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F_N represents the normal force

In mechanics, the normal force Failed to parse (Missing texvc executable; please see math/README to configure.): F_n\

(occasionally N) is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.

The normal force is one of the components of the ground reaction force and may coincide with it, for example considering a person standing still on the ground, in which case the ground reaction force reduces to the normal force. In another common situation, if an object hits a surface with some speed, and the surface can withstand it, the normal force provides for a rapid deceleration, which will depend on the flexibility of the surface.

Equations[link]

Weight (W), the frictional force (F_r), and the normal force (F_n) impacting a cube. Weight is mass (m) multiplied by gravity (g).

In a simple case such as an object resting upon a table, the normal force on the object is equal but in opposite direction to the gravitational force applied on the object (or the weight of the object), that is, Failed to parse (Missing texvc executable; please see math/README to configure.): N = mg , where m is mass, and g is the gravitational field strength (about 9.81 Nkg^-1 on Earth). The normal force here represents the force applied by the table against the object that prevents it from sinking through the table, and requires that the table is sturdy enough to deliver this normal force without breaking.

Where an object rests on an incline, the normal force is perpendicular to the plane the object rests on. Still, the normal force will be as large as necessary to prevent sinking through the surface, presuming the surface is sturdy enough. The strength of the force can be calculated as:

Failed to parse (Missing texvc executable; please see math/README to configure.): N = mg \cos(\theta)

where N is the normal force, m is the mass of the object, g is the gravitational field strength, and θ is the angle of the inclined surface measured from the horizontal.

The normal force is one of several forces which act on the object. In the simple situations so far considered, the most important other forces acting on it are friction and the force of gravity.

Using vectors[link]

In general, the magnitude of the normal force, N, is the projection of the net surface interaction force, T, in the normal direction, n, and so the normal force vector can be found by scaling the normal direction by the net surface interaction force. The surface interaction force, in turn, is equal to the dot product of the unit normal with the stress tensor describing the stress state of the surface. That is,

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{N}=\mathbf{n}\, N = \mathbf{n}\, (\mathbf{T}\cdot \mathbf{n}) = \mathbf{n}\, (\mathbf{n}\cdot \mathbf{\tau} \cdot \mathbf{n}).

Or, in indicial notation,

Failed to parse (Missing texvc executable; please see math/README to configure.): \ N_i = n_i N = n_i T_j n_j = n_i n_k \tau_{jk} n_j.

The parallel shear component of the contact force is known as the frictional force (Failed to parse (Missing texvc executable; please see math/README to configure.): F_fr\ ).

The static coefficient of friction for an object on an inclined plane can be calculated as follows:^[1]

Failed to parse (Missing texvc executable; please see math/README to configure.): \mu_s=\tan(\theta)

for an object on the point of sliding where Failed to parse (Missing texvc executable; please see math/README to configure.): \theta

is the angle between the slope and the horizontal.

Real-world applications[link]

For a person standing in an elevator either stationary or moving at constant velocity, the normal force on the person's feet balances the person's weight. In an elevator that is accelerating upward, the normal force is greater than the person's ground weight and so the person's perceived weight increases (making the person feel heavier). In an elevator that is accelerating downward, the normal force is less than the person's ground weight and so a passenger's perceived weight decreases. If a passenger were to stand on a "weighing scale", such as a conventional bathroom scale, while riding the elevator, the scale will be reading the normal force it delivers to the passenger's feet, and will be different than the person's ground weight if the elevator cab is accelerating up or down. The weighing scale measures normal force (which varies as the elevator cab accelerates), not gravitational force (which does not vary as the cab accelerates). It is impossible to measure true gravitational force without knowledge of the motion of one's immediate environment.

When we define upward to be the positive direction, constructing Newton's second law and solving for the normal force on a passenger yields the following equation:

Failed to parse (Missing texvc executable; please see math/README to configure.): N = m(g + a)

Lagrangian Mechanics[link]

In Lagrangian Mechanics, the normal force plays an important part in its formalization. Suppose a smooth surface, Failed to parse (Missing texvc executable; please see math/README to configure.): \Sigma , is defined by the explicit equation Failed to parse (Missing texvc executable; please see math/README to configure.): f(x,y,z)=0 . Furthermore, suppose a particle must move along this surface. The equation of motion would be given by

Failed to parse (Missing texvc executable; please see math/README to configure.): m\mathbf{a}=\mathbf{F}+\mathbf{N}

Where Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{a}

is the acceleration of the particle,

References[link]

The Normal is the recording artist name used by English music producer Daniel Miller, a film editor at the time, who is best known as the founder of the record label Mute Records.

Background[link]

In 1977, Miller had split up with his girlfriend. A friend suggested that he read a book he himself had just finished. The book was Crash (1973) by J.G. Ballard.^[1] He felt that Ballard's writing took him five minutes into the future; the novel was to be a major influence in the music he would produce as The Normal.^[1] Miller was disillusioned by the fact you needed to learn three chords to be in a punk band, so he decided to purchase a synthesiser. His thinking was that you only needed to learn to press one key on a synthesiser.^[1] After buying a Korg 700s synthesiser from Macari's music shop in London,^[1] Miller recorded and released a single under the name The Normal. This was "T.V.O.D."/"Warm Leatherette". Both tracks were minimalist electronic songs influenced by the Crash novel.^[1] He wanted the sound of the recordings to be visual, like driving along a highway between large buildings then going through a tunnel.^[1] The single was recorded in Daniel Miller's house using a TEAC four track tape recorder and the Korg synthesiser.^[2]

"Live at West Runton Pavilion", The Normal's second release, done with another Mute Records act, Robert Rental, wasn't well-received. A strange release, it was a one-sided album (side two was left blank) of improvised electronic noises, in a plain purple dust jacket. Marat Records released the record in Germany as Daniel Miller Robert Rental Live, with a black and white picture sleeve, catalogue No. Marat Rough 017.

Influence on other artists[link]

Songs by The Normal have been covered and performed by many notable artists such as Grace Jones, Chicks on Speed/Hell on a split-7", Giddle and Boyd Rice and in 2006 by Trent Reznor with Jeordie White and Peter Murphy.^[3] A recent cover of "Warm Leatherette" was performed live by Duran Duran in November 2007, and as part of an electro medley during their 2008 tour,^[4] in support of their album Red Carpet Massacre.

Discography[link]

• The Normal - "T.V.O.D." / "Warm Leatherette" (Mute Records 1978)
• Robert Rental & The Normal - Live At West Runton Pavilion, 6-3-79 (Rough Trade 1980)

References[link]

Notes[link]

External links[link]

• The Normal at Mute Records Official site
• The Normal at Allmusic
• The Normal Discography at discogs.com