116-547: An explosive (or explosive material ) is a reactive substance that contains a great amount of potential energy that can produce an explosion if released suddenly, usually accompanied by the production of light , heat , sound , and pressure . An explosive charge is a measured quantity of explosive material, which may either be composed solely of one ingredient or be a mixture containing at least two substances. The potential energy stored in an explosive material may, for example, be: Explosive materials may be categorized by
232-717: 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
348-625: 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
464-471: A bulk density of about 840 kg/m . In surface mining applications, it is typically loaded into boreholes by dedicated trucks that mix the AN and FO components immediately before the product is dispensed. In underground mining applications, ANFO is typically blow-loaded. AN is highly hygroscopic , readily absorbing water from air. In humid environments, absorbed water interferes with its explosive function. AN
580-467: A fertilizer in the agricultural industry . It is also found in instant cold packs . In many countries, its purchase and use are restricted to buyers who have obtained the proper license. Unmixed ammonium nitrate can decompose explosively, and has been responsible for several industrial disasters, including the following: Environmental hazards include eutrophication in confined waters and nitrate/gas oil contamination of ground or surface water. ANFO
696-412: 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
812-661: 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
928-402: 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
1044-420: A chemically pure compound, such as nitroglycerin , or a mixture of a fuel and an oxidizer , such as black powder or grain dust and air. Some chemical compounds are unstable in that, when shocked, they react, possibly to the point of detonation. Each molecule of the compound dissociates into two or more new molecules (generally gases) with the release of energy. The above compositions may describe most of
1160-634: A degree of water resistance. Explosives based on ammonium nitrate have little or no water resistance as ammonium nitrate is highly soluble in water and is hygroscopic. Many explosives are toxic to some extent. Manufacturing inputs can also be organic compounds or hazardous materials that require special handling due to risks (such as carcinogens ). The decomposition products, residual solids, or gases of some explosives can be toxic, whereas others are harmless, such as carbon dioxide and water. Examples of harmful by-products are: "Green explosives" seek to reduce environment and health impacts. An example of such
1276-404: 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}} }
SECTION 10
#17327831594641392-508: A hideaway in the Athens suburb of Kareas. The material was believed to be linked to attacks previously carried out by the "Revolutionary Struggle" terrorist group. In January 2010, President Hamid Karzai of Afghanistan also issued a decree banning the use, production, storage, purchase, or sale of ammonium nitrate, after an investigation showed militants in the Taliban insurgency had used
1508-433: A number of more exotic explosive materials, and exotic methods of causing explosions. Examples include nuclear explosives , and abruptly heating a substance to a plasma state with a high-intensity laser or electric arc . Laser- and arc-heating are used in laser detonators, exploding-bridgewire detonators , and exploding foil initiators , where a shock wave and then detonation in conventional chemical explosive material
1624-570: A physical shock signal. In other situations, different signals such as electrical or physical shock, or, in the case of laser detonation systems, light, are used to initiate an action, i.e., an explosion. A small quantity, usually milligrams, is sufficient to initiate a larger charge of explosive that is usually safer to handle. Potential energy U = 1 ⁄ 2 ⋅ k ⋅ x ( elastic ) U = 1 ⁄ 2 ⋅ C ⋅ V ( electric ) U = − m ⋅ B ( magnetic ) In physics , potential energy
1740-683: A practical measure, primary explosives are sufficiently sensitive that they can be reliably initiated with a blow from a hammer; however, PETN can also usually be initiated in this manner, so this is only a very broad guideline. Additionally, several compounds, such as nitrogen triiodide , are so sensitive that they cannot even be handled without detonating. Nitrogen triiodide is so sensitive that it can be reliably detonated by exposure to alpha radiation . Primary explosives are often used in detonators or to trigger larger charges of less sensitive secondary explosives . Primary explosives are commonly used in blasting caps and percussion caps to translate
1856-399: A reaction to be classified as a detonation as opposed to just a deflagration, the propagation of the reaction shockwave through the material being tested must be faster than the speed of sound through that material. The speed of sound through a liquid or solid material is usually orders of magnitude faster than the speed of sound through air or other gases. Traditional explosives mechanics
1972-438: 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
2088-752: A short time, several ANFO bombs exploded near four apartment buildings. In November 2009, the government of the North West Frontier Province (NWFP) of Pakistan imposed a ban on ammonium sulfate , ammonium nitrate, and calcium ammonium nitrate fertilizers in the Upper Dir , Lower Dir , Swat , Chitral and Malakand districts (the former Malakand Division ) following reports that those chemicals were used by militants to make explosives. In April 2010, police in Greece confiscated 180 kg of ANFO and other related material stashed in
2204-735: A smaller number are manufactured specifically for the purpose of being used as explosives. The remainder are too dangerous, sensitive, toxic, expensive, unstable, or prone to decomposition or degradation over short time spans. In contrast, some materials are merely combustible or flammable if they burn without exploding. The distinction, however, is not very clear. Certain materials—dusts, powders, gases, or volatile organic liquids—may be simply combustible or flammable under ordinary conditions, but become explosive in specific situations or forms, such as dispersed airborne clouds , or confinement or sudden release . Early thermal weapons , such as Greek fire , have existed since ancient times. At its roots,
2320-567: 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
2436-618: A thermodynamically favorable process in addition to one that propagates very rapidly. Thus, explosives are substances that contain a large amount of energy stored in chemical bonds . The energetic stability of the gaseous products and hence their generation comes from the formation of strongly bonded species like carbon monoxide, carbon dioxide, and nitrogen gas, which contain strong double and triple bonds having bond strengths of nearly 1 MJ/mole. Consequently, most commercial explosives are organic compounds containing –NO 2 , –ONO 2 and –NHNO 2 groups that, when detonated, release gases like
SECTION 20
#17327831594642552-757: 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
2668-873: 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
2784-707: Is mining . Whether the mine is on the surface or is buried underground, the detonation or deflagration of either a high or low explosive in a confined space can be used to liberate a fairly specific sub-volume of a brittle material (rock) in a much larger volume of the same or similar material. The mining industry tends to use nitrate-based explosives such as emulsions of fuel oil and ammonium nitrate solutions, mixtures of ammonium nitrate prills (fertilizer pellets) and fuel oil ( ANFO ) and gelatinous suspensions or slurries of ammonium nitrate and combustible fuels. In materials science and engineering, explosives are used in cladding ( explosion welding ). A thin plate of some material
2900-466: 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
3016-427: Is a pure substance ( molecule ) that in a chemical reaction can contribute some atoms of one or more oxidizing elements, in which the fuel component of the explosive burns. On the simplest level, the oxidizer may itself be an oxidizing element , such as gaseous or liquid oxygen . The availability and cost of explosives are determined by the availability of the raw materials and the cost, complexity, and safety of
3132-456: 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
3248-402: Is an important consideration in selecting an explosive for a particular purpose. The explosive in an armor-piercing projectile must be relatively insensitive, or the shock of impact would cause it to detonate before it penetrated to the point desired. The explosive lenses around nuclear charges are also designed to be highly insensitive, to minimize the risk of accidental detonation. The index of
3364-438: Is an important element influencing the yield of the energy transmitted for both atmospheric over-pressure and ground acceleration. By definition, a "low explosive", such as black powder, or smokeless gunpowder has a burn rate of 171–631 m/s. In contrast, a "high explosive", whether a primary, such as detonating cord , or a secondary, such as TNT or C-4, has a significantly higher burn rate about 6900–8092 m/s. Stability
3480-520: Is based on the shock-sensitive rapid oxidation of carbon and hydrogen to carbon dioxide, carbon monoxide and water in the form of steam. Nitrates typically provide the required oxygen to burn the carbon and hydrogen fuel. High explosives tend to have the oxygen, carbon and hydrogen contained in one organic molecule, and less sensitive explosives like ANFO are combinations of fuel (carbon and hydrogen fuel oil) and ammonium nitrate . A sensitizer such as powdered aluminum may be added to an explosive to increase
3596-763: 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
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3712-443: Is created by laser- or electric-arc heating. Laser and electric energy are not currently used in practice to generate most of the required energy, but only to initiate reactions. To determine the suitability of an explosive substance for a particular use, its physical properties must first be known. The usefulness of an explosive can only be appreciated when the properties and the factors affecting them are fully understood. Some of
3828-467: Is described as a non-ideal high explosive , as its explosive velocity is far from the thermodynamic ideal due to its porosity and the phase separation of its two components. In the mining industry, the term ANFO specifically describes a mixture of solid ammonium nitrate prills and diesel fuel. Other explosives based on the ANFO chemistry exist; the most commonly used are emulsions . They differ from ANFO in
3944-454: 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 , = ∫
4060-439: 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 ,
4176-452: Is evaluated by a tailored series of tests to assess the material for its intended use. Of the tests listed below, cylinder expansion and air-blast tests are common to most testing programs, and the others support specific applications. In addition to strength, explosives display a second characteristic, which is their shattering effect or brisance (from the French meaning to "break"). Brisance
4292-409: 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
4408-436: Is fully water-soluble; as such, it cannot be loaded into boreholes that contain standing water. When used in wet mining conditions, considerable effort must be taken to remove standing water and install a liner in the borehole; it is generally more productive to instead use a water-resistant explosive such as emulsion. In most jurisdictions, ammonium nitrate doesn't need to be classified as an explosive for transport purposes; it
4524-484: Is highly insensitive, making it a tertiary explosive (or a "blasting agent"). Without a sensitizer, it cannot be detonated by a typical (such as No. 8) blasting cap with the small amount of primary explosives within. A larger quantity of secondary explosive, known as a primer or a booster , must be used. One or two sticks of dynamite were historically used; current practice is to use Tovex or cast boosters of pentolite (TNT/ PETN or similar compositions). ANFO
4640-472: Is important in determining the effectiveness of an explosion in fragmenting shells, bomb casings, and grenades . The rapidity with which an explosive reaches its peak pressure ( power ) is a measure of its brisance. Brisance values are primarily employed in France and Russia. The sand crush test is commonly employed to determine the relative brisance in comparison to TNT. No test is capable of directly comparing
4756-462: 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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4872-410: Is merely an oxidizer . Mines typically prepare ANFO on-site using the same diesel fuel that powers their vehicles. While many fuels can theoretically be used, the low volatility and cost of diesel make it ideal. ANFO under most conditions is detonator –insensitive, so it is legally classified as a blasting agent (tertiary explosive) and not a high explosive . Ammonium nitrate is widely used as
4988-639: 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
5104-400: Is placed atop a thick layer of a different material, both layers typically of metal. Atop the thin layer is placed an explosive. At one end of the layer of explosive, the explosion is initiated. The two metallic layers are forced together at high speed and with great force. The explosion spreads from the initiation site throughout the explosive. Ideally, this produces a metallurgical bond between
5220-496: 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
5336-413: Is technically a high explosive in that it decomposes through detonation rather than deflagration at a velocity higher than the speed of sound in the material, but the low sensitivity means that it is not generally regulated as such. ANFO has a moderate velocity compared to other industrial explosives, measuring 3,200 m/s in 130 mm (5 in) diameter, unconfined, at ambient temperature. It
5452-410: 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
5568-407: 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
5684-473: Is the ability of an explosive to be stored without deterioration . The following factors affect the stability of an explosive: The term power or performance as applied to an explosive refers to its ability to do work. In practice it is defined as the explosive's ability to accomplish what is intended in the way of energy delivery (i.e., fragment projection, air blast, high-velocity jet, underwater shock and bubble energy, etc.). Explosive power or performance
5800-410: Is the lead-free primary explosive copper(I) 5-nitrotetrazolate, an alternative to lead azide . Explosive material may be incorporated in the explosive train of a device or system. An example is a pyrotechnic lead igniting a booster, which causes the main charge to detonate. The most widely used explosives are condensed liquids or solids converted to gaseous products by explosive chemical reactions and
5916-464: 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
SECTION 50
#17327831594646032-487: 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
6148-406: Is used to describe an explosive phenomenon whereby the decomposition is propagated by a shock wave traversing the explosive material at speeds greater than the speed of sound within the substance. The shock front is capable of passing through the high explosive material at supersonic speeds — typically thousands of metres per second. In addition to chemical explosives, there are
6264-604: 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:
6380-646: The Revolutionary Armed Forces of Colombia and ETA . In 1992, Shining Path perpetrated the Tarata bombing in Lima, Peru , using two ANFO truck bombs. A more sophisticated variant of ANFO (ammonium nitrate with nitromethane as the fuel, called ANNM) was used in the 1995 Oklahoma City bombing . The Shijiazhuang bombings rocked the city of Shijiazhuang, China, on 16 March 2001. A total of 108 people were killed, and 38 others injured when, within
6496-491: 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
6612-470: The 1950s. It has found wide use in coal mining , quarrying , metal ore mining , and civil construction in applications where its low cost and ease of use may outweigh the benefits of other explosives, such as water resistance, oxygen balance, higher detonation velocity , or performance in small-diameter columns. The mining industry accounts for an estimated 90% of the more than 2.5 thousand tonnes (5.5 million pounds) of explosives used annually in
6728-502: 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
6844-865: The Tax Office building in Bastia on 28 February 1987. The ANFO car bomb was adopted by the Provisional IRA in 1972 and, by 1973, the Troubles were consuming 21,000 kilograms (47,000 pounds) of ammonium nitrate for the majority of bombs. The Ulster Volunteer Force (UVF) also made use of ANFO bombs, often mixing in gelignite as a booster, in the Dublin and Monaghan bombings of May 1974 which killed 34 people & injured almost 300, ANFO car bombs were used in Dublin. It has also seen use by groups such as
6960-615: The United States. ANFO is also widely used in avalanche hazard mitigation . The chemistry of ANFO detonation is the reaction of ammonium nitrate with a long-chain alkane (C n H 2n+2 ) to form nitrogen , carbon dioxide , and water . In an ideal stoichiometrically balanced reaction, ANFO is composed of about 94.5% AN and 5.5% FO by weight. In practice, a slight excess of fuel oil is added, as underdosing results in reduced performance while overdosing merely results in more post-blast fumes. When detonation conditions are optimal,
7076-412: The aforementioned (e.g., nitroglycerin , TNT , HMX , PETN , nitrocellulose ). An explosive is classified as a low or high explosive according to its rate of combustion : low explosives burn rapidly (or deflagrate ), while high explosives detonate . While these definitions are distinct, the problem of precisely measuring rapid decomposition makes practical classification of explosives difficult. For
SECTION 60
#17327831594647192-447: The aforementioned gases are the only products. In practical use, such conditions are impossible to attain, and blasts produce moderate amounts of toxic gases such as carbon monoxide and nitrogen oxides ( NO x ). The fuel component of ANFO is typically diesel, but kerosene , coal dust, racing fuel, or even molasses have been used instead. Finely powdered aluminium in the mixture will sensitise it to detonate more readily. ANFO
7308-413: 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,
7424-479: The capacity of an explosive to be initiated into detonation in a sustained manner. It is defined by the power of the detonator which is certain to prime the explosive to a sustained and continuous detonation. Reference is made to the Sellier-Bellot scale that consists of a series of 10 detonators, from n. 1 to n. 10 , each of which corresponds to an increasing charge weight. In practice, most of
7540-425: The choice being determined by the characteristics of the explosive. Dependent upon the method employed, an average density of the loaded charge can be obtained that is within 80–99% of the theoretical maximum density of the explosive. High load density can reduce sensitivity by making the mass more resistant to internal friction . However, if density is increased to the extent that individual crystals are crushed,
7656-470: 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
7772-713: 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
7888-499: 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}} }
8004-421: The development of pressure within rounds of ammunition and separation of mixtures into their constituents. Volatility affects the chemical composition of the explosive such that a marked reduction in stability may occur, which results in an increase in the danger of handling. The introduction of water into an explosive is highly undesirable since it reduces the sensitivity, strength, and velocity of detonation of
8120-498: The energy of the detonation. Once detonated, the nitrogen portion of the explosive formulation emerges as nitrogen gas and toxic nitric oxides . The chemical decomposition of an explosive may take years, days, hours, or a fraction of a second. The slower processes of decomposition take place in storage and are of interest only from a stability standpoint. Of more interest are the other two rapid forms besides decomposition: deflagration and detonation. In deflagration, decomposition of
8236-601: The energy released by those reactions. The gaseous products of complete reaction are typically carbon dioxide , steam , and nitrogen . Gaseous volumes computed by the ideal gas law tend to be too large at high pressures characteristic of explosions. Ultimate volume expansion may be estimated at three orders of magnitude, or one liter per gram of explosive. Explosives with an oxygen deficit will generate soot or gases like carbon monoxide and hydrogen , which may react with surrounding materials such as atmospheric oxygen . Attempts to obtain more precise volume estimates must consider
8352-495: 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,
8468-444: The explosive material is propagated by a flame front which moves relatively slowly through the explosive material, i.e. at speeds less than the speed of sound within the substance (which is usually still higher than 340 m/s or 1,220 km/h in most liquid or solid materials) in contrast to detonation, which occurs at speeds greater than the speed of sound. Deflagration is a characteristic of low explosive material. This term
8584-651: The explosive material, but a practical explosive will often include small percentages of other substances. For example, dynamite is a mixture of highly sensitive nitroglycerin with sawdust , powdered silica , or most commonly diatomaceous earth , which act as stabilizers. Plastics and polymers may be added to bind powders of explosive compounds; waxes may be incorporated to make them safer to handle; aluminium powder may be introduced to increase total energy and blast effects. Explosive compounds are also often "alloyed": HMX or RDX powders may be mixed (typically by melt-casting) with TNT to form Octol or Cyclotol . An oxidizer
8700-441: The explosive may become more sensitive. Increased load density also permits the use of more explosive, thereby increasing the power of the warhead . It is possible to compress an explosive beyond a point of sensitivity, known also as dead-pressing , in which the material is no longer capable of being reliably initiated, if at all. Volatility is the readiness with which a substance vaporizes . Excessive volatility often results in
8816-414: The explosive properties of two or more compounds; it is important to examine the data from several such tests (sand crush, trauzl , and so forth) in order to gauge relative brisance. True values for comparison require field experiments. Density of loading refers to the mass of an explosive per unit volume. Several methods of loading are available, including pellet loading, cast loading, and press loading,
8932-409: The explosive. Hygroscopicity is a measure of a material's moisture-absorbing tendencies. Moisture affects explosives adversely by acting as an inert material that absorbs heat when vaporized, and by acting as a solvent medium that can cause undesired chemical reactions. Sensitivity, strength, and velocity of detonation are reduced by inert materials that reduce the continuity of the explosive mass. When
9048-429: The explosives on the market today are sensitive to an n. 8 detonator, where the charge corresponds to 2 grams of mercury fulminate . The velocity with which the reaction process propagates in the mass of the explosive. Most commercial mining explosives have detonation velocities ranging from 1,800 m/s to 8,000 m/s. Today, velocity of detonation can be measured with accuracy. Together with density it
9164-416: 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
9280-409: The first time in warfare. The Chinese would incorporate explosives fired from bamboo or bronze tubes known as bamboo firecrackers. The Chinese also inserted live rats inside the bamboo firecrackers; when fired toward the enemy, the flaming rats created great psychological ramifications—scaring enemy soldiers away and causing cavalry units to go wild. The first useful explosive stronger than black powder
9396-423: 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
9512-411: 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
9628-797: 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
9744-417: 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
9860-524: 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
9976-474: 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
10092-529: The history of chemical explosives lies in the history of gunpowder . During the Tang dynasty in the 9th century, Taoist Chinese alchemists were eagerly trying to find the elixir of immortality. In the process, they stumbled upon the explosive invention of black powder made from coal, saltpeter, and sulfur in 1044. Gunpowder was the first form of chemical explosives and by 1161, the Chinese were using explosives for
10208-399: 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
10324-400: 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 )) ,
10440-431: 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
10556-450: The manufacturing operations. A primary explosive is an explosive that is extremely sensitive to stimuli such as impact , friction , heat , static electricity , or electromagnetic radiation . Some primary explosives are also known as contact explosives . A relatively small amount of energy is required for initiation . As a very general rule, primary explosives are considered to be those compounds that are more sensitive than PETN . As
10672-401: 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
10788-436: The moisture content evaporates during detonation, cooling occurs, which reduces the temperature of reaction. Stability is also affected by the presence of moisture since moisture promotes decomposition of the explosive and, in addition, causes corrosion of the explosive's metal container. Explosives considerably differ from one another as to their behavior in the presence of water. Gelatin dynamites containing nitroglycerine have
10904-442: The molecule is said to have a zero oxygen balance. The molecule is said to have a positive oxygen balance if it contains more oxygen than is needed and a negative oxygen balance if it contains less oxygen than is needed. The sensitivity, strength , and brisance of an explosive are all somewhat dependent upon oxygen balance and tend to approach their maxima as oxygen balance approaches zero. A chemical explosive may consist of either
11020-457: The more important characteristics are listed below: Sensitivity refers to the ease with which an explosive can be ignited or detonated, i.e., the amount and intensity of shock , friction , or heat that is required. When the term sensitivity is used, care must be taken to clarify what kind of sensitivity is under discussion. The relative sensitivity of a given explosive to impact may vary greatly from its sensitivity to friction or heat. Some of
11136-453: 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,
11252-723: The physical form the reactants take. The most notable properties of emulsions are water resistance and higher bulk density. While the density of pure crystalline ammonium nitrate is 1700 kg/m , individual prills of explosive-grade AN measure approximately 1300 kg/m . Their lower density is due to the presence of a small spherical air pocket within each prill: this is the primary difference between AN sold for blasting and that sold for agricultural use. These voids are necessary to sensitize ANFO: they create so-called "hot spots". Finely powdered aluminium can be added to ANFO to increase both sensitivity and energy; in commercial usages however, this has fallen out of favor due to cost. ANFO has
11368-409: The possibility of such side reactions, condensation of steam, and aqueous solubility of gases like carbon dioxide. Oxygen balance is an expression that is used to indicate the degree to which an explosive can be oxidized. If an explosive molecule contains just enough oxygen to convert all of its carbon to carbon dioxide, all of its hydrogen to water, and all of its metal to metal oxide with no excess,
11484-412: 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
11600-467: 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
11716-1090: 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
11832-558: The speed at which they expand. Materials that detonate (the front of the chemical reaction moves faster through the material than the speed of sound ) are said to be "high explosives" and materials that deflagrate are said to be "low explosives". Explosives may also be categorized by their sensitivity . Sensitive materials that can be initiated by a relatively small amount of heat or pressure are primary explosives and materials that are relatively insensitive are secondary or tertiary explosives . A wide variety of chemicals can explode;
11948-418: 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
12064-404: 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
12180-471: 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
12296-490: The sum of the masses of the two initial layers. There are applications where a shock wave, and electrostatics, can result in high velocity projectiles such as in an electrostatic particle accelerator . An explosion is a type of spontaneous chemical reaction that, once initiated, is driven by both a large exothermic change (great release of heat) and a large positive entropy change (great quantities of gases are released) in going from reactants to products, thereby constituting
12412-755: 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
12528-408: 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,
12644-499: The test methods used to determine sensitivity relate to: Specific explosives (usually but not always highly sensitive on one or more of the three above axes) may be idiosyncratically sensitive to such factors as pressure drop, acceleration, the presence of sharp edges or rough surfaces, incompatible materials, or even — in rare cases — nuclear or electromagnetic radiation. These factors present special hazards that may rule out any practical utility. Sensitivity
12760-472: The total energy of the universe can meaningfully be considered; see inflation theory for more on this. ANFO ANFO ( / ˈ æ n f oʊ / AN -foh ) (or AN/FO , for ammonium nitrate/fuel oil ) is a widely used bulk industrial high explosive . It consists of 94% porous prilled ammonium nitrate (NH 4 NO 3 ) (AN), which acts as the oxidizing agent and absorbent for the fuel, and 6% number 2 fuel oil (FO). The use of ANFO originated in
12876-552: 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
12992-425: The two layers. As the length of time the shock wave spends at any point is small, we can see mixing of the two metals and their surface chemistries, through some fraction of the depth, and they tend to be mixed in some way. It is possible that some fraction of the surface material from either layer eventually gets ejected when the end of material is reached. Hence, the mass of the now "welded" bilayer, may be less than
13108-698: 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
13224-488: 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
13340-798: Was nitroglycerin , developed in 1847. Since nitroglycerin is a liquid and highly unstable, it was replaced by nitrocellulose , trinitrotoluene ( TNT ) in 1863, smokeless powder , dynamite in 1867 and gelignite (the latter two being sophisticated stabilized preparations of nitroglycerin rather than chemical alternatives, both invented by Alfred Nobel ). World War I saw the adoption of TNT in artillery shells. World War II saw extensive use of new explosives (see: List of explosives used during World War II ) . In turn, these have largely been replaced by more powerful explosives such as C-4 and PETN . However, C-4 and PETN react with metal and catch fire easily, yet unlike TNT, C-4 and PETN are waterproof and malleable. The largest commercial application of explosives
13456-702: Was used in 1970 when protests by students became violent at the University of Wisconsin–Madison , who learned how to make and use ANFO from a Wisconsin Conservation Department booklet entitled Pothole Blasting for Wildlife , resulting in the Sterling Hall bombing . ANFO used to be widely used by the FLNC ( National Liberation Front of Corsica ), along with f15 explosive. Five containers of 500 kilograms (1,100 pounds) each were used to blow up
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