential energy - Gravitational field - Gradient

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: extbf{F}=- abla U

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The derivative of force with respect to time is called yank. Higher order derivatives are sometimes used, but they lack names because of their rarity.

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In most explanations 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.

Related Topics:
Mechanics - Ernst Mach - Clifford Truesdell - Walter Noll

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