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Lever
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This article is about the simple machine. For other uses, see Lever (disambiguation).
Lever
Levers can be used to exert a large force over a small distance at one end by exerting only a small force over a greater distance at the other.
Classification
Simple machine
Industry
Construction
Weight
Mass times gravitational acceleration
Fuel source
potential and kinetic energy {mechanical energy }
Components
fulcrum or pivot, load and effort
A lever (/ˈliːvər/ or US: /ˈlɛvər/) is a machine consisting of a beam or rigid rod pivoted at a fixed hinge, or fulcrum. A lever is a rigid body capable of rotating on a point on itself. On the basis of the location of fulcrum, load and effort, the lever is divided into three types. It is one of the six simple machines identified by Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide leverage. The ratio of the output force to the input force is the mechanical advantage of the lever.
Contents
[hide]
1 Etymology
2 Early use
3 Force and levers
4 Classes of levers
5 Law of the lever
6 Virtual work and the law of the lever
7 See also
8 Notes
9 References
10 External links
Etymology[edit]
The word "lever" entered English about 1300 from Old French, in which the word was levier. This sprang from the stem of the verb lever, meaning "to raise". The verb, in turn, goes back to the Latin levare, itself from the adjective levis, meaning "light" (as in "not heavy"). The word's primary origin is the Proto-Indo-European (PIE) stem legwh-, meaning "light", "easy" or "nimble", among other things. The PIE stem also gave rise to the English word "light".[1]
Early use[edit]
The earliest remaining writings regarding levers date from the 3rd century BCE and were provided by Archimedes. 'Give me a place to stand, and I shall move the Earth with it' is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria). The distance required to do this might be exemplified in astronomical terms as the approximate distance to the Circinus galaxy (roughly 3.6 times the distance to the Andromeda Galaxy) - about 9 million light years.[citation needed]
It is assumed[by whom?] that in ancient Egypt, constructors used the lever to move and uplift obelisks weighing more than 100 tons.
Force and levers[edit]
A lever in balance
A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there is no friction in the hinge or bending in the beam. In this case, the power into the lever equals the power out, and the ratio of output to input force is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the law of the lever.
The mechanical advantage of a lever can be determined by considering the balance of moments or torque, T, about the fulcrum.
T 1 = F 1 a , {\displaystyle T_{1}=F_{1}a,\!} T 2 = F 2 b {\displaystyle T_{2}=F_{2}b\!}
where F1 is the input force to the lever and F2 is the output force. The distances a and b are the perpendicular distances between the forces and the fulcrum.
Since the moments of torque must be balanced, T 1 = T 2 {\displaystyle T_{1}=T_{2}\!} . So, F 1 a = F 2 b {\displaystyle F_{1}a=F_{2}b\!} .
The mechanical advantage of the lever is the ratio of output force to input force,
M A = F 2 F 1 = a b . {\displaystyle MA={\frac {F_{2}}{F_{1}}}={\frac {a}{b}}.\!}
This relationship shows that the mechanical advantage can be computed from ratio of the distances from the fulcrum to where the input and output forces are applied to the lever, assuming no losses due to friction, flexibility or wear. This remains true even though the horizontal distance (perpendicular to the pull of gravity) of both a and b change (diminish) as the lever changes to any position away from the horizontal.
Classes of levers[edit]
Three classes of levers
Levers are classified by the relative positions of the fulcrum, effort and resistance (or load). It is common to call the input force the effort and the output force the load or the resistance. This allows the identification of three classes of levers by the relative locations of the fulcrum, the resistance and the effort:[2]
Class 1: Fulcrum in the middle: the effort is applied on one side of the fulcrum and the resistance (or load) on the other side, for example, a seesaw, a crowbar or a pair of scissors. Mechanical advantage may be greater than, less than, or equal to 1.
Class 2: Resistance (or load) in the middle: the effort is applied on one side of the resistance and the fulcrum is located on the other side, for example, a wheelbarrow, a nutcracker, a bottle opener or the brake pedal of a car. Load arm is smaller than the effort arm. Mechanical advantage is always greater than 1. It is also called force multiplier lever.
Class 3: Effort in the middle: the resistance (or load) is on one side of the effort and the fulcrum is located on the other side, for example, a pair of tweezers or the human mandible. The effort arm is smaller than the load arm. Mechanical advantage is always less than 1. It is also called speed multiplier lever.
These cases are described by the mnemonic fre 123 where the fulcrum is in the middle for the 1st class lever, the resistance is in the middle for the 2nd class lever, and the effort is in the middle for the 3rd class lever.
Law of the lever[edit]
The lever is a movable bar that pivots on a fulcrum attached to a fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot.
Assuming the lever does not dissipate or store energy, the power into the lever must equal the power out of the lever. As the lever rotates around the fulcrum, points farther from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point farther from the pivot must be less than the force located at a point closer in, because power is the product of force and velocity.[3]
If a and b are distances from the fulcrum to points A and B and the force FA applied to A is the input and the force FB applied at B is the output, the ratio of the velocities of points A and B is given by a/b, so we have the ratio of the output force to the input force, or mechanical advantage, is given by
M A = F B F A = a b . {\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}}.}
This is the law of the lever, which was proven by Archimedes using geometric reasoning.[4] It shows that if the distance a from the fulcrum to where the input force is applied (point A) is greater than the distance b from fulcrum to where the output force is applied (point B), then the lever amplifies the input force. On the other hand, if the distance a from the fulcrum to the input force is less than the distance b from the fulcrum to the output force, then the lever reduces the input force.
The use of velocity in the static analysis of a lever is an application of the principle of virtual work.
Virtual work and the law of the lever[edit]
A lever is modeled as a rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever is operated by applying an input force FA at a point A located by the coordinate vector rA on the bar. The lever then exerts an output force FB at the point B located by rB. The rotation of the lever about the fulcrum P is defined by the rotation angle θ in radians.
This is an engraving from Mechanics Magazine published in London in 1824.
Let the coordinate vector of the point P that defines the fulcrum be rP, and introduce the lengths
a = | r A − r P | , b = | r B − r P | , {\displaystyle a=|\mathbf {r} _{A}-\mathbf {r} _{P}|,\quad b=|\mathbf {r} _{B}-\mathbf {r} _{P}|,}
which are the distances from the fulcrum to the input point A and to the output point B, respectively.
Now introduce the unit vectors eA and eB from the fulcrum to the point A and B, so
r A − r P = a e A , r B − r P = b e B . {\displaystyle \mathbf {r} _{A}-\mathbf {r} _{P}=a\mathbf {e} _{A},\quad \mathbf {r} _{B}-\mathbf {r} _{P}=b\mathbf {e} _{B}.}
The velocity of the points A and B are obtained as
v A = θ ˙ a e A ⊥ , v B = θ ˙ b e B ⊥ , {\displaystyle \mathbf {v} _{A}={\dot {\theta }}a\mathbf {e} _{A}^{\perp },\quad \mathbf {v} _{B}={\dot {\theta }}b\mathbf {e} _{B}^{\perp },}
where eA⊥ and eB⊥ are unit vectors perpendicular to eA and eB, respectively.
The angle θ is the generalized coordinate that defines the configuration of the lever, and the generalized force associated with this coordinate is given by
F θ = F A ⋅ ∂ v A ∂ θ ˙ − F B ⋅ ∂ v B ∂ θ ˙ = a ( F A ⋅ e A ⊥ ) − b ( F B ⋅ e B ⊥ ) = a F A − b F B , {\displaystyle F_{\theta }=\mathbf {F} _{A}\cdot {\frac {\partial \mathbf {v} _{A}}{\partial {\dot {\theta }}}}-\mathbf {F} _{B}\cdot {\frac {\partial \mathbf {v} _{B}}{\partial {\dot {\theta }}}}=a(\mathbf {F} _{A}\cdot \mathbf {e} _{A}^{\perp })-b(\mathbf {F} _{B}\cdot \mathbf {e} _{B}^{\perp })=aF_{A}-bF_{B},}
where FA and FB are components of the forces that are perpendicular to the radial segments PA and PB. The principle of virtual work states that at equilibrium the generalized force is zero, that is
F θ = a F A − b F B = 0. {\displaystyle F_{\theta }=aF_{A}-bF_{B}=0.\,\!}
Thus, the ratio of the output force FB to the input force FA is obtained as
M A = F B F A = a b , {\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}},}
which is the mechanical advantage of the lever.
This equation shows that if the distance a from the fulcrum to the point A where the input force is applied is greater than the distance b from fulcrum to the point B where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point A is less than from the fulcrum to the output point B, then the lever reduces the magnitude of the input force.
See also[edit]
Applied mechanics
Crowbar (tool)
Heavy equipment
Linkage (mechanical)
Mechanical advantage
Mechanism (engineering)
Simple machine
Tipping point (physics)
Tools
Virtual work
Notes[edit]
References[edit]
Jump up ^ Etymology of the word "lever" in the Online Etymological Dictionary
Jump up ^ Davidovits, Paul (2008). "Chapter 1". Physics in Biology and Medicine, Third edition. Academic Press. p. 10. ISBN 978-0-12-369411-9.
Jump up ^ Uicker, John; Pennock, Gordon; Shigley, Joseph (2010). Theory of Machines and Mechanisms (4th ed.). Oxford University Press, USA. ISBN 978-0-19-537123-9.
Jump up ^ Usher, A. P. (1929). A History of Mechanical Inventions. Harvard University Press (reprinted by Dover Publications 1988). p. 94. ISBN 978-0-486-14359-0. OCLC 514178. Retrieved 7 April 2013.
External links[edit]
Wikimedia Commons has media related to Levers.
Look up lever in Wiktionary, the free dictionary.
Lever at Diracdelta science and engineering encyclopedia
A Simple Lever by Stephen Wolfram, Wolfram Demonstrations Project.
Levers: Simple Machines at EnchantedLearning.com
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Inclined plane
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text:
Pied crow
From Wikipedia, the free encyclopedia
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Pied crow
In Etosha National Park, Namibia
Conservation status

Least Concern (IUCN 3.1)[1]
Scientific classification
Kingdom: Animalia
Phylum: Chordata
Class: Aves
Order: Passeriformes
Family: Corvidae
Genus: Corvus
Species: C. albus
Binomial name
Corvus albus
Statius Muller, 1776
The pied crow (Corvus albus) is a widely distributed African bird species in the crow genus.
Structurally, the pied crow is better thought of as a small crow-sized Raven (except the lack of throat hackles, fan-shaped tail and other more crow-like traits), especially as it can hybridise with the Somali crow (sometimes called the Dwarf Raven) where their ranges meet in the Horn of Africa. Its behaviour, though, is more typical of the Eurasian carrion crows, and it may be a modern link (along with the Somali crow) between the Eurasian crows and the common raven.
Contents
[hide]
1 Description
1.1 Measurements
1.2 Identification
1.3 Vocalisation
2 Taxonomy
3 Distribution and habitat
4 Behaviour
4.1 Diet
4.2 Reproduction
5 References
5.1 Cited text
6 External links
Description[edit]
It is approximately the size of the European carrion crow (46–52 cm in length) but has a longer bill, slightly longer tail and wings, and longer legs. As its name suggests, its glossy black head and neck are interrupted by a large area of white feathering from the shoulders down to the lower breast but the tail, bill and wings are black. The eyes of a fully matured bird are dark brown. The white plumage of immature birds is often mixed with black. It resembles the White-necked and thick-billed ravens but is much smaller, less stocky and has a smaller bill.[2]
in Ghana
In flight
Measurements[edit]
Length 46 – 52 cm [3]
Wingspan 85 to 98 centimetres (17 unsexed birds)[3]
Weight 520g [3]
Identification[edit]
In southern Africa the range overlaps with the white-necked raven. The pied crow is smaller and has a white chest and belly with a black, more delicate beak compared to the black chest and belly of the larger white-necked raven which also has a white tipped and weightier beak.[4]
Vocalisation[edit]
The voice is described as a harsh "ar-ar-ar-ar" or "karh-karh-karh" and lacks the whispering note of the White-necked raven.[5]
Taxonomy[edit]
The pied crow was first described in 1776 by Statius Muller. Its specific name is the Latin adjective albus, meaning "white". Recent findings indicate that based on mitochondrial DNA, common ravens (C. corax) from the north of the United States are more closely related to those in Europe and Asia than to those in the California clade, and that common ravens in the California clade (C. corax sinuatus) are more closely related to the Chihuahuan raven (C. cryptoleucus) than to those in the Holarctic clade.[6] while ravens in the Holarctic clade are more closely related to the pied crow (C. albus) than they are to the California clade.[7] Thus, the common raven species as traditionally delimited is considered to be paraphyletic.[7]
Distribution and habitat[edit]
This species, Africa's most widespread member of the genus Corvus, occurs from Sub-Saharan Africa, specifically Senegal, Sudan, Somalia and Eritrea down to the Cape of Good Hope and on the large island of Madagascar, the Comoros islands, Aldabra group islands, Zanzibar, Pemba and Fernando Po. Although the species is still a vagrant north of the Sahara, a breeding case [8] and a number of long-staying birds [9][10] were observed during the last few years in Morocco. It inhabits mainly open country with villages and towns nearby. It does not occur in the equatorial rainforest region. It is rarely seen very far from human habitation, though it is not as tied to the urban way of life as the house crow (Corvus splendens) of Asia, and may be encountered far from human habitation in Eritrea.[2]
Behaviour[edit]
Pied crows are generally encountered in pairs or small groups, although an abundant source of food may bring large numbers of birds. The species behaves in a similar manner to the hooded and carrion crows.[11] In Dakar, birds have been observed mobbing passing ospreys and snake eagles but avoiding black kites.
Diet[edit]
All of its food is obtained from the ground such as insects and other small invertebrates, small reptiles, small mammals, young birds and eggs, grain, peanuts, carrion and any scraps of human food and sometimes fruit and even mushrooms.[12] It has been recorded killing and eating roosting bats and is frequently seen scavenging around slaughterhouses in large numbers.
Reproduction[edit]
The nest is usually built in tall, isolated trees, though sometimes smaller ones are used, depending on availability. The cross supports of telephone poles are also frequently used, and both sexes build the nest. A clutch of 3–6 eggs is laid from September to November (depending on latitude) and are pale green spotted with various shades of brown. The eggs are normally covered when the incubating female leaves the nest. Incubation is 18–19 days and the young are usually fledged by around 45 days. Both sexes rear the young.[11]
References[edit]
Jump up ^ BirdLife International (2013). "Corvus albus". IUCN Red List of Threatened Species. Version 2013.2. International Union for Conservation of Nature. Retrieved 26 November 2013.
^ Jump up to: a b Goodwin, p. 132
^ Jump up to: a b c Roberts' Birds of Southern Africa. The John Voelker Bird Book Fund. p. 474. ISBN 0-620-17583-4.
Jump up ^ Roberts' Birds of Southern Africa. The John Voelker Bird Book Fund. pp. 474–477. ISBN 0-620-17583-4.
Jump up ^ Goodwin, p. 134
Jump up ^ US Geological Survey. "California Ravens Are a Breed Apart". Retrieved 2007-05-11.
^ Jump up to: a b Feldman, Christopher R.; Omland, Kevin E. (March 2005). "Phylogenetics of the common raven complex (Corvus: Corvidae) and the utility of ND4, COI and intron 7 of the β-fibrinogen gene in avian molecular systematics". Zoologica Scripta. 34 (2): 145–156. doi:10.1111/j.1463-6409.2005.00182.x.
Jump up ^ Batty, C. 2010. Pied Crows in Western Sahara, Morocco.Dutch Birding 32: 329.
Jump up ^ MaghrebOrnitho. 2015. Pied Crow (Corvus albus) near Fnideq, northern Morocco. Consulted: 11 February 2017.
Jump up ^ MaghrebOrnitho. 2017. The resident Pied Crow at Mhamid, eastern Sahara (2015-2017). Consulted: 11 February 2017.
^ Jump up to: a b Goodwin, p. 133
Jump up ^ Goodwin, pp. 132-33
Cited text[edit]
Goodwin D. (1983). Crows of the World. Queensland University Press, St Lucia, Qld. ISBN 0-7022-1015-3.
External links[edit]
Wikimedia Commons has media related to Corvus albus.
Pied Crow - Species text in The Atlas of Southern African Birds.
Pied Crow videos, photos & sounds on the Internet Bird Collection
How many tortoises do a pair of Pied Crows Corvus alba need to kill to feed their chicks? - Paper in ejournal Ornithological Observations
[show]
v
t
e
Extant species of family Corvidae
Kingdom: Animalia
Phylum: Chordata
Class: Aves
Subclass: Neornithes
Superorder: Neognathae
Order: Passeriformes
[show]
Family Corvidae
Choughs
Pyrrhocorax
Alpine chough (P. graculus)
Red-billed chough (P. pyrrhocorax)
Treepies
Crypsirina
Hooded treepie (C. cucullata)
Black racket-tailed treepie (C. temia)
Dendrocitta
Andaman treepie (D. bayleyi)
Bornean treepie (D. cinerascens)
Grey treepie (D. formosae)
Black-faced treepie (D. frontalis)
White-bellied treepie (D. leucogastra)
Sumatran treepie (D. occipitalis)
Rufous treepie (D. vagabunda)
Platysmurus
Black magpie (P. leucopterus)
Bornean black magpie (P. l. aterrimus)
Temnurus
Ratchet-tailed treepie (T. temnurus)
Oriental
magpies
Cissa
Common green magpie (C. chinensis)
Indochinese green magpie (C. hypoleuca)
Bornean green magpie (C. jefferyi)
Javan green magpie (C. thalassina)
Urocissa
Taiwan blue magpie (U. caerulea)
Red-billed blue magpie (U. erythrorhyncha)
Yellow-billed blue magpie (U. flavirostris)
Sri Lanka blue magpie (U. ornata)
White-winged magpie (U. whiteheadi)
Old World jays
Garrulus
Eurasian jay (G. glandarius)
Lanceolated jay (G. lanceolatus)
Lidth's jay (G. lidthi)
Podoces
(Ground jays)
Biddulph's ground jay (P. biddulphi)
Henderson's ground jay (P. hendersoni)
Pander's ground jay (P. panderi)
Persian ground jay (P. pleskei)
Ptilostomus
Piapiac (P. afer)
Stresemann's
bushcrow
Zavattariornis
Stresemann's bushcrow (Z. stresemanni)
[hide]
Family Corvidae (continued)
Nutcrackers
Nucifraga
Spotted nutcracker (N. caryocatactes)
Clark's nutcracker (N. columbiana)
Holarctic
magpies
Pica
Black-billed magpie (P. hudsonia)
Yellow-billed magpie (P. nuttalli)
Eurasian magpie (P. pica)
Korean magpie (P. sericea)
True crows
(crows, ravens,
jackdaws and rooks)
Corvus
Australian and Melanesian species
Little crow (C. bennetti)
Australian raven (C. coronoides)
Bismarck crow (C. insularis)
Brown-headed crow (C. fuscicapillus)
Bougainville crow (C. meeki)
Little raven (C. mellori)
New Caledonian crow (C. moneduloides)
Torresian crow (C. orru)
Forest raven (C. tasmanicus)
Grey crow (C. tristis)
Long-billed crow (C. validus)
White-billed crow (C. woodfordi)
Pacific island species
Hawaiian crow (C. hawaiiensis)
Mariana crow (C. kubaryi)
Tropical Asian species
Daurian jackdaw (C. dauuricus)
Slender-billed crow (C. enca)
Flores crow (C. florensis)
Large-billed crow (C. macrorhynchos)
Eastern jungle crow (C. levaillantii)
Indian jungle crow (C. culminatus)
House crow (C. splendens)
Collared crow (C. torquatus)
Piping crow (C. typicus)
Banggai crow (C. unicolor)
Violet crow (C. violaceus)
Eurasian and North African species
Mesopotamian crow (C. capellanus)
Hooded crow (C. cornix)
Carrion crow (C. corone)
Rook (C. frugilegus)
Jackdaw (C. monedula )
Eastern carrion crow (C. orientalis)
Fan-tailed raven (C. rhipidurus)
Brown-necked raven (C. ruficollis)
Holarctic species
Common raven (C. corax)
North and Central American species
American crow (C. brachyrhynchos)
Northwestern crow (C. caurinus)
Chihuahuan raven (C. cryptoleucus)
Tamaulipas crow (C. imparatus)
Jamaican crow (C. jamaicensis)
White-necked crow (C. leucognaphalus)
Cuban crow (C. nasicus)
Fish crow (C. ossifragus)
Palm crow (C. palmarum)
Sinaloan crow (C. sinaloae)
Tropical African species
White-necked raven (C. albicollis)
Pied crow (C. albus)
Cape crow (C. capensis)
Thick-billed raven (C. crassirostris)
Somali crow (C. edithae)
[show]
Family Corvidae (continued)
Azure-winged
magpies
Cyanopica
Iberian magpie (C. cooki)
Azure-winged magpie (C. cyanus)
Grey jays
Perisoreus
Grey jay (P. canadensis)
Siberian jay (P. infaustus)
Sichuan jay (P. internigrans)
New World jays
Aphelocoma
(Scrub jays)
California scrub jay (A. californica)
Island scrub jay (A. insularis)
Woodhouse's scrub jay (A. woodhouseii)
Florida scrub jay (A. coerulescens)
Mexican jay (A. ultramarina)
Unicolored jay (A. unicolor)
Calocitta
(Magpie-Jays)
Black-throated magpie-jay (C. colliei)
White-throated Magpie-jay (C. formosa)
Cyanocitta
Blue jay (C. cristata)
Steller's jay (C. stelleri)
Cyanocorax
Black-chested jay (C. affinis)
Purplish-backed jay (C. beecheii)
Azure jay (C. caeruleus)
Cayenne jay (C. cayanus)
Plush-crested jay (C. chrysops)
Curl-crested jay (C. cristatellus)
Purplish jay (C. cyanomelas)
White-naped jay (C. cyanopogon)
Tufted jay (C. dickeyi)
Azure-naped jay (C. heilprini)
Bushy-crested jay (C. melanocyaneus)
Brown jay (C. morio)
White-tailed jay (C. mystacalis)
San Blas jay (C. sanblasianus)
Violaceous jay (C. violaceus)
Green jay (C. ynca)
Yucatan jay (C. yucatanicus)
Cyanolyca
Silvery-throated jay (C. argentigula)
Black-collared jay (C. armillata)
Azure-hooded jay (C. cucullata)
White-throated jay (C. mirabilis)
Dwarf jay (C. nana)
Beautiful jay (C. pulchra)
Black-throated jay (C. pumilo)
Turquoise jay (C. turcosa)
White-collared jay (C. viridicyana)
Gymnorhinus
Pinyon jay (G. cyanocephalus)
Taxon identifiers
Wd: Q949603
ADW: Corvus_albus
eBird: piecro1
EoL: 917338
GBIF: 2482519
iNaturalist: 8038
ITIS: 559490
IUCN: 22735894
NCBI: 30421
WoRMS: 221035
Retrieved from "https://en.wikipedia.org/w/index.php?title=Pied_crow&oldid=826034520"
Categories:
IUCN Red List least concern species
Corvus (genus)
Birds of Sub-Saharan Africa
Birds described in 1776
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