Foot-pound (energy)
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Foot-pound (energy)
The foot-pound force (symbol: ft⋅lbf, ft⋅lbf, or ft⋅lb ) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a force of one pound-force (lbf) through a linear displacement of one foot. The corresponding SI unit is the joule. Usage The foot-pound is often used to specify the muzzle energy of a bullet in small arms ballistics, particularly in the United States. The term ''foot-pound'' is also used as a unit of torque (see ''pound-foot (torque)''). In the United States this is often used to specify, for example, the tightness of a fastener (such as screws and nuts) or the output of an engine. Although they are dimensionally equivalent, energy (a scalar) and torque (a Euclidean vector) are distinct physical quantities. Both energy and torque can be expressed as a product of a force vector with a displacement vector (hence pounds and feet); energy i ...
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English Engineering Units
Some fields of engineering in the United States use a system of measurement of physical quantities known as the English Engineering Units. Despite its name, the system is based on United States customary units of measure; it is not used in England. A similar system, termed British Engineering Units by Halliday and Resnick (1974), was a system that used the slug as the unit of mass, and in which Newton's law retains the form ''F=ma''. Modern British engineering practice has used SI base units since at least the late 1970s. Definition The English Engineering Units is a system of consistent units used in the United States. The set is defined by the following units, with a comparison of their definitive conversions to their International System of Units counterparts. Units for other physical quantities are derived from this set as needed. In English Engineering Units, the pound-mass and the pound-force are distinct base units, and Newton's Second Law of Motion takes the f ...
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United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territories, nine Minor Outlying Islands, and 326 Indian reservations. The United States is also in free association with three Pacific Island sovereign states: the Federated States of Micronesia, the Marshall Islands, and the Republic of Palau. It is the world's third-largest country by both land and total area. It shares land borders with Canada to its north and with Mexico to its south and has maritime borders with the Bahamas, Cuba, Russia, and other nations. With a population of over 333 million, it is the most populous country in the Americas and the third most populous in the world. The national capital of the United States is Washington, D.C. and its most populous city and principal financial center is New York City. Paleo-Americ ...
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Calorie
The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of one kilogram of water by one degree Celsius (or one kelvin). The small calorie or gram calorie was defined as the amount of heat needed to cause the same increase in one gram of water. Thus, 1 large calorie is equal to 1000 small calories. In nutrition and food science, the term ''calorie'' and the symbol ''cal'' almost always refers to the large unit. It is generally used in publications and package labels to express the energy value of foods in per serving or per weight, recommended dietary caloric intake, metabolic rates, etc. Some authors recommend the spelling ''Calorie'' and the symbol ''Cal'' (both with a capital C) to avoid confusion; however, this convention is often ignored. In physics and chemistry the word ''calorie'' and i ...
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British Thermal Unit
The British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United States customary units. The modern SI unit for heat energy is the joule (J); one BTU equals about 1055  J (varying within the range 1054–1060 J depending on the specific definition; see below). While units of heat are often supplanted by energy units in scientific work, they are still used in some fields. For example, in the United States the price of natural gas is quoted in dollars per the amount of natural gas that would give 1 million BTUs (1 "MMBtu") of heat energy if burned. Definitions A BTU was originally defined as the amount of heat required to raise the temperature of 1 avoirdupois pound of liquid water by 1 degree Fahrenheit at a constant pressure of one atmospheric unit. There are several different definitions of the BTU that differ slightly. This ref ...
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Cross Product
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product). If two vectors have the same direction or have the exact opposite direction from each other (that is, they are ''not'' linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendic ...
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Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In mo ...
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Euclidean Vector
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a '' directed line segment'', or graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \overrightarrow . A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word ''vector'' means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations whic ...
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Scalar (physics)
In physics, scalars (or scalar quantities) are physical quantities that are unaffected by changes to a vector space basis (i.e., a coordinate system transformation). Scalars are often accompanied by units of measurement, as in "10 cm". Examples of scalar quantities are mass, distance, charge, volume, time, speed, and the magnitude of physical vectors in general (such as velocity). A change of a vector space basis changes the description of a vector in terms of the basis used but does not change the vector itself, while a scalar has nothing to do with this change. In classical physics, like Newtonian mechanics, rotations and reflections preserve scalars, while in relativity, Lorentz transformations or space-time translations preserve scalars. The term "scalar" has origin in the multiplication of vectors by a unitless scalar, which is a ''uniform scaling'' transformation. Relationship with the mathematical concept A scalar in physics is also a scalar in mathematics, as an eleme ...
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Dimensional Analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or the SI than in others, due to the regular 10-base in all units. ''Commensurable'' physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measure, e.g. yards and metres, pounds (mass) and kilograms, seconds and years. ''Incommensurable'' physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are expressed in, e.g. metres and ...
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Engine
An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy. Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric power generation), heat energy (e.g. geothermal), chemical energy, electric potential and nuclear energy (from nuclear fission or nuclear fusion). Many of these processes generate heat as an intermediate energy form, so heat engines have special importance. Some natural processes, such as atmospheric convection cells convert environmental heat into motion (e.g. in the form of rising air currents). Mechanical energy is of particular importance in transportation, but also plays a role in many industrial processes such as cutting, grinding, crushing, and mixing. Mechanical heat engines convert heat into work via various thermodynamic processes. The internal combustion engine is perhaps the most common example of a mechanical heat engine, in which he ...
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Nut (hardware)
A nut is a type of fastener with a screw thread, threaded hole. Nuts are almost always used in conjunction with a mating bolt (fastener), bolt to fasten multiple parts together. The two partners are kept together by a combination of their threads' friction (with slight deformation (engineering)#Elastic deformation, elastic deformation), a slight Tension (physics), stretching of the bolt, and compression (physics), compression of the parts to be held together. In applications where vibration or rotation may work a nut loose, various locking mechanisms may be employed: lock washers, jam nuts, eccentric double nuts, specialist adhesive thread-locking fluid such as Loctite, safety pins (split pins) or lockwire in conjunction with castellated nuts, nylon inserts (nyloc nut), or slightly oval-shaped threads. Square nuts, as well as bolt heads, were the first shape made and used to be the most common largely because they were much easier to manufacture, especially by hand. While rare to ...
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Screw
A screw and a bolt (see '' Differentiation between bolt and screw'' below) are similar types of fastener typically made of metal and characterized by a helical ridge, called a ''male thread'' (external thread). Screws and bolts are used to fasten materials by the engagement of the screw thread with a similar ''female thread'' (internal thread) in a matching part. Screws are often self-threading (also known as self-tapping) where the thread cuts into the material when the screw is turned, creating an internal thread that helps pull fastened materials together and prevents pull-out. There are many screws for a variety of materials; materials commonly fastened by screws include wood, sheet metal, and plastic. Explanation A screw is a combination of simple machines: it is, in essence, an inclined plane wrapped around a central shaft, but the inclined plane (thread) also comes to a sharp edge around the outside, which acts as a wedge as it pushes into the fastened material, and th ...
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