147-593: The Governor Edmund G. Brown California Aqueduct is a system of canals, tunnels, and pipelines that conveys water collected from the Sierra Nevada Mountains and valleys of Northern and Central California to Southern California . Named after California Governor Edmund Gerald "Pat" Brown Sr. , the over 400-mile (640 km) aqueduct is the principal feature of the California State Water Project . The aqueduct begins at
294-717: 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
441-408: 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 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
588-625: 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
735-661: 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
882-404: 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}} }
1029-532: A foreman working for Sacramento pioneer John Sutter , found shiny metal in the tailrace of a lumber mill Marshall was building for Sutter on the American River . Rumors soon started to spread and were confirmed in March 1848 by San Francisco newspaper publisher and merchant Samuel Brannan . Brannan strode through the streets of San Francisco, holding aloft a vial of gold, shouting "Gold! Gold! Gold from
1176-419: 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 the pair "actual" vs "potential" going back to work by Aristotle . In his 1867 discussion of
1323-527: A halt on significant compaction and a recovery in ground water levels now with less ground water pumping. The aqueduct has been increasing in subsidence rates rapidly, even though it was relatively stable for many years after being constructed. The Tulare Basin is subsiding at a rate of about one foot per year, as measured by NASA's GRACE satellite. The Central Valley, where a large portion of the California Aqueduct runs through, has been affected by
1470-509: A long segment, built at a slight grade, and arrives at a pumping station powered by Path 66 or Path 15 . The pumping station raises the water, where it again gradually flows downhill to the next station. However, where there are substantial drops, the water's potential energy is recaptured by hydroelectric plants. The initial pumping station fed by the Sacramento River Delta raises the water 240 ft (73 m), while
1617-460: 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 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
SECTION 10
#17327725644101764-571: A portion of the area, a triangle whose vertices are Reno, Nevada ; Fresno, California ; and Las Vegas, Nevada , has been dubbed the " Nevada Triangle ", in reference to the Bermuda Triangle . Some counts put the number of crashes in the triangle at 2,000, including millionaire and record-breaking flyer Steve Fossett . Hypotheses that the crashes are related in some way to the United States Air Force 's Area 51 , or to
1911-445: 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 the force. The negative sign provides the convention that work done against a force field increases potential energy, while work done by
2058-448: A powerful stream or jet of water at gold-bearing gravel beds. It is estimated that by the mid-1880s, 11 million troy ounces (340 metric tons) of gold (worth approximately US$ 16 billion in 2020 prices) had been recovered by "hydraulicking". A consequence of these extraction methods was that large amounts of gravel, silt , heavy metals , and other pollutants were washed into streams and rivers. As of 1999 , many areas still bear
2205-706: A publication of his photographs under the title Parmelian Prints of the High Sierras , commented, "The name Sierra is already a plural. To add an s is a linguistic, Californian, and mountaineering sin." The Sierra Nevada lies primarily in Central and Eastern California , with the Carson Range , a small but historically important spur, extending into Nevada. West-to-east, the Sierra Nevada's elevation increases gradually from 500 feet (150 m) in
2352-438: 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
2499-593: A series of pumps culminating at the Edmonston Pumping Plant raises the water 1,926 ft (587 m) over the Tehachapi Mountains. A typical section has a concrete -lined channel 40 feet (12 m) at the base and an average water depth of about 30 ft (9.1 m). The widest section of the aqueduct is 110 feet (34 m) and the deepest is 32 feet (9.8 m). Channel capacity is 13,100 cubic feet per second (370 m/s) and
2646-565: A sharp decline. From October 2011 to September 2015 measurements made on groundwater levels in the San Joaquin Valley's aquifers recorded a loss of 14 km/year, a total of 56 km. During this same period up to 1,000 mm of land subsidence was measured in the San Joaquin Valley. Concerns around groundwater depletion have contributed to legislation to reduce the demand for groundwater and incentivize farmers to use sustainable irrigation practices. Measurement of this subsidence
2793-501: A short period, and the lightning can start fires. Summer high temperatures average 42–90 °F (6–32 °C). Winters are comparatively mild, and the temperature is usually only just low enough to sustain a heavy snowpack. For example, Tuolumne Meadows , at 8,600 feet (2,600 m) elevation, has winter daily highs about 40 °F (4 °C) with daily lows about 10 °F (−12 °C). The growing season lasts 20 to 230 days, strongly dependent on elevation. The highest elevations of
2940-567: 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
3087-757: Is W = U ( x A ) − U ( x B ) . {\displaystyle W=U(\mathbf {x} _{\text{A}})-U(\mathbf {x} _{\text{B}}).} In this case, the application of the del operator to the work function yields, ∇ W = − ∇ U = − ( ∂ U ∂ x , ∂ U ∂ y , ∂ U ∂ z ) = F , {\displaystyle {\nabla W}=-{\nabla U}=-\left({\frac {\partial U}{\partial x}},{\frac {\partial U}{\partial y}},{\frac {\partial U}{\partial z}}\right)=\mathbf {F} ,} and
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#17327725644103234-447: Is Mount Lyell (13,120 ft or 3,999 m). The Sierra rises to almost 14,000 feet (4,300 m) with Mount Humphreys near Bishop, California . Finally, near Lone Pine , Mount Whitney is at 14,505 feet (4,421 m), the highest point in the contiguous United States . South of Mount Whitney, the elevation of the range quickly dwindles. The crest elevation is almost 10,000 feet (3,000 m) near Lake Isabella , but south of
3381-873: 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
3528-466: 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
3675-456: 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
3822-402: 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 is that potential energy is the energy difference between the energy of an object in
3969-425: Is being used to recreate maps to closely watch the progression of the land around the aqueduct. Subsidence can put land, both private and public, at risk of infrastructure damage. Bridges, levees, roads, and groundwater wells are either at risk of damage or have been damaged already. With subsidence progression, underground aquifers could be at risk and water storage from them could be threatened. Damage and sinking of
4116-680: Is both direct and indirect. The Sacramento River , along with its tributaries the Feather River and American River , flows southwards through the Sacramento Valley for about 447 miles (719 km). In the San Joaquin Valley, the San Joaquin River flows roughly northwest for 365 miles (587 km), picking up tributaries such as the Merced River , Tuolumne River , Stanislaus River and Mokelumne River . In
4263-763: 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
4410-455: 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: the kinetic energy of random motions of particles and the potential energy of their configuration. Forces derivable from
4557-415: 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, the force can be defined as the negative of the vector gradient of
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4704-454: 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 , = ∫
4851-449: Is done in a few ways. Originally, subsidence was recorded based on land surveying, repeating the surveying, and along with monitoring compaction by recording the data from extensometers at multiple sites. Since then, Global Positioning Systems (GPS) has been used along with land surveying to record subsidence and compaction. More recently, interferometric synthetic aperture radar (InSAR) has been used to monitor subsidence along with GPS. InSAR
4998-456: Is either protected from development or strictly managed. The mountain range is home to three National Parks – Yosemite , Kings Canyon , and Sequoia – and two national monuments – Devils Postpile and Giant Sequoia . Ten national forests span much of the mountain range's remaining area. Within these national parks, monuments, and forests lie 26 wilderness areas , which together protect 15.4% of
5145-439: 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 ,
5292-409: 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
5439-615: Is featured in an episode of California's Gold with Huell Howser . Sierra Nevada (U.S.) The Sierra Nevada ( / s i ˌ ɛr ə n ɪ ˈ v æ d ə , - ˈ v ɑː d -/ see- ERR -ə nih- VA(H)D -ə ) is a mountain range in the Western United States , between the Central Valley of California and the Great Basin . The vast majority of the range lies in the state of California , although
5586-542: Is higher in the east. A list of biotic zones, and corresponding elevations, is presented below: Archaeological excavations placed Martis people of Paleo-Indians in northcentral Sierra Nevada during the period of 3,000 BCE to 500 CE. The earliest identified sustaining indigenous people in the Sierra Nevada were the Northern Paiute tribes on the east side, with the Mono tribe and Sierra Miwok tribe on
5733-639: Is located at the southern end. Land subsidence has occurred along the aqueduct and has had a steady increase since its relatively stable state post construction of the aqueduct. The aqueduct serves 35 million people and 5.7 million acres of farmland, and begins at the San Joaquin-Sacramento River Delta at the Banks Pumping Plant , which pumps from the Clifton Court Forebay . Water is pumped by
5880-462: 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,
6027-639: 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
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6174-496: 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
6321-464: 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
6468-771: Is the source of much of the sedimentary rock in California. In the Cretaceous , a subduction zone formed at the edge of the continent. This means that an oceanic plate started to dive beneath the North American Plate . Magma, formed through the subduction of the ancient Farallon Plate , rose in plumes ( plutons ) deep underground, their combined mass forming what is called the Sierra Nevada batholith . These plutons formed at various times, from 115 Ma to 87 Ma. The earlier plutons formed in
6615-487: 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
6762-429: 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
6909-698: Is usually dry nowadays because the rivers feeding it have been diverted for agricultural purposes. The rivers of the Central Valley converge in the Sacramento-San Joaquin Delta , a complex network of marshy channels, distributaries and sloughs that wind around islands mainly used for agriculture. Here the freshwater of the rivers merges with tidewater, and eventually reach the Pacific Ocean after passing through Suisun Bay , San Pablo Bay , upper San Francisco Bay and finally
7056-704: The Angeles National Forest to supply the western Los Angeles basin. It passes through parts of Kern and Los Angeles counties. West Branch facilities include When it was open, the California Aqueduct Bikeway was the longest of the paved paths in the Los Angeles area , at 107 miles (172 km) long from Quail Lake near Gorman in the Sierra Pelona Mountains through the desert to Silverwood Lake in
7203-462: The Basin and Range Province . As this andesitic volcanism began waning about five million years ago, the rivers were able to begin eroding away the 100s of meters of volcanic deposits and resume the incision that had been halted by the first period of volcanism. Some studies have argued that this recent incision is a sign of recent tectonic uplift. Other geologists claim that the elevations of many of
7350-580: The Carson Range spur lies primarily in Nevada . The Sierra Nevada is part of the American Cordillera , an almost continuous chain of mountain ranges that forms the western "backbone" of the Americas. The Sierra runs 400 mi (640 km) north-south, and its width ranges from 50 mi (80 km) to 80 mi (130 km) across east–west. Notable features include General Sherman ,
7497-661: The Carson River runs into Carson Sink , the Walker River into Walker Lake ; Rush , Lee Vining and Mill Creeks flow into Mono Lake ; and the Owens River into dry Owens Lake . Although none of the eastern rivers reach the sea, many of the streams from Mono Lake southwards are diverted into the Los Angeles Aqueduct which provides water to Southern California . The height of the mountains in
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#17327725644107644-487: The Central Valley to more than 14,000 feet (4,300 m) atop the highest peaks of its crest 50 to 75 miles (80 to 121 km) to the east. The east slope forms the steep Sierra Escarpment . Unlike its surroundings, the range receives a substantial amount of snowfall and precipitation due to orographic lift . The Sierra Nevada's irregular northern boundary stretches from the Susan River and Fredonyer Pass to
7791-936: The Clifton Court Forebay at the southwestern corner of the Sacramento–San Joaquin River Delta . The aqueduct then heads south, eventually splitting into three branches: the Coastal Branch, ending at Lake Cachuma in Santa Barbara County ; the West Branch, conveying water to Castaic Lake in Los Angeles County ; and the East Branch, connecting Silverwood Lake in San Bernardino County . The Department of Water Resources (DWR) operates and maintains
7938-601: The Golden Gate . Many of the islands now lie below sea level because of intensive agriculture, and have a high risk of flooding, which would cause salt water to rush back into the delta, especially when there is too little fresh water flowing in from the Valley. The Sacramento River carries far more water than the San Joaquin, with an estimated 22 million acre-feet (27 km) of virgin annual runoff, as compared to
8085-484: 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 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
8232-595: The Nevadan orogeny , granite formed deep underground. The range started to uplift less than five million years ago, and erosion by glaciers exposed the granite and formed the light-colored mountains and cliffs that make up the range. The uplift caused a wide range of elevations and climates in the Sierra Nevada, which are reflected by the presence of five life zones (areas with similar plant and animal communities). Uplift continues due to faulting caused by tectonic forces, creating spectacular fault block escarpments along
8379-611: The North Fork Feather River . It represents where the granitic bedrock of the Sierra Nevada dives below the southern extent of Cenozoic igneous surface rock from the Cascade Range . It is bounded on the west by California 's Central Valley , on the east by the Basin and Range Province , and on the southeast by the Mojave Desert . The southern boundary is at Tehachapi Pass . Physiographically,
8526-531: The San Bernardino Mountains . This path was closed in 1988 due to bicyclist safety and liability issues. It is expected to remain closed indefinitely due to the continued liability issues and an increased focus on security, especially after the September 11, 2001 attacks . Two major river systems drain and define the two parts of the Central Valley . Their impact on the California Aqueduct
8673-529: The San Joaquin Valley to the rest of the state in the 1870s. This facilitated the nationwide distribution of lumber. In addition, technological advancements, such as the shay locomotive and the v-shaped log flume , made it easier to transport lumber across mountainous terrain. The tourism potential of the Sierra Nevada was recognized early in the European history of the range. Yosemite Valley
8820-537: The United States started to move to California via Sonora and Walker Passes . In the winter of 1844, Lt. John C. Frémont , accompanied by Kit Carson , was the first European American to see Lake Tahoe . The Frémont party camped at 8,050 ft (2,450 m). The California Gold Rush began at Sutter's Mill , near Coloma , in the western foothills of the Sierra. On January 24, 1848, James W. Marshall,
8967-464: The endorheic basin of Tulare Lake , which rarely overflows into the San Joaquin during wet years. The eastern slope watershed of the Sierra is much narrower; its rivers flow out into the endorheic Great Basin of eastern California and western Nevada . From north to south, the Susan River flows into intermittent Honey Lake , the Truckee River flows from Lake Tahoe into Pyramid Lake ,
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#17327725644109114-742: The American River!" On August 19, 1848, the New York Herald was the first major newspaper on the East Coast to report the discovery of gold. On December 5, 1848, President James Polk confirmed the discovery of gold in an address to Congress . Soon, waves of immigrants from around the world, later called the "forty-niners", invaded the Gold Country of California or "Mother Lode". Miners lived in tents, wood shanties, or deck cabins removed from abandoned ships. Wherever gold
9261-919: The Banks Pumping Plant to the Bethany Reservoir . The reservoir serves as a forebay for the South Bay Aqueduct via the South Bay Pumping Plant . From the Bethany Reservoir, the aqueduct flows by gravity approximately 60 mi (97 km) to the O'Neill Forebay at the San Luis Reservoir . From the O'Neill Forebay, it flows approximately 16 mi (26 km) to the Dos Amigos Pumping Plant . After Dos Amigos,
9408-572: The California Aqueduct, including one pumped-storage hydroelectric plant, Gianelli Power Plant . Gianelli is located at the base of San Luis Dam , which forms San Luis Reservoir , the largest offstream reservoir in the United States. The Castaic Power Plant, while similar and which is owned and operated by the Los Angeles Department of Water and Power , is located on the northern end of Castaic Lake , while Castaic Dam
9555-668: The Chrisman Pumping Plant. Chrisman is the last pumping plant before Edmonston Pumping Plant , which is 13 mi (21 km) from Chrisman. South of the plant the west branch splits off in a southwesterly direction to serve the Los Angeles Basin . At Edmonston Pumping Plant it is pumped 1,926 ft (587 m) over the Tehachapi Mountains . Water flows through the aqueduct in a series of abrupt rises and gradual falls. The water flows down
9702-647: The Devils Den Pump Plant, and terminates at Tank 5 on Vandenberg Space Force Base in Santa Barbara County . The Central Coast Water Authority (CCWA) extension, completed in 1997, is a (30–39 in) (76–99 cm) diameter pipeline that travels 42 mi (68 km) from Vandenberg through Vandenberg Village , Lompoc , Buellton , and Solvang where it terminates at Lake Cachuma in Los Padres National Forest . Coastal Branch facilities include: The aqueduct splits off into
9849-569: The East Branch and West Branch in extreme southern Kern County, north of the Los Angeles County line. The East Branch supplies Lake Palmdale and terminates at Lake Perris , in the area of the San Gorgonio Pass . It passes through parts of Kern, Los Angeles, San Bernardino, and Riverside counties. East Branch facilities include: The West Branch continues to head towards its terminus at Pyramid Lake and Castaic Lake in
9996-502: 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
10143-739: The Pacific Ocean at San Francisco . The northern third of the western Sierra is part of the Sacramento River watershed (including the Feather , Yuba , and American River tributaries), and the middle third is drained by the San Joaquin River (including the Mokelumne , Stanislaus , Tuolumne , and Merced River tributaries). The southern third of the range is drained by the Kings , Kaweah , Tule , and Kern rivers, which flow into
10290-722: The Park in 1906. In the same year, Sequoia National Park was formed to protect the Giant Sequoia: all logging of the Sequoia ceased at that time. In 1903, the city of San Francisco proposed building a hydroelectric dam to flood Hetch Hetchy Valley . The city and the Sierra Club argued over the dam for 10 years, until the U.S. Congress passed the Raker Act in 1913 and allowed dam building to proceed. O'Shaughnessy Dam
10437-431: The San Joaquin's approximately 6 million acre-feet (7.4 km). Intensive agricultural and municipal water consumption has reduced the present rate of outflow to about 17 million acre-feet (21 km) for the Sacramento and 3 million acre-feet (3.7 km) for the San Joaquin; however, these figures still vary widely from year to year. Over 25 million people, living both in the valley and in other regions of
10584-478: The Sierra Nevada increases gradually from north to south. Between Fredonyer Pass and Lake Tahoe, the peaks range from 5,000 feet (1,500 m) to more than 9,000 feet (2,700 m). The crest near Lake Tahoe is roughly 9,000 feet (2,700 m) high, with several peaks approaching the height of Freel Peak (10,881 ft or 3,317 m). Farther south, the highest peak in Yosemite National Park
10731-559: The Sierra Nevada is influenced by the Mediterranean climate of California. During the fall, winter and spring, precipitation in the Sierra ranges from 20 to 80 in (510 to 2,030 mm) where it occurs mostly as snow above 6,000 ft (1,800 m). Precipitation is highest on the central and northern portions of the western slope between 5,000 and 8,000 feet (1,500 and 2,400 m) elevation, due to orographic lift . Above 8,000 feet (2,400 m), precipitation diminishes on
10878-508: The Sierra Nevada started in the early 1800s, when settlers relied on hand tools and ox-teams. Before the California Gold Rush, the industry was relatively small, and most of the lumber used in the state was imported. However, as the demand for lumber to support the mining industry increased, logging became a major industry in the region. Initially, most of the lumber produced in California was used in mining. The Comstock Lode
11025-431: The Sierra have an alpine climate . The Sierra Nevada snowpack is the major source of water and a significant source of electric power generation in California. Many reservoirs were constructed in the canyons of the Sierra throughout the 20th century, Several major aqueducts serving both agriculture and urban areas distribute Sierra water throughout the state. However, the Sierra casts a rain shadow , which greatly affects
11172-662: The Sierra is a section of the Cascade–Sierra Mountains province, which in turn is part of the larger Pacific Mountain System physiographic division. The California Geological Survey states that "the northern Sierra boundary is marked where bedrock disappears under the Cenozoic volcanic cover of the Cascade Range." The range is drained on its western slope by the Central Valley watershed, which discharges into
11319-497: The Sierra's 63,118 km (24,370 sq mi) from logging and grazing. The United States Forest Service and the Bureau of Land Management currently control 52% of the land in the Sierra Nevada. Logging and grazing are generally allowed on land controlled by these agencies, under federal regulations that balance recreation and development on the land. The California Bighorn Sheep Zoological Area near Mount Williamson in
11466-532: The Sierra. The combination of river and glacier erosion exposed the uppermost portions of the plutons emplaced millions of years before, leaving only a remnant of metamorphic rock on top of some Sierra peaks. Extension of the Basin and Range continues today, leading to downdropping of crustal blocks just east of the Sierra Nevada during large earthquakes, such as the Lone Pine earthquake of 1872. The climate of
11613-650: The Tuolumne and Merced River drainage. The group may have been the first non-indigenous people to see Yosemite Valley . The Walker Party probably visited either the Tuolumne or Merced Groves of giant sequoia , becoming the first non-indigenous people to see the giant trees, but journals relating to the Walker party were destroyed in 1839, in a print shop fire in Philadelphia. Starting in 1841, emigrants from
11760-444: The activities of extra-terrestrial aliens , have no evidence to support them. The Sierra Nevada is divided into a number of biotic zones , each of which is defined by its climate and supports a number of interdependent species. Life in the higher elevation zones adapted to colder weather, and to most of the precipitation falling as snow. The rain shadow of the Sierra causes the eastern slope to be warmer and drier: each life zone
11907-413: 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,
12054-751: The aqueduct flows about 95 mi (153 km) to where the Coastal Branch splits from the "main line". The split is approximately 16 mi (26 km) south-southeast of Kettleman City . After the coastal branch, the line continues by gravity another 66 mi (106 km) to the Buena Vista Pumping Plant. From the Buena Vista, it flows approximately 27 mi (43 km) to the Teerink Pumping Plant. After Teerink it flows about 2.5 mi (4.0 km) to
12201-568: The aqueduct passes through parts of Contra Costa, Alameda, San Joaquin, Stanislaus, Merced, Fresno, and Kings counties. The aqueduct then divides into three branches: the Coastal Branch in the Central Valley, and the East and West Branches after passing over the Tehachapi Mountains . The Coastal Branch splits from the main line 11.3 mi (18.2 km) south-southeast of Kettleman City transiting Kings County , Kern County , San Luis Obispo County , and Santa Barbara County to deliver water to
12348-560: The aqueduct's pumping systems, the study also considered the possibility of supplying power to irrigation systems in the Central Valley to reduce reliance on diesel-powered irrigation pumps. Similar canal-spanning solar installations have been demonstrated in India, including a steel truss design in Gujarat and a suspension cable design in Punjab . From its beginning until its first branch,
12495-505: The area around Yosemite National Park and what would become Kings Canyon National Park . James S. Hutchinson , a noted mountaineer, climbed the Palisades (1904) and Mount Humphreys (1905). By 1912, the USGS published a set of maps of the Sierra Nevada, and the era of exploration was over. Logging in the Sierra Nevada has significantly impacted the landscape. The logging industry in
12642-408: The canal of the aqueduct has already occurred from subsidence which has made the canal less reliable. Capacity has been compromised due to damage to the canals and therefore has caused problems and delays with delivering the water across the state, as well as higher rates and costs for power and operation. A documentary about the decline of the United States' infrastructure, The Crumbling of America ,
12789-470: 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
12936-538: The clay compresses, causing subsidence. In cases of groundwater removal, disruption to land on the surface and underground water storage can either be elastic, meaning recoverable, or inelastic, meaning permanent. Coarse-grained sediment which holds groundwater can be drained and recharged with minimal underground and surface level damage and the change that does occur is considered seasonal subsidence. However, fine-grained sediment takes longer to draw water out of and recharge and if groundwater levels are left low for too long,
13083-473: The climate and ecology of the central Great Basin . This rain shadow is largely responsible for Nevada being the driest state in the United States. Precipitation varies substantially from year to year. It is not uncommon for some years to receive precipitation totals far above or below normal. The height of the range and the steepness of the Sierra Escarpment, particularly at the southern end of
13230-454: The coastal cities of San Luis Obispo , Santa Maria , and Santa Barbara . The Coastal Branch is 116 mi (187 km) and has five pump stations. Phase I, an above-ground aqueduct totaling 15 mi (24 km) from where it branches from the California Aqueduct, was completed in 1968. With construction beginning in 1994, Phase II consists of 101 mi (163 km) of a 42–57-inch (1.07–1.45 m) diameter buried pipeline extending from
13377-557: The compaction of the sediment is permanent and causes irreversible land subsidence. This often occurs due to human interference, but can also happen from natural phenomena. Subsidence can happen over very large areas or small little sections of land. This has occurred along the California Aqueduct of the State Water Project since construction. Human causes include; pumping, mining and fracking. Natural causes include; earthquakes, erosion, glacial movement, soil compaction and
13524-713: 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
13671-499: 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}} }
13818-656: The crest and north of 37.2°N. In the Triassic and into the Jurassic , an island arc collided with the west coast of North America and raised a chain of volcanoes, in an event called the Nevadan orogeny . Nearly all subaerial Sierran Arc volcanoes have since disappeared; their remains were redeposited during the Great Valley Sequence and the subsequent Cenozoic filling of the Great Valley, which
13965-407: The eastern edge of the southern Sierra. The Sierra Nevada has played an important role in the history of California and the United States. The California gold rush occurred in the western foothills from 1848 through 1855. Due to its inaccessibility, the range was not fully explored until 1912. Used in 1542 by Juan Rodríguez Cabrillo to describe a Pacific Coast Range ( Santa Cruz Mountains ),
14112-495: 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,
14259-416: 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
14406-423: 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
14553-797: 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
14700-423: 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 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
14847-423: 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 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
14994-465: The formation of sinkholes. Groundwater use and pumping in the area was the major water use for farmers and agriculture in the 1920s, and over time, this over-pumping resulted in land subsidence and a decline in groundwater-level resources. In time, this resulted in major land subsidence by the 1970s with local areas having 1 to 28 feet of subsidence. With the creation and use of the California Aqueduct along these regions, surface water being transported put
15141-524: 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
15288-474: 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
15435-465: The highest peak in the range. In 1873, Mount Whitney was climbed for the first time by 3 men from Lone Pine, California, on a fishing trip. From 1892 to 1897 Theodore Solomons made the first attempt to map a route along the crest of the Sierra. Other people finished exploring and mapping the Sierra. Bolton Coit Brown explored the Kings River watershed in 1895–1899. Joseph N. LeConte mapped
15582-400: 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 )) ,
15729-522: The lake, the peaks reach only a modest 8,000 feet (2,400 m). There are several notable geographical features in the Sierra Nevada: Communities in the Sierra Nevada include Paradise , South Lake Tahoe , Truckee , Grass Valley , Lee Vining , Mammoth Lakes , Sonora , Nevada City , Placerville , Pollock Pines , Portola , Auburn , Colfax and Kennedy Meadows . Much of the Sierra Nevada consists of federal lands and
15876-490: The largest pumping plant capacity at Dos Amigos is 15,450 cubic feet per second (437 m/s). A 2021 study published in Nature Sustainability estimated that the installation of solar panels over the canal could potentially reduce annual water evaporation by 11–22 million US gallons per mile (27,000,000–51,000,000 L/km) of canal. While electricity generated by the solar panels could be used by
16023-683: The largest tree in the world by volume; Lake Tahoe , the largest alpine lake in North America; Mount Whitney at 14,505 ft (4,421 m), the highest point in the contiguous United States ; and Yosemite Valley sculpted by glaciers from one-hundred-million-year-old granite , containing high waterfalls . The Sierra is home to three national parks , twenty-six wilderness areas, ten national forests, and two national monuments. These areas include Yosemite , Sequoia , and Kings Canyon National Parks , as well as Devils Postpile National Monument . More than one hundred million years ago during
16170-495: The late 1800s due to several factors. The Timber and Stone Act of 1878 allowed individuals to claim ownership of old-growth timber tracts, which were later consolidated under joint-stock companies , such as those founded by Midwestern lumber magnates. These companies had the financial resources to transport timber from remote locations and build sawmills near the tracks of the Southern Pacific railroad which connected
16317-455: The late 1800s, the logging industry moved westward due to the depletion of white pine forests in the upper Midwest. This shift was encouraged by the positive portrayal of the Sierra Nevada as a promising timber region. In 1859, Horace Greely marveled, "I never saw anything so much like good timber in the course of any seventy-five miles' travel as I saw in crossing the Sierra Nevada." The logging industry experienced significant growth in
16464-401: 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
16611-499: The miners, provoking counter-attacks on native villages. The Native Americans, out-gunned, were often slaughtered. The Gold Rush populated the western foothills of the Sierra Nevada, but even by 1860, most of the Sierra was unexplored. The state legislature authorized the California Geological Survey to officially explore the Sierra (and survey the rest of the state). Josiah Whitney was appointed to head
16758-440: The modern rivers flowing down the range are only 100–300 meters (300–1,000 ft) lower than their ancient counterparts from 30–40 million years ago and the overall elevation and bedrock topography of the northern Sierra Nevada has changed little since at least 30–40 million years ago. About 2.5 Ma, the Earth's climate cooled, and ice ages started. Glaciers carved out characteristic U-shaped canyons throughout
16905-712: The mountains were amongst a group led by fur trapper Jedediah Smith , crossing north of the Yosemite area in May 1827, at Ebbetts Pass . In 1833, a subgroup of the Bonneville Expedition led by Joseph Reddeford Walker was sent westward to find an overland route to California . Eventually the party discovered a route along the Humboldt River across present-day Nevada , ascending the Sierra Nevada, starting near present-day Bridgeport and descending between
17052-409: The mountains. Washo and Maidu were also in this area prior to the era of European exploration and displacement. American exploration of the mountain range started in 1827. Although prior to the 1820s there were Spanish missions , pueblos (towns), presidios (forts), and ranchos along the coast of California, no Spanish explorers visited the Sierra Nevada. The first Americans to visit
17199-399: The northern Sierran valleys with volcanic deposits. These pyroclastic flows, which continued for about 10 million years, were followed by andesitic lahars which nearly completely buried the northern Sierran landscape such that only the tallest peaks emerged above a volcanic plain. This second period of volcanism appears to have been triggered by crustal extension associated with extension of
17346-696: The oldest being metasedimentary rocks from the Cambrian in the Mount Morrison region. These dark-colored hornfels , slates , marbles , and schists are found in the western foothills (notably around Coarsegold , west of the Tehachapi Pass ) and east of the Sierra Crest. The earliest granite of the Sierra started to form in the Triassic period. This granite is mostly found east of
17493-521: The plural ( Smokies , Rockies , Cascades , etc.), since Sierra is already pluralized in its native language, some locals who live in "the Sierra" are not hesitant to admonish those who refer to the area as "the Sierras". However, there are historical and literary references that use the plural, such as the 1871 collection of Joaquin Miller poems, Songs of the Sierras . Ansel Adams , in response to
17640-412: 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
17787-467: 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
17934-401: 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 the work over any trajectory between these two points. It
18081-422: The pumping of groundwater and subsequent land subsidence. Farmers in and near the Central Valley have become reliant on groundwater especially with recent droughts impacting the amount of readily accessible surface water. However, overuse of groundwater can cause irreversible damage. During the 2011-2017 California drought , a record high drought, groundwater and its storage capabilities in the San Joaquin Valley saw
18228-1090: 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
18375-420: The range, produces a wind phenomenon known as the "Sierra Rotor". This is a horizontal rotation of the atmosphere just east of the crest of the Sierra, set in motion as an effect of strong westerly winds. Because of the large number of airplanes that have crashed in the Sierra Nevada, primarily due to the complex weather and atmospheric conditions such as downdrafts and microbursts caused by geography there,
18522-421: 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, the term "actual energy" gradually faded. Potential energy
18669-559: The scars of hydraulic mining, since the resulting exposed earth and downstream gravel deposits do not support plant life. It is estimated that by 1855, at least 300,000 gold-seekers, merchants, and other immigrants had arrived in California from around the world. The huge numbers of newcomers brought by the Gold Rush drove Native Americans out of their traditional hunting, fishing and food-gathering areas. To protect their homes and livelihood, some Native Americans responded by attacking
18816-564: The south part of the San Joaquin Valley, the alluvial fan of the Kings River and another one from Coast Ranges streams have created a divide and resultantly the currently dry Tulare basin of the Central Valley, into which flow four major Sierra Nevada rivers, the Kings, Kaweah , Tule and Kern . This basin, usually endorheic , formerly filled during heavy snowmelt and spilled out into the San Joaquin River. Called Tulare Lake , it
18963-458: The southern Sierra was established to protect the endangered Sierra Nevada bighorn sheep . Starting in 1981, hikers were unable to enter the Area from May 15 through December 15, in order to protect the sheep. As of 2010, the restriction has been lifted and access to the Area is open for the whole year. The earliest rocks in the Sierra Nevada are metamorphic roof pendants of Paleozoic age,
19110-418: 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
19257-401: The state, rely on the water carried by these rivers. Land subsidence is when the land gradually or suddenly sinks or settles due to movement or removal of natural materials such as water, minerals, oil and natural gases. More often than not, subsidence occurs when large quantities of groundwater are removed from sediment or rocks. As groundwater is drawn from deep underground layers of clay,
19404-404: 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
19551-425: The survey. Men of the survey, including William H. Brewer , Charles F. Hoffmann and Clarence King , explored the backcountry of what would become Yosemite National Park in 1863. In 1864, they explored the area around Kings Canyon . In 1869, John Muir started his wanderings in the Sierra Nevada range, and in 1871, King was the first to climb Mount Langley , mistakenly believing he had summited Mount Whitney ,
19698-755: 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
19845-490: The term "Sierra Nevada" was a general identification of less familiar ranges toward the interior. In 1776, Pedro Font 's map applied the name to the range currently known as the Sierra Nevada. The literal translation is "snowy mountains", from sierra "a range of mountains", 1610s, from Spanish sierra "jagged mountain range", lit. "saw", from Latin serra "a saw"; and from fem. of Spanish nevado "snowy". While many mountain ranges are unanimously referred to in
19992-552: 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
20139-698: 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
20286-424: The water from an entire river into a sluice alongside the river, and then dig for gold in the newly exposed river bottom. By 1853, most of the easily accessible gold had been collected, and attention turned to extracting gold from more difficult locations. Hydraulic mining was used on ancient gold-bearing gravel beds on hillsides and bluffs in the gold fields. In hydraulic mining, a high-pressure hose directed
20433-529: The western half of the Sierra, while the later plutons formed in the eastern half of the Sierra. At this time, the Sierra Nevada formed the western ramp of a high plateau to the east, the Nevadaplano . During this period, rivers cut deep canyons into the range, generating topographic relief similar to the modern Sierra Nevada. This period of incision was halted approximately 30 million years ago by vast outpourings of pyroclastic flows from Nevada which filled
20580-509: The western side, and the Kawaiisu and Tübatulabal tribes in the southern Sierra. Today, some historic intertribal trade route trails over mountain passes are known artifact locations, such as Duck Pass with its obsidian arrowheads . The California and Sierra Native American tribes were predominantly peaceful, with occasional territorial disputes between the Paiute and Sierra Miwok tribes in
20727-511: The western slope up to the crest, since most of the precipitation has been wrung out at lower elevations. Most parts of the range east of the crest are in a rain shadow , and receive less than 25 inches of precipitation per year. While most summer days are dry, afternoon thunderstorms are common, particularly during the North American Monsoon in mid and late summer. Some of these summer thunderstorms drop over an inch of rain in
20874-470: Was a major center for logging, with operations supplying lumber for the construction of mine structures, such as tunnels, shafts, and buildings, as well as fuel for the mines. Dan DeQuille observed in 1876, "the Comstock Lode may truthfully be said to be the tomb of the forests of the Sierra. Millions upon millions of feet of lumber are annually buried in the mines, nevermore to be resurrected.” In
21021-539: Was commissioned by the U.S. A&E network in the late 2000s. The documentary is typically shown on the History television channel in the United States, although other educational broadcasters globally have shown it. It features the Clifton Court Forebay (a primary intake point for California Aqueduct) as a "strategic piece of California freshwater infrastructure" subject to shutdown for up to two years if struck by an earthquake of magnitude 7.5 or greater. The aqueduct
21168-440: Was completed in 1923. Potential energy U = 1 ⁄ 2 ⋅ k ⋅ x ( elastic ) U = 1 ⁄ 2 ⋅ C ⋅ V ( electric ) U = − m ⋅ B ( magnetic ) In physics , potential energy 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
21315-479: Was discovered, hundreds of miners would collaborate to put up a camp and stake their claims. Because the gold in the California gravel beds was so richly concentrated, the early forty-niners simply panned for gold in California's rivers and streams. However, panning cannot take place on a large scale, and miners and groups of miners graduated to more complex placer mining. Groups of prospectors would divert
21462-440: Was first protected by the federal government in 1864. The Valley and Mariposa Grove were ceded to California in 1866 and turned into a state park. John Muir perceived overgrazing by sheep and logging of giant sequoia to be a problem in the Sierra. Muir successfully lobbied for the protection of the rest of Yosemite National Park: Congress created an Act to protect the park in 1890. The Valley and Mariposa Grove were added to
21609-440: 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 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
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