An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy .
108-568: 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; thus heat engines have special importance. Some natural processes, such as atmospheric convection cells convert environmental heat into motion (e.g. in
216-717: A b d d t Φ ( r ( t ) ) d t = Φ ( r ( b ) ) − Φ ( r ( a ) ) = Φ ( x B ) − Φ ( x A ) . {\displaystyle {\begin{aligned}\int _{\gamma }\nabla \Phi (\mathbf {r} )\cdot d\mathbf {r} &=\int _{a}^{b}\nabla \Phi (\mathbf {r} (t))\cdot \mathbf {r} '(t)dt,\\&=\int _{a}^{b}{\frac {d}{dt}}\Phi (\mathbf {r} (t))dt=\Phi (\mathbf {r} (b))-\Phi (\mathbf {r} (a))=\Phi \left(\mathbf {x} _{B}\right)-\Phi \left(\mathbf {x} _{A}\right).\end{aligned}}} For
324-625: A bow or a catapult) that is deformed under tension or compression (or stressed in formal terminology). It arises as a consequence of a force that tries to restore the object to its original shape, which is most often the electromagnetic force between the atoms and molecules that constitute the object. If the stretch is released, the energy is transformed into kinetic energy . The gravitational potential function, also known as gravitational potential energy , is: U = − G M m r , {\displaystyle U=-{\frac {GMm}{r}},} The negative sign follows
432-451: A fuel cell without side production of NO x , but this is an electrochemical engine not a heat engine. The word engine derives from Old French engin , from the Latin ingenium –the root of the word ingenious . Pre-industrial weapons of war, such as catapults , trebuchets and battering rams , were called siege engines , and knowledge of how to construct them
540-412: A spring or the force of gravity . The action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential. This work is stored in the force field, which is said to be stored as potential energy. If the external force is removed the force field acts on the body to perform the work as it moves the body back to the initial position, reducing
648-462: A 2009 British television family drama starring Anna Bray, David Calder, Reece Douglas Ingenious Media , a division of London-based Ingenious Capital Management Limited, also known as Ingenious See also [ edit ] Ingenuity (disambiguation) Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Ingenious . If an internal link led you here, you may wish to change
756-661: A body by a force field is obtained from the gradient of the work, or potential, in the direction of the velocity v of the point of application, that is P ( t ) = − ∇ U ⋅ v = F ⋅ v . {\displaystyle P(t)=-{\nabla U}\cdot \mathbf {v} =\mathbf {F} \cdot \mathbf {v} .} Examples of work that can be computed from potential functions are gravity and spring forces. For small height changes, gravitational potential energy can be computed using U g = m g h , {\displaystyle U_{g}=mgh,} where m
864-402: A certain scalar function, called a scalar potential . The potential energy is related to, and can be obtained from, this potential function. There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of
972-482: A chemical reaction, but are not heat engines. Examples include: An electric motor uses electrical energy to produce mechanical energy , usually through the interaction of magnetic fields and current-carrying conductors . The reverse process, producing electrical energy from mechanical energy, is accomplished by a generator or dynamo . Traction motors used on vehicles often perform both tasks. Electric motors can be run as generators and vice versa, although this
1080-453: A cold cylinder, which are attached to reciprocating pistons 90° out of phase. The gas receives heat at the hot cylinder and expands, driving the piston that turns the crankshaft . After expanding and flowing through the recuperator, the gas rejects heat at the cold cylinder and the ensuing pressure drop leads to its compression by the other (displacement) piston, which forces it back to the hot cylinder. Non-thermal motors usually are powered by
1188-404: A distance r is given by Coulomb's Law F = 1 4 π ε 0 Q q r 2 r ^ , {\displaystyle \mathbf {F} ={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r^{2}}}\mathbf {\hat {r}} ,} where r ^ {\displaystyle \mathbf {\hat {r}} }
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#17327718495341296-546: A few limited-production battery-powered electric vehicles have appeared, they have not proved competitive owing to costs and operating characteristics. In the 21st century the diesel engine has been increasing in popularity with automobile owners. However, the gasoline engine and the Diesel engine, with their new emission-control devices to improve emission performance, have not yet been significantly challenged. A number of manufacturers have introduced hybrid engines, mainly involving
1404-412: A gas as in a Stirling engine , or steam as in a steam engine or an organic liquid such as n-pentane in an Organic Rankine cycle . The fluid can be of any composition; gas is by far the most common, although even single-phase liquid is sometimes used. In the case of the steam engine, the fluid changes phases between liquid and gas. Air-breathing combustion engines are combustion engines that use
1512-463: A heat difference to induce high-amplitude sound waves. In general, thermoacoustic engines can be divided into standing wave and travelling wave devices. Stirling engines can be another form of non-combustive heat engine. They use the Stirling thermodynamic cycle to convert heat into work. An example is the alpha type Stirling engine, whereby gas flows, via a recuperator , between a hot cylinder and
1620-425: A heat engine). Chemical heat engines which employ air (ambient atmospheric gas) as a part of the fuel reaction are regarded as airbreathing engines. Chemical heat engines designed to operate outside of Earth's atmosphere (e.g. rockets , deeply submerged submarines ) need to carry an additional fuel component called the oxidizer (although there exist super-oxidizers suitable for use in rockets, such as fluorine ,
1728-459: A large scale required efficient electrical generators and electrical distribution networks. To reduce the electric energy consumption from motors and their associated carbon footprints , various regulatory authorities in many countries have introduced and implemented legislation to encourage the manufacture and use of higher efficiency electric motors. A well-designed motor can convert over 90% of its input energy into useful power for decades. When
1836-489: A majority of the models. Several three-cylinder, two-stroke-cycle models were built while most engines had straight or in-line cylinders. There were several V-type models and horizontally opposed two- and four-cylinder makes too. Overhead camshafts were frequently employed. The smaller engines were commonly air-cooled and located at the rear of the vehicle; compression ratios were relatively low. The 1970s and 1980s saw an increased interest in improved fuel economy , which caused
1944-438: A more powerful oxidant than oxygen itself); or the application needs to obtain heat by non-chemical means, such as by means of nuclear reactions . All chemically fueled heat engines emit exhaust gases. The cleanest engines emit water only. Strict zero-emissions generally means zero emissions other than water and water vapour. Only heat engines which combust pure hydrogen (fuel) and pure oxygen (oxidizer) achieve zero-emission by
2052-560: A nuclear power plant uses the heat from the nuclear reaction to produce steam and drive a steam engine, or a gas turbine in a rocket engine may be driven by decomposing hydrogen peroxide . Apart from the different energy source, the engine is often engineered much the same as an internal or external combustion engine. Another group of noncombustive engines includes thermoacoustic heat engines (sometimes called "TA engines") which are thermoacoustic devices that use high-amplitude sound waves to pump heat from one place to another, or conversely use
2160-563: A pressure just above atmospheric to drive the piston helped by a partial vacuum. Improving on the design of the 1712 Newcomen steam engine , the Watt steam engine, developed sporadically from 1763 to 1775, was a great step in the development of the steam engine. Offering a dramatic increase in fuel efficiency , James Watt 's design became synonymous with steam engines, due in no small part to his business partner, Matthew Boulton . It enabled rapid development of efficient semi-automated factories on
2268-563: A previously unimaginable scale in places where waterpower was not available. Later development led to steam locomotives and great expansion of railway transportation . As for internal combustion piston engines , these were tested in France in 1807 by de Rivaz and independently, by the Niépce brothers . They were theoretically advanced by Carnot in 1824. In 1853–57 Eugenio Barsanti and Felice Matteucci invented and patented an engine using
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#17327718495342376-608: A railroad electric locomotive , rather than an electric motor. Some motors are powered by potential or kinetic energy, for example some funiculars , gravity plane and ropeway conveyors have used the energy from moving water or rocks, and some clocks have a weight that falls under gravity. Other forms of potential energy include compressed gases (such as pneumatic motors ), springs ( clockwork motors ) and elastic bands . Historic military siege engines included large catapults , trebuchets , and (to some extent) battering rams were powered by potential energy. A pneumatic motor
2484-569: A return to smaller V-6 and four-cylinder layouts, with as many as five valves per cylinder to improve efficiency. The Bugatti Veyron 16.4 operates with a W16 engine , meaning that two V8 cylinder layouts are positioned next to each other to create the W ;shape sharing the same crankshaft. The largest internal combustion engine ever built is the Wärtsilä-Sulzer RTA96-C , a 14-cylinder, 2-stroke turbocharged diesel engine that
2592-438: A scalar field, the work of those forces along a curve C is computed by evaluating the scalar field at the start point A and the end point B of the curve. This means the work integral does not depend on the path between A and B and is said to be independent of the path. Potential energy U = − U ′( x ) is traditionally defined as the negative of this scalar field so that work by the force field decreases potential energy, that
2700-723: A small gasoline engine coupled with an electric motor and with a large battery bank, these are starting to become a popular option because of their environment awareness. Exhaust gas from a spark ignition engine consists of the following: nitrogen 70 to 75% (by volume), water vapor 10 to 12%, carbon dioxide 10 to 13.5%, hydrogen 0.5 to 2%, oxygen 0.2 to 2%, carbon monoxide : 0.1 to 6%, unburnt hydrocarbons and partial oxidation products (e.g. aldehydes ) 0.5 to 1%, nitrogen monoxide 0.01 to 0.4%, nitrous oxide <100 ppm, sulfur dioxide 15 to 60 ppm, traces of other compounds such as fuel additives and lubricants, also halogen and metallic compounds, and other particles. Carbon monoxide
2808-449: A source of water power to provide additional power to watermills and water-raising machines. In the medieval Islamic world , such advances made it possible to mechanize many industrial tasks previously carried out by manual labour . In 1206, al-Jazari employed a crank - conrod system for two of his water-raising machines. A rudimentary steam turbine device was described by Taqi al-Din in 1551 and by Giovanni Branca in 1629. In
2916-567: A special form if the force F is related to a scalar field U ′( x ) so that F = ∇ U ′ = ( ∂ U ′ ∂ x , ∂ U ′ ∂ y , ∂ U ′ ∂ z ) . {\displaystyle \mathbf {F} ={\nabla U'}=\left({\frac {\partial U'}{\partial x}},{\frac {\partial U'}{\partial y}},{\frac {\partial U'}{\partial z}}\right).} This means that
3024-429: A strict definition (in practice, one type of rocket engine). If hydrogen is burnt in combination with air (all airbreathing engines), a side reaction occurs between atmospheric oxygen and atmospheric nitrogen resulting in small emissions of NO x . If a hydrocarbon (such as alcohol or gasoline) is burnt as fuel, CO 2 , a greenhouse gas , is emitted. Hydrogen and oxygen from air can be reacted into water by
3132-431: A torque include the familiar automobile gasoline and diesel engines, as well as turboshafts . Examples of engines which produce thrust include turbofans and rockets . When the internal combustion engine was invented, the term motor was initially used to distinguish it from the steam engine—which was in wide use at the time, powering locomotives and other vehicles such as steam rollers . The term motor derives from
3240-561: A water-powered mill was built in Kaberia of the kingdom of Mithridates during the 1st century BC. Use of water wheels in mills spread throughout the Roman Empire over the next few centuries. Some were quite complex, with aqueducts , dams , and sluices to maintain and channel the water, along with systems of gears , or toothed-wheels made of wood and metal to regulate the speed of rotation. More sophisticated small devices, such as
3348-757: Is W = U ( x A ) − U ( x B ) . {\displaystyle W=U(\mathbf {x} _{\text{A}})-U(\mathbf {x} _{\text{B}}).} In this case, the application of the del operator to the work function yields, ∇ W = − ∇ U = − ( ∂ U ∂ x , ∂ U ∂ y , ∂ U ∂ z ) = F , {\displaystyle {\nabla W}=-{\nabla U}=-\left({\frac {\partial U}{\partial x}},{\frac {\partial U}{\partial y}},{\frac {\partial U}{\partial z}}\right)=\mathbf {F} ,} and
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3456-873: Is a vector of length 1 pointing from M to m and G is the gravitational constant . Let the mass m move at the velocity v then the work of gravity on this mass as it moves from position r ( t 1 ) to r ( t 2 ) is given by W = − ∫ r ( t 1 ) r ( t 2 ) G M m r 3 r ⋅ d r = − ∫ t 1 t 2 G M m r 3 r ⋅ v d t . {\displaystyle W=-\int _{\mathbf {r} (t_{1})}^{\mathbf {r} (t_{2})}{\frac {GMm}{r^{3}}}\mathbf {r} \cdot d\mathbf {r} =-\int _{t_{1}}^{t_{2}}{\frac {GMm}{r^{3}}}\mathbf {r} \cdot \mathbf {v} \,dt.} The position and velocity of
3564-466: Is a function of the state a system is in, and is defined relative to that for a particular state. This reference state is not always a real state; it may also be a limit, such as with the distances between all bodies tending to infinity, provided that the energy involved in tending to that limit is finite, such as in the case of inverse-square law forces. Any arbitrary reference state could be used; therefore it can be chosen based on convenience. Typically
3672-416: Is a machine that converts potential energy in the form of compressed air into mechanical work . Pneumatic motors generally convert the compressed air to mechanical work through either linear or rotary motion. Linear motion can come from either a diaphragm or piston actuator, while rotary motion is supplied by either a vane type air motor or piston air motor. Pneumatic motors have found widespread success in
3780-456: Is a vector of length 1 pointing from Q to q and ε 0 is the vacuum permittivity . The work W required to move q from A to any point B in the electrostatic force field is given by the potential function U ( r ) = 1 4 π ε 0 Q q r . {\displaystyle U(r)={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r}}.} The potential energy
3888-763: Is calculated using its velocity, v = ( v x , v y , v z ) , to obtain W = ∫ 0 t F ⋅ v d t = − ∫ 0 t k x v x d t = − ∫ 0 t k x d x d t d t = ∫ x ( t 0 ) x ( t ) k x d x = 1 2 k x 2 {\displaystyle W=\int _{0}^{t}\mathbf {F} \cdot \mathbf {v} \,dt=-\int _{0}^{t}kxv_{x}\,dt=-\int _{0}^{t}kx{\frac {dx}{dt}}dt=\int _{x(t_{0})}^{x(t)}kx\,dx={\frac {1}{2}}kx^{2}} For convenience, consider contact with
3996-454: Is done by introducing a parameterized curve γ ( t ) = r ( t ) from γ ( a ) = A to γ ( b ) = B , and computing, ∫ γ ∇ Φ ( r ) ⋅ d r = ∫ a b ∇ Φ ( r ( t ) ) ⋅ r ′ ( t ) d t , = ∫
4104-439: Is equal to the work done against gravity in lifting it. The work done equals the force required to move it upward multiplied with the vertical distance it is moved (remember W = Fd ). The upward force required while moving at a constant velocity is equal to the weight, mg , of an object, so the work done in lifting it through a height h is the product mgh . Thus, when accounting only for mass , gravity , and altitude ,
4212-409: Is evidenced by water in an elevated reservoir or kept behind a dam. If an object falls from one point to another point inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy will decrease by the same amount. Consider a book placed on top of a table. As the book is raised from the floor to the table, some external force works against
4320-534: Is highly toxic, and can cause carbon monoxide poisoning , so it is important to avoid any build-up of the gas in a confined space. Catalytic converters can reduce toxic emissions, but not eliminate them. Also, resulting greenhouse gas emissions, chiefly carbon dioxide , from the widespread use of engines in the modern industrialized world is contributing to the global greenhouse effect – a primary concern regarding global warming . Some engines convert heat from noncombustive processes into mechanical work, for example
4428-462: Is measured. Choosing the convention that K = 0 (i.e. in relation to a point at infinity) makes calculations simpler, albeit at the cost of making U negative; for why this is physically reasonable, see below. Given this formula for U , the total potential energy of a system of n bodies is found by summing, for all n ( n − 1 ) 2 {\textstyle {\frac {n(n-1)}{2}}} pairs of two bodies,
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4536-587: Is negligible and we can assume that the force of gravity on a particular object is constant. Near the surface of the Earth, for example, we assume that the acceleration due to gravity is a constant g = 9.8 m/s ( standard gravity ). In this case, a simple expression for gravitational potential energy can be derived using the W = Fd equation for work , and the equation W F = − Δ U F . {\displaystyle W_{F}=-\Delta U_{F}.} The amount of gravitational potential energy held by an elevated object
4644-710: Is not always practical. Electric motors are ubiquitous, being found in applications as diverse as industrial fans, blowers and pumps, machine tools, household appliances, power tools , and disk drives . They may be powered by direct current (for example a battery powered portable device or motor vehicle), or by alternating current from a central electrical distribution grid. The smallest motors may be found in electric wristwatches. Medium-size motors of highly standardized dimensions and characteristics provide convenient mechanical power for industrial uses. The very largest electric motors are used for propulsion of large ships, and for such purposes as pipeline compressors, with ratings in
4752-496: Is possible with the real number system. Since physicists abhor infinities in their calculations, and r is always non-zero in practice, the choice of U = 0 {\displaystyle U=0} at infinity is by far the more preferable choice, even if the idea of negative energy in a gravity well appears to be peculiar at first. The negative value for gravitational energy also has deeper implications that make it seem more reasonable in cosmological calculations where
4860-427: Is reached with a coolant temperature of around 110 °C (230 °F). Earlier automobile engine development produced a much larger range of engines than is in common use today. Engines have ranged from 1- to 16-cylinder designs with corresponding differences in overall size, weight, engine displacement , and cylinder bores . Four cylinders and power ratings from 19 to 120 hp (14 to 90 kW) were followed in
4968-410: Is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position. From around 1840 scientists sought to define and understand energy and work . The term "potential energy" was coined by William Rankine a Scottish engineer and physicist in 1853 as part of a specific effort to develop terminology. He chose the term as part of
5076-407: Is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine , although it has links to the ancient Greek philosopher Aristotle 's concept of potentiality . Common types of potential energy include
5184-464: Is the mass in kilograms, g is the local gravitational field (9.8 metres per second squared on Earth), h is the height above a reference level in metres, and U is the energy in joules. In classical physics, gravity exerts a constant downward force F = (0, 0, F z ) on the center of mass of a body moving near the surface of the Earth. The work of gravity on a body moving along a trajectory r ( t ) = ( x ( t ), y ( t ), z ( t )) , such as
5292-487: Is the trajectory taken from A to B. Because the work done is independent of the path taken, then this expression is true for any trajectory, C , from A to B. The function U ( x ) is called the potential energy associated with the applied force. Examples of forces that have potential energies are gravity and spring forces. In this section the relationship between work and potential energy is presented in more detail. The line integral that defines work along curve C takes
5400-534: Is then cooled, compressed and reused (closed cycle), or (less commonly) dumped, and cool fluid pulled in (open cycle air engine). " Combustion " refers to burning fuel with an oxidizer , to supply the heat. Engines of similar (or even identical) configuration and operation may use a supply of heat from other sources such as nuclear, solar, geothermal or exothermic reactions not involving combustion; but are not then strictly classed as external combustion engines, but as external thermal engines. The working fluid can be
5508-707: The Antikythera Mechanism used complex trains of gears and dials to act as calendars or predict astronomical events. In a poem by Ausonius in the 4th century AD, he mentions a stone-cutting saw powered by water. Hero of Alexandria is credited with many such wind and steam powered machines in the 1st century AD, including the Aeolipile and the vending machine , often these machines were associated with worship, such as animated altars and automated temple doors. Medieval Muslim engineers employed gears in mills and water-raising machines, and used dams as
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#17327718495345616-604: The Coulomb force is called electric potential energy ; work of the strong nuclear force or weak nuclear force acting on the baryon charge is called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels , is the work of the Coulomb force during rearrangement of configurations of electrons and nuclei in atoms and molecules. Thermal energy usually has two components:
5724-662: The Volkswagen Beetle , the Citroën 2CV , some Porsche and Subaru cars, many BMW and Honda motorcycles . Opposed four- and six-cylinder engines continue to be used as a power source in small, propeller-driven aircraft . The continued use of internal combustion engines in automobiles is partly due to the improvement of engine control systems, such as on-board computers providing engine management processes, and electronically controlled fuel injection. Forced air induction by turbocharging and supercharging have increased
5832-407: The club and oar (examples of the lever ), are prehistoric . More complex engines using human power , animal power , water power , wind power and even steam power date back to antiquity. Human power was focused by the use of simple engines, such as the capstan , windlass or treadmill , and with ropes , pulleys , and block and tackle arrangements; this power was transmitted usually with
5940-733: The combustion of a fuel causes rapid pressurisation of the gaseous combustion products in the combustion chamber, causing them to expand and drive a piston , which turns a crankshaft . Unlike internal combustion engines, a reaction engine (such as a jet engine ) produces thrust by expelling reaction mass , in accordance with Newton's third law of motion . Apart from heat engines, electric motors convert electrical energy into mechanical motion, pneumatic motors use compressed air , and clockwork motors in wind-up toys use elastic energy . In biological systems, molecular motors , like myosins in muscles , use chemical energy to create forces and ultimately motion (a chemical engine, but not
6048-491: The gravitational potential energy of an object, the elastic potential energy of a deformed spring, and the electric potential energy of an electric charge in an electric field . The unit for energy in the International System of Units (SI) is the joule (symbol J). Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on
6156-399: The oxygen in atmospheric air to oxidise ('burn') the fuel, rather than carrying an oxidiser , as in a rocket . Theoretically, this should result in a better specific impulse than for rocket engines. A continuous stream of air flows through the air-breathing engine. This air is compressed, mixed with fuel, ignited and expelled as the exhaust gas . In reaction engines , the majority of
6264-424: The pistons or turbine blades or a nozzle , and by moving it over a distance, generates mechanical work . An external combustion engine (EC engine) is a heat engine where an internal working fluid is heated by combustion of an external source, through the engine wall or a heat exchanger . The fluid then, by expanding and acting on the mechanism of the engine produces motion and usable work . The fluid
6372-471: The 13th century, the solid rocket motor was invented in China. Driven by gunpowder, this simplest form of internal combustion engine was unable to deliver sustained power, but was useful for propelling weaponry at high speeds towards enemies in battle and for fireworks . After invention, this innovation spread throughout Europe. The Watt steam engine was the first type of steam engine to make use of steam at
6480-520: The Latin verb moto which means 'to set in motion', or 'maintain motion'. Thus a motor is a device that imparts motion. Motor and engine are interchangeable in standard English. In some engineering jargons, the two words have different meanings, in which engine is a device that burns or otherwise consumes fuel, changing its chemical composition, and a motor is a device driven by electricity , air , or hydraulic pressure, which does not change
6588-502: The Moon's gravity is weaker. "Height" in the common sense of the term cannot be used for gravitational potential energy calculations when gravity is not assumed to be a constant. The following sections provide more detail. The strength of a gravitational field varies with location. However, when the change of distance is small in relation to the distances from the center of the source of the gravitational field, this variation in field strength
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#17327718495346696-413: The approximation that g is constant is no longer valid, and we have to use calculus and the general mathematical definition of work to determine gravitational potential energy. For the computation of the potential energy, we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation , with respect to the distance r between the two bodies. Using that definition,
6804-433: The chemical composition of its energy source. However, rocketry uses the term rocket motor , even though they consume fuel. A heat engine may also serve as a prime mover —a component that transforms the flow or changes in pressure of a fluid into mechanical energy . An automobile powered by an internal combustion engine may make use of various motors and pumps, but ultimately all such devices derive their power from
6912-470: The choice of zero point is arbitrary. Given that there is no reasonable criterion for preferring one particular finite r over another, there seem to be only two reasonable choices for the distance at which U becomes zero: r = 0 {\displaystyle r=0} and r = ∞ {\displaystyle r=\infty } . The choice of U = 0 {\displaystyle U=0} at infinity may seem peculiar, and
7020-447: The combustion energy (heat) exits the engine as exhaust gas, which provides thrust directly. Typical air-breathing engines include: The operation of engines typically has a negative impact upon air quality and ambient sound levels . There has been a growing emphasis on the pollution producing features of automotive power systems. This has created new interest in alternate power sources and internal-combustion engine refinements. Though
7128-713: The consequence that gravitational energy is always negative may seem counterintuitive, but this choice allows gravitational potential energy values to be finite, albeit negative. The singularity at r = 0 {\displaystyle r=0} in the formula for gravitational potential energy means that the only other apparently reasonable alternative choice of convention, with U = 0 {\displaystyle U=0} for r = 0 {\displaystyle r=0} , would result in potential energy being positive, but infinitely large for all nonzero values of r , and would make calculations involving sums or differences of potential energies beyond what
7236-499: The convention that work is gained from a loss of potential energy. The gravitational force between two bodies of mass M and m separated by a distance r is given by Newton's law of universal gravitation F = − G M m r 2 r ^ , {\displaystyle \mathbf {F} =-{\frac {GMm}{r^{2}}}\mathbf {\hat {r}} ,} where r ^ {\displaystyle \mathbf {\hat {r}} }
7344-489: The efficiency of a motor is raised by even a few percentage points, the savings, in kilowatt hours (and therefore in cost), are enormous. The electrical energy efficiency of a typical industrial induction motor can be improved by: 1) reducing the electrical losses in the stator windings (e.g., by increasing the cross-sectional area of the conductor , improving the winding technique, and using materials with higher electrical conductivities , such as copper ), 2) reducing
7452-496: The electrical losses in the rotor coil or casting (e.g., by using materials with higher electrical conductivities, such as copper), 3) reducing magnetic losses by using better quality magnetic steel , 4) improving the aerodynamics of motors to reduce mechanical windage losses, 5) improving bearings to reduce friction losses , and 6) minimizing manufacturing tolerances . For further discussion on this subject, see Premium efficiency ). By convention, electric engine refers to
7560-402: The engine. Another way of looking at it is that a motor receives power from an external source, and then converts it into mechanical energy, while an engine creates power from pressure (derived directly from the explosive force of combustion or other chemical reaction, or secondarily from the action of some such force on other substances such as air, water, or steam). Simple machines , such as
7668-495: The equation is: U = m g h {\displaystyle U=mgh} where U is the potential energy of the object relative to its being on the Earth's surface, m is the mass of the object, g is the acceleration due to gravity, and h is the altitude of the object. Hence, the potential difference is Δ U = m g Δ h . {\displaystyle \Delta U=mg\Delta h.} However, over large variations in distance,
7776-416: The fact that d d t r − 1 = − r − 2 r ˙ = − r ˙ r 2 . {\displaystyle {\frac {d}{dt}}r^{-1}=-r^{-2}{\dot {r}}=-{\frac {\dot {r}}{r^{2}}}.} The electrostatic force exerted by a charge Q on another charge q separated by
7884-635: The first half of the 20th century, a trend of increasing engine power occurred, particularly in the U.S. models. Design changes incorporated all known methods of increasing engine capacity, including increasing the pressure in the cylinders to improve efficiency, increasing the size of the engine, and increasing the rate at which the engine produces work. The higher forces and pressures created by these changes created engine vibration and size problems that led to stiffer, more compact engines with V and opposed cylinder layouts replacing longer straight-line arrangements. Optimal combustion efficiency in passenger vehicles
7992-423: The force F is said to be "derivable from a potential". This also necessarily implies that F must be a conservative vector field . The potential U defines a force F at every point x in space, so the set of forces is called a force field . Given a force field F ( x ), evaluation of the work integral using the gradient theorem can be used to find the scalar function associated with potential energy. This
8100-411: The force can be defined as the negative of the vector gradient of the potential field. If the work for an applied force is independent of the path, then the work done by the force is evaluated from the start to the end of the trajectory of the point of application. This means that there is a function U ( x ), called a "potential", that can be evaluated at the two points x A and x B to obtain
8208-797: The force field F , let v = d r / dt , then the gradient theorem yields, ∫ γ F ⋅ d r = ∫ a b F ⋅ v d t , = − ∫ a b d d t U ( r ( t ) ) d t = U ( x A ) − U ( x B ) . {\displaystyle {\begin{aligned}\int _{\gamma }\mathbf {F} \cdot d\mathbf {r} &=\int _{a}^{b}\mathbf {F} \cdot \mathbf {v} \,dt,\\&=-\int _{a}^{b}{\frac {d}{dt}}U(\mathbf {r} (t))\,dt=U(\mathbf {x} _{A})-U(\mathbf {x} _{B}).\end{aligned}}} The power applied to
8316-417: The force. The negative sign provides the convention that work done against a force field increases potential energy, while work done by the force field decreases potential energy. Common notations for potential energy are PE , U , V , and E p . Potential energy is the energy by virtue of an object's position relative to other objects. Potential energy is often associated with restoring forces such as
8424-691: The forces multiplied and the speed reduced . These were used in cranes and aboard ships in Ancient Greece , as well as in mines , water pumps and siege engines in Ancient Rome . The writers of those times, including Vitruvius , Frontinus and Pliny the Elder , treat these engines as commonplace, so their invention may be more ancient. By the 1st century AD, cattle and horses were used in mills , driving machines similar to those powered by humans in earlier times. According to Strabo ,
8532-403: 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 heat from
8640-526: The free-piston principle that was possibly the first 4-cycle engine. The invention of an internal combustion engine which was later commercially successful was made during 1860 by Etienne Lenoir . In 1877, the Otto cycle was capable of giving a far higher power-to-weight ratio than steam engines and worked much better for many transportation applications such as cars and aircraft. The first commercially successful automobile, created by Karl Benz , added to
8748-524: The gravitational force. If the book falls back to the floor, the "falling" energy the book receives is provided by the gravitational force. Thus, if the book falls off the table, this potential energy goes to accelerate the mass of the book and is converted into kinetic energy . When the book hits the floor this kinetic energy is converted into heat, deformation, and sound by the impact. The factors that affect an object's gravitational potential energy are its height relative to some reference point, its mass, and
8856-474: The gravitational potential energy of a system of masses m 1 and M 2 at a distance r using the Newtonian constant of gravitation G is U = − G m 1 M 2 r + K , {\displaystyle U=-G{\frac {m_{1}M_{2}}{r}}+K,} where K is an arbitrary constant dependent on the choice of datum from which potential
8964-633: The hand-held tool industry and continual attempts are being made to expand their use to the transportation industry. However, pneumatic motors must overcome efficiency deficiencies before being seen as a viable option in the transportation industry. A hydraulic motor derives its power from a pressurized liquid . This type of engine is used to move heavy loads and drive machinery. Potential energy U = 1 ⁄ 2 ⋅ k ⋅ x ( elastic ) U = 1 ⁄ 2 ⋅ C ⋅ V ( electric ) U = − m ⋅ B ( magnetic ) In physics , potential energy
9072-411: The heat of a combustion process. The internal combustion engine is an engine in which the combustion of a fuel (generally, fossil fuel ) occurs with an oxidizer (usually air) in a combustion chamber . In an internal combustion engine the expansion of the high temperature and high pressure gases, which are produced by the combustion, directly applies force to components of the engine, such as
9180-399: The initial and final positions of the body in space. These forces, whose total work is path independent, are called conservative forces . If the force acting on a body varies over space, then one has a force field ; such a field is described by vectors at every point in space, which is in-turn called a vector field . A conservative vector field can be simply expressed as the gradient of
9288-400: The integral of the vertical component of velocity is the vertical distance. The work of gravity depends only on the vertical movement of the curve r ( t ) . A horizontal spring exerts a force F = (− kx , 0, 0) that is proportional to its deformation in the axial or x direction. The work of this spring on a body moving along the space curve s ( t ) = ( x ( t ), y ( t ), z ( t )) ,
9396-525: The interest in light and powerful engines. The lightweight gasoline internal combustion engine, operating on a four-stroke Otto cycle, has been the most successful for light automobiles, while the thermally more-efficient Diesel engine is used for trucks and buses. However, in recent years, turbocharged Diesel engines have become increasingly popular in automobiles, especially outside of the United States, even for quite small cars. In 1896, Karl Benz
9504-431: The kinetic energy of random motions of particles and the potential energy of their configuration. Forces derivable from a potential are also called conservative forces . The work done by a conservative force is W = − Δ U {\displaystyle W=-\Delta U} where Δ U {\displaystyle \Delta U} is the change in the potential energy associated with
9612-401: The mass m are given by r = r e r , v = r ˙ e r + r θ ˙ e t , {\displaystyle \mathbf {r} =r\mathbf {e} _{r},\qquad \mathbf {v} ={\dot {r}}\mathbf {e} _{r}+r{\dot {\theta }}\mathbf {e} _{t},} where e r and e t are
9720-453: The pair "actual" vs "potential" going back to work by Aristotle . In his 1867 discussion of the same topic Rankine describes potential energy as ‘energy of configuration’ in contrast to actual energy as 'energy of activity'. Also in 1867, William Thomson introduced "kinetic energy" as the opposite of "potential energy", asserting that all actual energy took the form of 1 / 2 mv . Once this hypothesis became widely accepted,
9828-412: The potential energy of a system depends on the relative positions of its components only, so the reference state can also be expressed in terms of relative positions. Gravitational energy is the potential energy associated with gravitational force , as work is required to elevate objects against Earth's gravity. The potential energy due to elevated positions is called gravitational potential energy, and
9936-467: The potential energy of the system of those two bodies. Considering the system of bodies as the combined set of small particles the bodies consist of, and applying the previous on the particle level we get the negative gravitational binding energy . This potential energy is more strongly negative than the total potential energy of the system of bodies as such since it also includes the negative gravitational binding energy of each body. The potential energy of
10044-647: The power output of smaller displacement engines that are lighter in weight and more fuel-efficient at normal cruise power.. Similar changes have been applied to smaller Diesel engines, giving them almost the same performance characteristics as gasoline engines. This is especially evident with the popularity of smaller diesel engine-propelled cars in Europe. Diesel engines produce lower hydrocarbon and CO 2 emissions, but greater particulate and NO x pollution, than gasoline engines. Diesel engines are also 40% more fuel efficient than comparable gasoline engines. In
10152-1090: The radial and tangential unit vectors directed relative to the vector from M to m . Use this to simplify the formula for work of gravity to, W = − ∫ t 1 t 2 G m M r 3 ( r e r ) ⋅ ( r ˙ e r + r θ ˙ e t ) d t = − ∫ t 1 t 2 G m M r 3 r r ˙ d t = G M m r ( t 2 ) − G M m r ( t 1 ) . {\displaystyle W=-\int _{t_{1}}^{t_{2}}{\frac {GmM}{r^{3}}}(r\mathbf {e} _{r})\cdot ({\dot {r}}\mathbf {e} _{r}+r{\dot {\theta }}\mathbf {e} _{t})\,dt=-\int _{t_{1}}^{t_{2}}{\frac {GmM}{r^{3}}}r{\dot {r}}dt={\frac {GMm}{r(t_{2})}}-{\frac {GMm}{r(t_{1})}}.} This calculation uses
10260-418: The spring occurs at t = 0 , then the integral of the product of the distance x and the x -velocity, xv x , is x /2. The function U ( x ) = 1 2 k x 2 , {\displaystyle U(x)={\frac {1}{2}}kx^{2},} is called the potential energy of a linear spring. Elastic potential energy is the potential energy of an elastic object (for example
10368-404: The strength of the gravitational field it is in. Thus, a book lying on a table has less gravitational potential energy than the same book on top of a taller cupboard and less gravitational potential energy than a heavier book lying on the same table. An object at a certain height above the Moon's surface has less gravitational potential energy than at the same height above the Earth's surface because
10476-471: The stretch of the spring or causing a body to fall. Consider a ball whose mass is m dropped from height h . The acceleration g of free fall is approximately constant, so the weight force of the ball mg is constant. The product of force and displacement gives the work done, which is equal to the gravitational potential energy, thus U g = m g h . {\displaystyle U_{g}=mgh.} The more formal definition
10584-755: The system of bodies as such is the negative of the energy needed to separate the bodies from each other to infinity, while the gravitational binding energy is the energy needed to separate all particles from each other to infinity. U = − m ( G M 1 r 1 + G M 2 r 2 ) {\displaystyle U=-m\left(G{\frac {M_{1}}{r_{1}}}+G{\frac {M_{2}}{r_{2}}}\right)} therefore, U = − m ∑ G M r , {\displaystyle U=-m\sum G{\frac {M}{r}},} As with all potential energies, only differences in gravitational potential energy matter for most physical purposes, and
10692-408: The term "actual energy" gradually faded. Potential energy is closely linked with forces . If the work done by a force on a body that moves from A to B does not depend on the path between these points (if the work is done by a conservative force), then the work of this force measured from A assigns a scalar value to every other point in space and defines a scalar potential field. In this case,
10800-442: The thousands of kilowatts . Electric motors may be classified by the source of electric power, by their internal construction, and by their application. The physical principle of production of mechanical force by the interactions of an electric current and a magnetic field was known as early as 1821. Electric motors of increasing efficiency were constructed throughout the 19th century, but commercial exploitation of electric motors on
10908-649: The total energy of the universe can meaningfully be considered; see inflation theory for more on this. ingenious#Latin From Misplaced Pages, the 💕 [REDACTED] Look up ingenious in Wiktionary, the free dictionary. Ingenious may refer to: Ingenious (board game) (2004) by Reiner Knizia Ingenious (2009 American film) , a 2009 drama comedy romance film, originally titled Lightbulb , starring Dallas Roberts, Jeremy Renner, Ayelet Zurer Ingenious (2009 British film) ,
11016-552: The track of a roller coaster is calculated using its velocity, v = ( v x , v y , v z ) , to obtain W = ∫ t 1 t 2 F ⋅ v d t = ∫ t 1 t 2 F z v z d t = F z Δ z . {\displaystyle W=\int _{t_{1}}^{t_{2}}{\boldsymbol {F}}\cdot {\boldsymbol {v}}\,dt=\int _{t_{1}}^{t_{2}}F_{z}v_{z}\,dt=F_{z}\Delta z.} where
11124-698: The units of U ′ must be this case, work along the curve is given by W = ∫ C F ⋅ d x = ∫ C ∇ U ′ ⋅ d x , {\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {x} =\int _{C}\nabla U'\cdot d\mathbf {x} ,} which can be evaluated using the gradient theorem to obtain W = U ′ ( x B ) − U ′ ( x A ) . {\displaystyle W=U'(\mathbf {x} _{\text{B}})-U'(\mathbf {x} _{\text{A}}).} This shows that when forces are derivable from
11232-488: The work over any trajectory between these two points. It is tradition to define this function with a negative sign so that positive work is a reduction in the potential, that is W = ∫ C F ⋅ d x = U ( x A ) − U ( x B ) {\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {x} =U(\mathbf {x} _{\text{A}})-U(\mathbf {x} _{\text{B}})} where C
11340-523: Was designed to power the Emma Mærsk , the largest container ship in the world when launched in 2006. This engine has a mass of 2,300 tonnes, and when running at 102 rpm (1.7 Hz) produces over 80 MW, and can use up to 250 tonnes of fuel per day. An engine can be put into a category according to two criteria: the form of energy it accepts in order to create motion, and the type of motion it outputs. Combustion engines are heat engines driven by
11448-436: Was granted a patent for his design of the first engine with horizontally opposed pistons. His design created an engine in which the corresponding pistons move in horizontal cylinders and reach top dead center simultaneously, thus automatically balancing each other with respect to their individual momentum. Engines of this design are often referred to as “flat” or “boxer” engines due to their shape and low profile. They were used in
11556-461: Was merely a water pump, with the engine being transported to the fire by horses. In modern usage, the term engine typically describes devices, like steam engines and internal combustion engines, that burn or otherwise consume fuel to perform mechanical work by exerting a torque or linear force (usually in the form of thrust ). Devices converting heat energy into motion are commonly referred to simply as engines . Examples of engines which exert
11664-473: Was often treated as a military secret. The word gin , as in cotton gin , is short for engine . Most mechanical devices invented during the Industrial Revolution were described as engines—the steam engine being a notable example. However, the original steam engines, such as those by Thomas Savery , were not mechanical engines but pumps. In this manner, a fire engine in its original form
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