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113-436: Lowari Top experiences a seasonal closure due to heavy snow accumulation, rendering it impassable for vehicular transportation. This closure typically extends from the latter part of November to the ending days of May each year. The Pass entail inherent risks. A significant concern may be the imminent threat posed by avalanches, which can occur abruptly. This is dangerous, as there are high mountains on each side of Lowari Top, and

226-432: A {\displaystyle F=ma} , is valid. Non-inertial reference frames accelerate in relation to another inertial frame. A body rotating with respect to an inertial frame is not an inertial frame. When viewed from an inertial frame, particles in the non-inertial frame appear to move in ways not explained by forces from existing fields in the reference frame. Hence, it appears that there are other forces that enter

339-413: A Legendre transformation on the generalized coordinates, velocities and momenta; therefore, both contain the same information for describing the dynamics of a system. There are other formulations such as Hamilton–Jacobi theory , Routhian mechanics , and Appell's equation of motion . All equations of motion for particles and fields, in any formalism, can be derived from the widely applicable result called

452-514: A baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made of a large number of collectively acting point particles. The center of mass of a composite object behaves like a point particle. Classical mechanics assumes that matter and energy have definite, knowable attributes such as location in space and speed. Non-relativistic mechanics also assumes that forces act instantaneously (see also Action at

565-412: A configuration space M {\textstyle M} and a smooth function L {\textstyle L} within that space called a Lagrangian. For many systems, L = T − V , {\textstyle L=T-V,} where T {\textstyle T} and V {\displaystyle V} are the kinetic and potential energy of

678-997: A close relationship with geometry (notably, symplectic geometry and Poisson structures ) and serves as a link between classical and quantum mechanics . In this formalism, the dynamics of a system are governed by Hamilton's equations, which express the time derivatives of position and momentum variables in terms of partial derivatives of a function called the Hamiltonian: d q d t = ∂ H ∂ p , d p d t = − ∂ H ∂ q . {\displaystyle {\frac {\mathrm {d} {\boldsymbol {q}}}{\mathrm {d} t}}={\frac {\partial {\mathcal {H}}}{\partial {\boldsymbol {p}}}},\quad {\frac {\mathrm {d} {\boldsymbol {p}}}{\mathrm {d} t}}=-{\frac {\partial {\mathcal {H}}}{\partial {\boldsymbol {q}}}}.} The Hamiltonian

791-424: A critical temperature gradient. Large, angular snow crystals are indicators of weak snow, because such crystals have fewer bonds per unit volume than small, rounded crystals that pack tightly together. Consolidated snow is less likely to slough than loose powdery layers or wet isothermal snow; however, consolidated snow is a necessary condition for the occurrence of slab avalanches , and persistent instabilities within

904-463: A deadly avalanche can come at any moment without warning. Several people traversing the Pass in winters become the victims of avalanche fatalities. Their bodies are buried under the snow and it is only when the summer comes and the snow melts that their bodies are found. Nevertheless, Lowari Top remains popular because it is the shortest route from Chitral to Peshawar . The other way would be down

1017-416: A decrease in the magnitude of velocity " v " is referred to as deceleration , but generally any change in the velocity over time, including deceleration, is referred to as acceleration. While the position, velocity and acceleration of a particle can be described with respect to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in which

1130-447: A distance ). The position of a point particle is defined in relation to a coordinate system centered on an arbitrary fixed reference point in space called the origin O . A simple coordinate system might describe the position of a particle P with a vector notated by an arrow labeled r that points from the origin O to point P . In general, the point particle does not need to be stationary relative to O . In cases where P

1243-559: A drag force that was proportional to the square of the speed of its flow: He and others subsequently derived other formulae that take other factors into account, with the Voellmy-Salm-Gubler and the Perla-Cheng-McClung models becoming most widely used as simple tools to model flowing (as opposed to powder snow) avalanches. Since the 1990s many more sophisticated models have been developed. In Europe much of

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1356-428: A fictitious centrifugal force and Coriolis force . A force in physics is any action that causes an object's velocity to change; that is, to accelerate. A force originates from within a field , such as an electro-static field (caused by static electrical charges), electro-magnetic field (caused by moving charges), or gravitational field (caused by mass), among others. Newton was the first to mathematically express

1469-463: A fracture at the bottom called the stauchwall. The crown and flank fractures are vertical walls in the snow delineating the snow that was entrained in the avalanche from the snow that remained on the slope. Slabs can vary in thickness from a few centimetres to three metres. Slab avalanches account for around 90% of avalanche-related fatalities. The largest avalanches form turbulent suspension currents known as powder snow avalanches or mixed avalanches,

1582-450: A kind of gravity current . These consist of a powder cloud, which overlies a dense avalanche. They can form from any type of snow or initiation mechanism, but usually occur with fresh dry powder. They can exceed speeds of 300 km/h (190 mph), and masses of 1,000,000 tons; their flows can travel long distances along flat valley bottoms and even uphill for short distances. In contrast to powder snow avalanches, wet snow avalanches are

1695-607: A long term, lasting from days to years. Experts interpret the recorded data and are able to recognize upcoming ruptures in order to initiate appropriate measures. Such systems (e.g. the monitoring of the Weissmies glacier in Switzerland ) can recognize events several days in advance. Modern radar technology enables the monitoring of large areas and the localization of avalanches at any weather condition, by day and by night. Complex alarm systems are able to detect avalanches within

1808-411: A low velocity suspension of snow and water, with the flow confined to the track surface (McClung, 1999, p. 108). The low speed of travel is due to the friction between the sliding surface of the track and the water saturated flow. Despite the low speed of travel (≈10–40 km/h), wet snow avalanches are capable of generating powerful destructive forces, due to the large mass and density. The body of

1921-400: A number of methods including hand-tossed charges, helicopter-dropped bombs, Gazex concussion lines, and ballistic projectiles launched by air cannons and artillery. Passive preventive systems such as snow fences and light walls can be used to direct the placement of snow. Snow builds up around the fence, especially the side that faces the prevailing winds . Downwind of the fence, snow build-up

2034-729: A particular formalism based on Newton's laws of motion . Newtonian mechanics in this sense emphasizes force as a vector quantity. In contrast, analytical mechanics uses scalar properties of motion representing the system as a whole—usually its kinetic energy and potential energy . The equations of motion are derived from the scalar quantity by some underlying principle about the scalar's variation . Two dominant branches of analytical mechanics are Lagrangian mechanics , which uses generalized coordinates and corresponding generalized velocities in configuration space , and Hamiltonian mechanics , which uses coordinates and corresponding momenta in phase space . Both formulations are equivalent by

2147-413: A persistent weakness in the snowpack. When a slab lying on top of a persistent weakness is loaded by a force greater than the strength of the slab and persistent weak layer, the persistent weak layer can fail and generate an avalanche. Any wind stronger than a light breeze can contribute to a rapid accumulation of snow on sheltered slopes downwind. Wind slabs form quickly and, if present, weaker snow below

2260-400: A point significantly above the freezing point of water, may cause avalanche formation at any time of year. Persistent cold temperatures can either prevent new snow from stabilizing or destabilize the existing snowpack. Cold air temperatures on the snow surface produce a temperature gradient in the snow, because the ground temperature at the base of the snowpack is usually around 0 °C, and

2373-412: A point with only a small amount of snow moving initially; this is typical of wet snow avalanches or avalanches in dry unconsolidated snow. However, if the snow has sintered into a stiff slab overlying a weak layer, then fractures can propagate very rapidly, so that a large volume of snow, possibly thousands of cubic metres, can start moving almost simultaneously. A snowpack will fail when the load exceeds

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2486-487: A reformulation of Lagrangian mechanics . Introduced by Sir William Rowan Hamilton , Hamiltonian mechanics replaces (generalized) velocities q ˙ i {\displaystyle {\dot {q}}^{i}} used in Lagrangian mechanics with (generalized) momenta . Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has

2599-592: A short time in order to close (e.g. roads and rails) or evacuate (e.g. construction sites) endangered areas. An example of such a system is installed on the only access road of Zermatt in Switzerland. Two radars monitor the slope of a mountain above the road. The system automatically closes the road by activating several barriers and traffic lights within seconds such that no people are harmed. Avalanche accidents are broadly differentiated into 2 categories: accidents in recreational settings, and accidents in residential, industrial, and transportation settings. This distinction

2712-411: A solid body into a collection of points.) In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The behavior of very small particles, such as the electron , is more accurately described by quantum mechanics .) Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom , e.g.,

2825-417: A start zone where the avalanche originates, a track along which the avalanche flows, and a runout zone where the avalanche comes to rest. The debris deposit is the accumulated mass of the avalanched snow once it has come to rest in the run-out zone. For the image at left, many small avalanches form in this avalanche path every year, but most of these avalanches do not run the full vertical or horizontal length of

2938-415: A storm. Daytime exposure to sunlight will rapidly destabilize the upper layers of the snowpack if the sunlight is strong enough to melt the snow, thereby reducing its hardness. During clear nights, the snowpack can re-freeze when ambient air temperatures fall below freezing, through the process of long-wave radiative cooling, or both. Radiative heat loss occurs when the night air is significantly cooler than

3051-412: A sufficient quantity of airborne snow, this portion of the avalanche can become separated from the bulk of the avalanche and travel a greater distance as a powder snow avalanche. Scientific studies using radar , following the 1999 Galtür avalanche disaster , confirmed the hypothesis that a saltation layer forms between the surface and the airborne components of an avalanche, which can also separate from

3164-727: A three-month period throughout the Alps in Austria, France, Switzerland, Italy and Germany. This series of avalanches killed around 265 people and was termed the Winter of Terror . A mountain climbing camp on Lenin Peak, in what is now Kyrgyzstan, was wiped out in 1990 when an earthquake triggered a large avalanche that overran the camp. Forty-three climbers were killed. In 1993, the Bayburt Üzengili avalanche killed 60 individuals in Üzengili in

3277-413: A variety of factors such as the snow's shear strength (which is itself dependent upon crystal form) and the configuration of layers and inter-layer interfaces. The snowpack on slopes with sunny exposures is strongly influenced by sunshine . Diurnal cycles of thawing and refreezing can stabilize the snowpack by promoting settlement. Strong freeze-thaw cycles result in the formation of surface crusts during

3390-464: Is a limiting case of the Poincaré group used in special relativity . The limiting case applies when the velocity u is very small compared to c , the speed of light . The transformations have the following consequences: For some problems, it is convenient to use rotating coordinates (reference frames). Thereby one can either keep a mapping to a convenient inertial frame, or introduce additionally

3503-403: Is a rigid fence-like structure ( snow fence ) and may be constructed of steel , wood or pre-stressed concrete . They usually have gaps between the beams and are built perpendicular to the slope, with reinforcing beams on the downhill side. Rigid barriers are often considered unsightly, especially when many rows must be built. They are also expensive and vulnerable to damage from falling rocks in

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3616-408: Is based on the choice of mathematical formalism. Classical mechanics can be mathematically presented in multiple different ways. The physical content of these different formulations is the same, but they provide different insights and facilitate different types of calculations. While the term "Newtonian mechanics" is sometimes used as a synonym for non-relativistic classical physics, it can also refer to

3729-401: Is called the equation of motion . As an example, assume that friction is the only force acting on the particle, and that it may be modeled as a function of the velocity of the particle, for example: where λ is a positive constant, the negative sign states that the force is opposite the sense of the velocity. Then the equation of motion is This can be integrated to obtain where v 0

3842-579: Is called the Starting Point and typically occurs on a 30–45 degree slope. The body of the pathway is called the Track of the avalanche and usually occurs on a 20–30 degree slope. When the avalanche loses its momentum and eventually stops it reaches the Runout Zone. This usually occurs when the slope has reached a steepness that is less than 20 degrees. These degrees are not consistently true due to

3955-424: Is critically sensitive to small variations within the narrow range of meteorological conditions that allow for the accumulation of snow into a snowpack. Among the critical factors controlling snowpack evolution are: heating by the sun, radiational cooling , vertical temperature gradients in standing snow, snowfall amounts, and snow types. Generally, mild winter weather will promote the settlement and stabilization of

4068-412: Is equal to the change in kinetic energy E k of the particle: Conservative forces can be expressed as the gradient of a scalar function, known as the potential energy and denoted E p : If all the forces acting on a particle are conservative, and E p is the total potential energy (which is defined as a work of involved forces to rearrange mutual positions of bodies), obtained by summing

4181-408: Is flat enough to hold snow but steep enough to ski has the potential to generate an avalanche, regardless of the angle. The snowpack is composed of ground-parallel layers that accumulate over the winter. Each layer contains ice grains that are representative of the distinct meteorological conditions during which the snow formed and was deposited. Once deposited, a snow layer continues to evolve under

4294-470: Is lessened. This is caused by the loss of snow at the fence that would have been deposited and the pickup of the snow that is already there by the wind, which was depleted of snow at the fence. When there is a sufficient density of trees , they can greatly reduce the strength of avalanches. They hold snow in place and when there is an avalanche, the impact of the snow against the trees slows it down. Trees can either be planted or they can be conserved, such as in

4407-504: Is motivated by the observed difference in the causes of avalanche accidents in the two settings. In the recreational setting most accidents are caused by the people involved in the avalanche. In a 1996 study, Jamieson et al. (pages 7–20) found that 83% of all avalanches in the recreational setting were caused by those who were involved in the accident . In contrast, all the accidents in the residential, industrial, and transportation settings were due to spontaneous natural avalanches. Because of

4520-426: Is moving relative to O , r is defined as a function of t , time . In pre-Einstein relativity (known as Galilean relativity ), time is considered an absolute, i.e., the time interval that is observed to elapse between any given pair of events is the same for all observers. In addition to relying on absolute time , classical mechanics assumes Euclidean geometry for the structure of space. The velocity , or

4633-422: Is non-conservative. The kinetic energy E k of a particle of mass m travelling at speed v is given by For extended objects composed of many particles, the kinetic energy of the composite body is the sum of the kinetic energies of the particles. The work–energy theorem states that for a particle of constant mass m , the total work W done on the particle as it moves from position r 1 to r 2

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4746-402: Is sufficiently unsettled and cold enough for precipitated snow to accumulate into a seasonal snowpack. Continentality , through its potentiating influence on the meteorological extremes experienced by snowpacks, is an important factor in the evolution of instabilities, and consequential occurrence of avalanches faster stabilization of the snowpack after storm cycles. The evolution of the snowpack

4859-416: Is the initial velocity. This means that the velocity of this particle decays exponentially to zero as time progresses. In this case, an equivalent viewpoint is that the kinetic energy of the particle is absorbed by friction (which converts it to heat energy in accordance with the conservation of energy ), and the particle is slowing down. This expression can be further integrated to obtain the position r of

4972-515: Is thus equal to the rate of change of the momentum of the particle with time. Since the definition of acceleration is a = d v /d t , the second law can be written in the simplified and more familiar form: So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation , which

5085-845: The Kunar River to Jalalabad through hostile Afghan territory or the much longer route across Shandur Top to Gilgit . Lowari Top crosses the Hindu Raj Mountains, a spur of the higher Hindu Kush . On the Chitral side of Lowari Top are the people of Ashret , who speak the Palula language and were assigned by the Mehtar of Chitral to be the guardians of Lowari Top. On the Dir side reside Khowars , some of whom make their living as porters carrying loads across Lowari Top. In 1954,

5198-694: The Rogers Pass avalanche in British Columbia , Canada. During World War I , an estimated 40,000 to 80,000 soldiers died as a result of avalanches during the mountain campaign in the Alps at the Austrian-Italian front, many of which were caused by artillery fire. Some 10,000 men, from both sides, died in avalanches in December 1916. In the northern hemisphere winter of 1950–1951 approximately 649 avalanches were recorded in

5311-502: The angle of repose , depends on a variety of factors, such as crystal form and moisture content. Some forms of drier and colder snow will only stick to shallower slopes, while wet and warm snow can bond to very steep surfaces. In coastal mountains, such as the Cordillera del Paine region of Patagonia , deep snowpacks collect on vertical and even overhanging rock faces. The slope angle that can allow moving snow to accelerate depends on

5424-496: The avalanche dam on Mount Stephen in Kicking Horse Pass , have been constructed to protect people and property by redirecting the flow of avalanches. Deep debris deposits from avalanches will collect in catchments at the terminus of a run out, such as gullies and river beds. Slopes flatter than 25 degrees or steeper than 60 degrees typically have a lower incidence of avalanches. Human-triggered avalanches have

5537-511: The forces applied to it. Classical mechanics also describes the more complex motions of extended non-pointlike objects. Euler's laws provide extensions to Newton's laws in this area. The concepts of angular momentum rely on the same calculus used to describe one-dimensional motion. The rocket equation extends the notion of rate of change of an object's momentum to include the effects of an object "losing mass". (These generalizations/extensions are derived from Newton's laws, say, by decomposing

5650-429: The forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics . Dynamics goes beyond merely describing objects' behavior and also considers the forces which explain it. Some authors (for example, Taylor (2005) and Greenwood (1997) ) include special relativity within classical dynamics. Another division

5763-451: The principle of least action . One result is Noether's theorem , a statement which connects conservation laws to their associated symmetries . Alternatively, a division can be made by region of application: For simplicity, classical mechanics often models real-world objects as point particles , that is, objects with negligible size. The motion of a point particle is determined by a small number of parameters : its position, mass , and

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5876-413: The rate of change of displacement with time, is defined as the derivative of the position with respect to time: In classical mechanics, velocities are directly additive and subtractive. For example, if one car travels east at 60 km/h and passes another car traveling in the same direction at 50 km/h, the slower car perceives the faster car as traveling east at 60 − 50 = 10 km/h . However, from

5989-434: The revolutions in physics of the early 20th century , all of which revealed limitations in classical mechanics. The earliest formulation of classical mechanics is often referred to as Newtonian mechanics . It consists of the physical concepts based on the 17th century foundational works of Sir Isaac Newton , and the mathematical methods invented by Newton, Gottfried Wilhelm Leibniz , Leonhard Euler and others to describe

6102-463: The speed of light . With objects about the size of an atom's diameter, it becomes necessary to use quantum mechanics . To describe velocities approaching the speed of light, special relativity is needed. In cases where objects become extremely massive, general relativity becomes applicable. Some modern sources include relativistic mechanics in classical physics, as representing the field in its most developed and accurate form. Classical mechanics

6215-565: The stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his presentation to the Turin Academy of Science in 1760 culminating in his 1788 grand opus, Mécanique analytique . Lagrangian mechanics describes a mechanical system as a pair ( M , L ) {\textstyle (M,L)} consisting of

6328-509: The Khumbu Icefall), triggering a movement of broken ice chunks. The resulting movement is more analogous to a rockfall or a landslide than a snow avalanche. They are typically very difficult to predict and almost impossible to mitigate. As an avalanche moves down a slope it follows a certain pathway that is dependent on the slope's degree of steepness and the volume of snow/ice involved in the mass movement . The origin of an avalanche

6441-741: The Mehtar of Chitral was killed when his airplane crashed into Lowari Top. The word "Top" is believed not to be the English word "top" but a word from an ancient language no longer spoken there. The Lowari Top is one of the four major mountain passes to enter Chitral . The others are the Dorah Pass from Badakshan in Afghanistan , Shandur Top from Gilgit , and Broghol from the Wakhan Corridor in Afghanistan . The Lowari Tunnel

6554-517: The SAMOS-AT avalanche simulation software and the RAMMS software. Preventative measures are employed in areas where avalanches pose a significant threat to people, such as ski resorts , mountain towns, roads, and railways. There are several ways to prevent avalanches and lessen their power and develop preventative measures to reduce the likelihood and size of avalanches by disrupting the structure of

6667-474: The United States. In 2001 it was reported that globally an average of 150 people die each year from avalanches. Three of the deadliest recorded avalanches have killed over a thousand people each. Doug Fesler and Jill Fredston developed a conceptual model of the three primary elements of avalanches: terrain, weather, and snowpack. Terrain describes the places where avalanches occur, weather describes

6780-408: The ambient air temperature can be much colder. When a temperature gradient greater than 10 °C change per vertical meter of snow is sustained for more than a day, angular crystals called depth hoar or facets begin forming in the snowpack because of rapid moisture transport along the temperature gradient. These angular crystals, which bond poorly to one another and the surrounding snow, often become

6893-426: The avalanche's path to slow it down. Finally, along transportation corridors, large shelters, called snow sheds , can be built directly in the slide path of an avalanche to protect traffic from avalanches. Warning systems can detect avalanches which develop slowly, such as ice avalanches caused by icefalls from glaciers. Interferometric radars, high-resolution cameras, or motion sensors can monitor instable areas over

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7006-401: The building of a ski resort, to reduce the strength of avalanches. In turn, socio-environmental changes can influence the occurrence of damaging avalanches: some studies linking changes in land-use/land-cover patterns and the evolution of snow avalanche damage in mid latitude mountains show the importance of the role played by vegetation cover, that is at the root of the increase of damage when

7119-432: The bulk of the avalanche. Driving an avalanche is the component of the avalanche's weight parallel to the slope; as the avalanche progresses any unstable snow in its path will tend to become incorporated, so increasing the overall weight. This force will increase as the steepness of the slope increases, and diminish as the slope flattens. Resisting this are a number of components that are thought to interact with each other:

7232-435: The capability to capture and move ice, rocks, and trees. Avalanches occur in two general forms, or combinations thereof: slab avalanches made of tightly packed snow, triggered by a collapse of an underlying weak snow layer, and loose snow avalanches made of looser snow. After being set off, avalanches usually accelerate rapidly and grow in mass and volume as they capture more snow. If an avalanche moves fast enough, some of

7345-409: The depths, crystal forms, and layering of the seasonal snowpack. Slab avalanches are formed frequently in snow that has been deposited, or redeposited by wind. They have the characteristic appearance of a block (slab) of snow cut out from its surroundings by fractures. Elements of slab avalanches include a crown fracture at the top of the start zone, flank fractures on the sides of the start zones, and

7458-693: The difference in the causes of avalanche accidents, and the activities pursued in the two settings, avalanche and disaster management professionals have developed two related preparedness, rescue, and recovery strategies for each of the settings. Two avalanches occurred in March 1910 in the Cascade and Selkirk Mountain ranges; on 1 March the Wellington avalanche killed 96 in Washington state , United States. Three days later 62 railroad workers were killed in

7571-532: The early 20th century, notably the work of Professor Lagotala in preparation for the 1924 Winter Olympics in Chamonix . His method was developed by A. Voellmy and popularised following the publication in 1955 of his Ueber die Zerstoerungskraft von Lawinen (On the Destructive Force of Avalanches). Voellmy used a simple empirical formula, treating an avalanche as a sliding block of snow moving with

7684-402: The equations of motion solely as a result of the relative acceleration. These forces are referred to as fictitious forces , inertia forces, or pseudo-forces. Consider two reference frames S and S' . For observers in each of the reference frames an event has space-time coordinates of ( x , y , z , t ) in frame S and ( x' , y' , z' , t' ) in frame S' . Assuming time is measured

7797-534: The fact that each avalanche is unique depending on the stability of the snowpack that it was derived from as well as the environmental or human influences that triggered the mass movement. People caught in avalanches can die from suffocation , trauma, or hypothermia . From "1950–1951 to 2020–2021" there were 1,169 people who died in avalanches in the United States. For the 11-year period ending April 2006, 445 people died in avalanches throughout North America. On average, 28 people die in avalanches every winter in

7910-452: The flow of a wet snow avalanche can plough through soft snow, and can scour boulders, earth, trees, and other vegetation; leaving exposed and often scored ground in the avalanche track. Wet snow avalanches can be initiated from either loose snow releases, or slab releases, and only occur in snowpacks that are water saturated and isothermally equilibrated to the melting point of water. The isothermal characteristic of wet snow avalanches has led to

8023-460: The friction between the avalanche and the surface beneath; friction between the air and snow within the fluid; fluid-dynamic drag at the leading edge of the avalanche; shear resistance between the avalanche and the air through which it is passing, and shear resistance between the fragments within the avalanche itself. An avalanche will continue to accelerate until the resistance exceeds the forward force. Attempts to model avalanche behaviour date from

8136-470: The greatest incidence when the snow's angle of repose is between 35 and 45 degrees; the critical angle, the angle at which human-triggered avalanches are most frequent, is 38 degrees. When the incidence of human triggered avalanches is normalized by the rates of recreational use, however, hazard increases uniformly with slope angle, and no significant difference in hazard for a given exposure direction can be found. The rule of thumb is: A slope that

8249-866: The ground surface beneath the snowpack influences the stability of the snowpack, either being a source of strength or weakness. Avalanches are unlikely to form in very thick forests, but boulders and sparsely distributed vegetation can create weak areas deep within the snowpack through the formation of strong temperature gradients. Full-depth avalanches (avalanches that sweep a slope virtually clean of snow cover) are more common on slopes with smooth ground, such as grass or rock slabs. Generally speaking, avalanches follow drainages down-slope, frequently sharing drainage features with summertime watersheds. At and below tree line , avalanche paths through drainages are well defined by vegetation boundaries called trim lines , which occur where avalanches have removed trees and prevented regrowth of large vegetation. Engineered drainages, such as

8362-508: The influence of the meteorological conditions that prevail after deposition. For an avalanche to occur, it is necessary that a snowpack have a weak layer (or instability) below a slab of cohesive snow. In practice the formal mechanical and structural factors related to snowpack instability are not directly observable outside of laboratories, thus the more easily observed properties of the snow layers (e.g. penetration resistance, grain size, grain type, temperature) are used as index measurements of

8475-413: The likelihood of an avalanche. Observation and experience has shown that newly fallen snow requires time to bond with the snow layers beneath it, especially if the new snow falls during very cold and dry conditions. If ambient air temperatures are cold enough, shallow snow above or around boulders, plants, and other discontinuities in the slope, weakens from rapid crystal growth that occurs in the presence of

8588-407: The line connecting A and B , while the weak form does not. Illustrations of the weak form of Newton's third law are often found for magnetic forces. If a constant force F is applied to a particle that makes a displacement Δ r , the work done by the force is defined as the scalar product of the force and displacement vectors: More generally, if the force varies as a function of position as

8701-450: The local humidity, water vapour flux, temperature and heat flux. The top of the snowpack is also extensively influenced by incoming radiation and the local air flow. One of the aims of avalanche research is to develop and validate computer models that can describe the evolution of the seasonal snowpack over time. A complicating factor is the complex interaction of terrain and weather, which causes significant spatial and temporal variability of

8814-405: The mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames . An inertial frame is an idealized frame of reference within which an object with zero net force acting upon it moves with a constant velocity; that is, it is either at rest or moving uniformly in a straight line. In an inertial frame Newton's law of motion, F = m

8927-526: The mechanical properties of the snow (e.g. tensile strength , friction coefficients, shear strength , and ductile strength ). This results in two principal sources of uncertainty in determining snowpack stability based on snow structure: First, both the factors influencing snow stability and the specific characteristics of the snowpack vary widely within small areas and time scales, resulting in significant difficulty extrapolating point observations of snow layers across different scales of space and time. Second,

9040-421: The meteorological conditions that create the snowpack, and snowpack describes the structural characteristics of snow that make avalanche formation possible. Avalanche formation requires a slope shallow enough for snow to accumulate but steep enough for the snow to accelerate once set in motion by the combination of mechanical failure (of the snowpack) and gravity. The angle of the slope that can hold snow, called

9153-471: The motion of bodies under the influence of forces . Later, methods based on energy were developed by Euler, Joseph-Louis Lagrange , William Rowan Hamilton and others, leading to the development of analytical mechanics (which includes Lagrangian mechanics and Hamiltonian mechanics ). These advances, made predominantly in the 18th and 19th centuries, extended beyond earlier works; they are, with some modification, used in all areas of modern physics. If

9266-414: The new snow has insufficient time to bond to underlying snow layers. Rain has a similar effect. In the short term, rain causes instability because, like a heavy snowfall, it imposes an additional load on the snowpack and once rainwater seeps down through the snow, acts as a lubricant, reducing the natural friction between snow layers that holds the snowpack together. Most avalanches happen during or soon after

9379-427: The night and of unstable surface snow during the day. Slopes in the lee of a ridge or of another wind obstacle accumulate more snow and are more likely to include pockets of deep snow, wind slabs , and cornices , all of which, when disturbed, may result in avalanche formation. Conversely, the snowpack on a windward slope is often much shallower than on a lee slope. Avalanches and avalanche paths share common elements:

9492-526: The particle as a function of time. Important forces include the gravitational force and the Lorentz force for electromagnetism . In addition, Newton's third law can sometimes be used to deduce the forces acting on a particle: if it is known that particle A exerts a force F on another particle B , it follows that B must exert an equal and opposite reaction force , − F , on A . The strong form of Newton's third law requires that F and − F act along

9605-409: The particle moves from r 1 to r 2 along a path C , the work done on the particle is given by the line integral If the work done in moving the particle from r 1 to r 2 is the same no matter what path is taken, the force is said to be conservative . Gravity is a conservative force, as is the force due to an idealized spring , as given by Hooke's law . The force due to friction

9718-407: The path. The frequency with which avalanches form in a given area is known as the return period . The start zone of an avalanche must be steep enough to allow snow to accelerate once set in motion, additionally convex slopes are less stable than concave slopes because of the disparity between the tensile strength of snow layers and their compressive strength . The composition and structure of

9831-406: The perspective of the faster car, the slower car is moving 10 km/h to the west, often denoted as −10 km/h where the sign implies opposite direction. Velocities are directly additive as vector quantities ; they must be dealt with using vector analysis . Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector u = u d and the velocity of

9944-401: The potential energies corresponding to each force The decrease in the potential energy is equal to the increase in the kinetic energy This result is known as conservation of energy and states that the total energy , is constant in time. It is often useful, because many commonly encountered forces are conservative. Lagrangian mechanics is a formulation of classical mechanics founded on

10057-403: The present state of an object that obeys the laws of classical mechanics is known, it is possible to determine how it will move in the future , and how it has moved in the past. Chaos theory shows that the long term predictions of classical mechanics are not reliable. Classical mechanics provides accurate results when studying objects that are not extremely massive and have speeds not approaching

10170-414: The prevention of development in these areas. To mitigate the effect of avalanches the construction of artificial barriers can be very effective in reducing avalanche damage. There are several types: One kind of barrier ( snow net ) uses a net strung between poles that are anchored by guy wires in addition to their foundations. These barriers are similar to those used for rockslides . Another type of barrier

10283-550: The protective forest is deforested (because of demographic growth, intensive grazing and industrial or legal causes), and at the root of the decrease of damage because of the transformation of a traditional land-management system based on overexploitation into a system based on land marginalization and reforestation, something that has happened mainly since the mid-20th century in mountain environments of developed countries. In many areas, regular avalanche tracks can be identified and precautions can be taken to minimize damage, such as

10396-495: The province of Bayburt , Turkey . Dynamics (mechanics) This is an accepted version of this page Classical mechanics is a physical theory describing the motion of objects such as projectiles , parts of machinery , spacecraft , planets , stars , and galaxies . The development of classical mechanics involved substantial change in the methods and philosophy of physics. The qualifier classical distinguishes this type of mechanics from physics developed after

10509-804: The recent work was carried out as part of the SATSIE (Avalanche Studies and Model Validation in Europe) research project supported by the European Commission which produced the leading-edge MN2L model, now in use with the Service Restauration des Terrains en Montagne (Mountain Rescue Service) in France, and D2FRAM (Dynamical Two-Flow-Regime Avalanche Model), which was still undergoing validation as of 2007. Other known models are

10622-406: The relationship between force and momentum . Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law": The quantity m v is called the ( canonical ) momentum . The net force on a particle

10735-409: The relationship between readily observable snowpack characteristics and the snowpack's critical mechanical properties has not been completely developed. While the deterministic relationship between snowpack characteristics and snowpack stability is still a matter of ongoing scientific study, there is a growing empirical understanding of the snow composition and deposition characteristics that influence

10848-440: The same direction, this equation can be simplified to: Or, by ignoring direction, the difference can be given in terms of speed only: The acceleration , or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time): Acceleration represents the velocity's change over time. Velocity can change in magnitude, direction, or both. Occasionally,

10961-471: The same in all reference frames, if we require x = x' when t = 0 , then the relation between the space-time coordinates of the same event observed from the reference frames S' and S , which are moving at a relative velocity u in the x direction, is: This set of formulas defines a group transformation known as the Galilean transformation (informally, the Galilean transform ). This group

11074-400: The second object by the vector v = v e , where u is the speed of the first object, v is the speed of the second object, and d and e are unit vectors in the directions of motion of each object respectively, then the velocity of the first object as seen by the second object is: Similarly, the first object sees the velocity of the second object as: When both objects are moving in

11187-458: The secondary term of isothermal slides found in the literature (for example in Daffern, 1999, p. 93). At temperate latitudes wet snow avalanches are frequently associated with climatic avalanche cycles at the end of the winter season, when there is significant daytime warming. An ice avalanche occurs when a large piece of ice, such as from a serac or calving glacier, falls onto ice (such as

11300-416: The slab may not have time to adjust to the new load. Even on a clear day, wind can quickly load a slope with snow by blowing snow from one place to another. Top-loading occurs when wind deposits snow from the top of a slope; cross-loading occurs when wind deposits snow parallel to the slope. When a wind blows over the top of a mountain, the leeward, or downwind, side of the mountain experiences top-loading, from

11413-415: The snow may mix with the air, forming a powder snow avalanche . Though they appear to share similarities, avalanches are distinct from slush flows , mudslides , rock slides , and serac collapses. They are also different from large scale movements of ice . Avalanches can happen in any mountain range that has an enduring snowpack. They are most frequent in winter or spring, but may occur at any time of

11526-429: The snowpack can hide below well-consolidated surface layers. Uncertainty associated with the empirical understanding of the factors influencing snow stability leads most professional avalanche workers to recommend conservative use of avalanche terrain relative to current snowpack instability. Avalanches only occur in a standing snowpack. Typically winter seasons at high latitudes, high altitudes, or both have weather that

11639-423: The snowpack, and the heat stored in the snow is re-radiated into the atmosphere. When a slab avalanche forms, the slab disintegrates into increasingly smaller fragments as the snow travels downhill. If the fragments become small enough the outer layer of the avalanche, called a saltation layer, takes on the characteristics of a fluid . When sufficiently fine particles are present they can become airborne and, given

11752-460: The snowpack, such as melting due to solar radiation, is the second-largest cause of natural avalanches. Other natural causes include rain, earthquakes, rockfall, and icefall. Artificial triggers of avalanches include skiers, snowmobiles, and controlled explosive work. Contrary to popular belief, avalanches are not triggered by loud sound; the pressure from sound is orders of magnitude too small to trigger an avalanche. Avalanche initiation can start at

11865-479: The snowpack, while passive measures reinforce and stabilize the snowpack in situ . The simplest active measure is repeatedly traveling on a snowpack as snow accumulates; this can be by means of boot-packing, ski-cutting, or machine grooming . Explosives are used extensively to prevent avalanches, by triggering smaller avalanches that break down instabilities in the snowpack, and removing overburden that can result in larger avalanches. Explosive charges are delivered by

11978-402: The snowpack; conversely, very cold, windy, or hot weather will weaken the snowpack. At temperatures close to the freezing point of water, or during times of moderate solar radiation, a gentle freeze-thaw cycle will take place. The melting and refreezing of water in the snow strengthens the snowpack during the freezing phase and weakens it during the thawing phase. A rapid rise in temperature, to

12091-401: The strength. The load is straightforward; it is the weight of the snow. However, the strength of the snowpack is much more difficult to determine and is extremely heterogeneous. It varies in detail with properties of the snow grains, size, density, morphology, temperature, water content; and the properties of the bonds between the grains. These properties may all metamorphose in time according to

12204-436: The system, respectively. The stationary action principle requires that the action functional of the system derived from L {\textstyle L} must remain at a stationary point (a maximum , minimum , or saddle ) throughout the time evolution of the system. This constraint allows the calculation of the equations of motion of the system using Lagrange's equations. Hamiltonian mechanics emerged in 1833 as

12317-421: The top to the bottom of that lee slope. When the wind blows across a ridge that leads up the mountain, the leeward side of the ridge is subject to cross-loading. Cross-loaded wind-slabs are usually difficult to identify visually. Snowstorms and rainstorms are important contributors to avalanche danger. Heavy snowfall will cause instability in the existing snowpack, both because of the additional weight and because

12430-449: The warmer months. In addition to industrially manufactured barriers, landscaped barriers, called avalanche dams stop or deflect avalanches with their weight and strength. These barriers are made out of concrete, rocks, or earth. They are usually placed right above the structure, road, or railway that they are trying to protect, although they can also be used to channel avalanches into other barriers. Occasionally, earth mounds are placed in

12543-485: The year. In mountainous areas, avalanches are among the most serious natural hazards to life and property, so great efforts are made in avalanche control . There are many classification systems for the different forms of avalanches. Avalanches can be described by their size, destructive potential, initiation mechanism, composition, and dynamics . Most avalanches occur spontaneously during storms under increased load due to snowfall and/or erosion . Metamorphic changes in

12656-619: Was constructed beneath Lowari Pass by Sambu, a South Korean company in 2009. However, the tunnel was abandoned shortly thereafter and has since fallen into disrepair. The tunnel is functional as of December, 2019 and comprises over 8.5 Kilometres in length. Avalanche An avalanche is a rapid flow of snow down a slope , such as a hill or mountain. Avalanches can be triggered spontaneously, by factors such as increased precipitation or snowpack weakening, or by external means such as humans, other animals, and earthquakes . Primarily composed of flowing snow and air, large avalanches have

12769-413: Was traditionally divided into three main branches. Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in equilibrium with its environment. Kinematics describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering

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