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The French acquired a copy of the British war plans, including the activities of Shirley and Johnson. Shirley's efforts to fortify Oswego were bogged down in logistical difficulties, exacerbated by Shirley's inexperience in managing large expeditions. In conjunction, Shirley was made aware that the French were massing for an attack on Fort Oswego in his absence when he planned to attack Fort Niagara. As a response, Shirley left garrisons at Oswego, Fort Bull, and Fort Williams (the latter two located on the Oneida Carry between the Mohawk River and Wood Creek at present-day Rome, New York). Supplies for use in the projected attack on Niagara were cached at Fort Bull. |
Johnson's expedition was better organized than Shirley's, which was noticed by New France's governor, the Marquis de Vaudreuil. He had primarily been concerned about the extended supply line to the forts on the Ohio, and had sent Baron Dieskau to lead the defenses at Frontenac against Shirley's expected attack. When Johnson was seen as the larger threat, Vaudreuil sent Dieskau to Fort St. Frédéric to meet that threat. Dieskau planned to attack the British encampment at Fort Edward at the upper end of navigation on the Hudson River, but Johnson had strongly fortified it, and Dieskau's Indian support was reluctant to attack. The two forces finally met in the bloody Battle of Lake George between Fort Edward and Fort William Henry. The battle ended inconclusively, with both sides withdrawing from the field. Johnson's advance stopped at Fort William Henry, and the French withdrew to Ticonderoga Point, where they began the construction of Fort Carillon (later renamed Fort Ticonderoga after British capture in 1759). |
Colonel Monckton, in the sole British success that year, captured Fort Beauséjour in June 1755, cutting the French fortress at Louisbourg off from land-based reinforcements. To cut vital supplies to Louisbourg, Nova Scotia's Governor Charles Lawrence ordered the deportation of the French-speaking Acadian population from the area. Monckton's forces, including companies of Rogers' Rangers, forcibly removed thousands of Acadians, chasing down many who resisted, and sometimes committing atrocities. More than any other factor, the cutting off of supplies to Louisbourg led to its demise. The Acadian resistance, in concert with native allies, including the Mi'kmaq, was sometimes quite stiff, with ongoing frontier raids (against Dartmouth and Lunenburg among others). Other than the campaigns to expel the Acadians (ranging around the Bay of Fundy, on the Petitcodiac and St. John rivers, and Île Saint-Jean), the only clashes of any size were at Petitcodiac in 1755 and at Bloody Creek near Annapolis Royal in 1757. |
Following the death of Braddock, William Shirley assumed command of British forces in North America. At a meeting in Albany in December 1755, he laid out his plans for 1756. In addition to renewing the efforts to capture Niagara, Crown Point and Duquesne, he proposed attacks on Fort Frontenac on the north shore of Lake Ontario and an expedition through the wilderness of the Maine district and down the Chaudière River to attack the city of Quebec. Bogged down by disagreements and disputes with others, including William Johnson and New York's Governor Sir Charles Hardy, Shirley's plan had little support. |
Newcastle replaced him in January 1756 with Lord Loudoun, with Major General James Abercrombie as his second in command. Neither of these men had as much campaign experience as the trio of officers France sent to North America. French regular army reinforcements arrived in New France in May 1756, led by Major General Louis-Joseph de Montcalm and seconded by the Chevalier de Lévis and Colonel François-Charles de Bourlamaque, all experienced veterans from the War of the Austrian Succession. During that time in Europe, on May 18, 1756, England formally declared war on France, which expanded the war into Europe, which was later to be known as the Seven Years' War. |
Governor Vaudreuil, who harboured ambitions to become the French commander in chief (in addition to his role as governor), acted during the winter of 1756 before those reinforcements arrived. Scouts had reported the weakness of the British supply chain, so he ordered an attack against the forts Shirley had erected at the Oneida Carry. In the March Battle of Fort Bull, French forces destroyed the fort and large quantities of supplies, including 45,000 pounds of gunpowder. They set back any British hopes for campaigns on Lake Ontario, and endangered the Oswego garrison, already short on supplies. French forces in the Ohio valley also continued to intrigue with Indians throughout the area, encouraging them to raid frontier settlements. This led to ongoing alarms along the western frontiers, with streams of refugees returning east to get away from the action. |
The new British command was not in place until July. When he arrived in Albany, Abercrombie refused to take any significant actions until Loudoun approved them. Montcalm took bold action against his inertia. Building on Vaudreuil's work harassing the Oswego garrison, Montcalm executed a strategic feint by moving his headquarters to Ticonderoga, as if to presage another attack along Lake George. With Abercrombie pinned down at Albany, Montcalm slipped away and led the successful attack on Oswego in August. In the aftermath, Montcalm and the Indians under his command disagreed about the disposition of prisoners' personal effects. The Europeans did not consider them prizes and prevented the Indians from stripping the prisoners of their valuables, which angered the Indians. |
Loudoun, a capable administrator but a cautious field commander, planned one major operation for 1757: an attack on New France's capital, Quebec. Leaving a sizable force at Fort William Henry to distract Montcalm, he began organizing for the expedition to Quebec. He was then ordered by William Pitt, the Secretary of State responsible for the colonies, to attack Louisbourg first. Beset by delays of all kinds, the expedition was finally ready to sail from Halifax, Nova Scotia in early August. In the meantime French ships had escaped the British blockade of the French coast, and a fleet outnumbering the British one awaited Loudoun at Louisbourg. Faced with this strength, Loudoun returned to New York amid news that a massacre had occurred at Fort William Henry. |
French irregular forces (Canadian scouts and Indians) harassed Fort William Henry throughout the first half of 1757. In January they ambushed British rangers near Ticonderoga. In February they launched a daring raid against the position across the frozen Lake George, destroying storehouses and buildings outside the main fortification. In early August, Montcalm and 7,000 troops besieged the fort, which capitulated with an agreement to withdraw under parole. When the withdrawal began, some of Montcalm's Indian allies, angered at the lost opportunity for loot, attacked the British column, killing and capturing several hundred men, women, children, and slaves. The aftermath of the siege may have contributed to the transmission of smallpox into remote Indian populations; as some Indians were reported to have traveled from beyond the Mississippi to participate in the campaign and returned afterward having been exposed to European carriers. |
Vaudreuil and Montcalm were minimally resupplied in 1758, as the British blockade of the French coastline limited French shipping. The situation in New France was further exacerbated by a poor harvest in 1757, a difficult winter, and the allegedly corrupt machinations of François Bigot, the intendant of the territory. His schemes to supply the colony inflated prices and were believed by Montcalm to line his pockets and those of his associates. A massive outbreak of smallpox among western tribes led many of them to stay away from trading in 1758. While many parties to the conflict blamed others (the Indians blamed the French for bringing "bad medicine" as well as denying them prizes at Fort William Henry), the disease was probably spread through the crowded conditions at William Henry after the battle. Montcalm focused his meager resources on the defense of the St. Lawrence, with primary defenses at Carillon, Quebec, and Louisbourg, while Vaudreuil argued unsuccessfully for a continuation of the raiding tactics that had worked quite effectively in previous years. |
The British failures in North America, combined with other failures in the European theater, led to the fall from power of Newcastle and his principal military advisor, the Duke of Cumberland. Newcastle and Pitt joined in an uneasy coalition in which Pitt dominated the military planning. He embarked on a plan for the 1758 campaign that was largely developed by Loudoun. He had been replaced by Abercrombie as commander in chief after the failures of 1757. Pitt's plan called for three major offensive actions involving large numbers of regular troops, supported by the provincial militias, aimed at capturing the heartlands of New France. Two of the expeditions were successful, with Fort Duquesne and Louisbourg falling to sizable British forces. |
The third invasion was stopped with the improbable French victory in the Battle of Carillon, in which 3,600 Frenchmen famously and decisively defeated Abercrombie's force of 18,000 regulars, militia and Native American allies outside the fort the French called Carillon and the British called Ticonderoga. Abercrombie saved something from the disaster when he sent John Bradstreet on an expedition that successfully destroyed Fort Frontenac, including caches of supplies destined for New France's western forts and furs destined for Europe. Abercrombie was recalled and replaced by Jeffery Amherst, victor at Louisbourg. |
In the aftermath of generally poor French results in most theaters of the Seven Years' War in 1758, France's new foreign minister, the duc de Choiseul, decided to focus on an invasion of Britain, to draw British resources away from North America and the European mainland. The invasion failed both militarily and politically, as Pitt again planned significant campaigns against New France, and sent funds to Britain's ally on the mainland, Prussia, and the French Navy failed in the 1759 naval battles at Lagos and Quiberon Bay. In one piece of good fortune, some French supply ships managed to depart France, eluding the British blockade of the French coast. |
British victories continued in all theaters in the Annus Mirabilis of 1759, when they finally captured Ticonderoga, James Wolfe defeated Montcalm at Quebec (in a battle that claimed the lives of both commanders), and victory at Fort Niagara successfully cut off the French frontier forts further to the west and south. The victory was made complete in 1760 when, despite losing outside Quebec City in the Battle of Sainte-Foy, the British were able to prevent the arrival of French relief ships in the naval Battle of the Restigouche while armies marched on Montreal from three sides. |
In September 1760, and before any hostilities erupted, Governor Vaudreuil negotiated from Montreal a capitulation with General Amherst. Amherst granted Vaudreuil's request that any French residents who chose to remain in the colony would be given freedom to continue worshiping in their Roman Catholic tradition, continued ownership of their property, and the right to remain undisturbed in their homes. The British provided medical treatment for the sick and wounded French soldiers and French regular troops were returned to France aboard British ships with an agreement that they were not to serve again in the present war. |
The war in North America officially ended with the signing of the Treaty of Paris on 10 February 1763, and war in the European theatre of the Seven Years' War was settled by the Treaty of Hubertusburg on 15 February 1763. The British offered France the choice of surrendering either its continental North American possessions east of the Mississippi or the Caribbean islands of Guadeloupe and Martinique, which had been occupied by the British. France chose to cede the former, but was able to negotiate the retention of Saint Pierre and Miquelon, two small islands in the Gulf of St. Lawrence, along with fishing rights in the area. They viewed the economic value of the Caribbean islands' sugar cane to be greater and easier to defend than the furs from the continent. The contemporaneous French philosopher Voltaire referred to Canada disparagingly as nothing more than a few acres of snow. The British, for their part, were happy to take New France, as defence of their North American colonies would no longer be an issue and also because they already had ample places from which to obtain sugar. Spain, which traded Florida to Britain to regain Cuba, also gained Louisiana, including New Orleans, from France in compensation for its losses. Great Britain and Spain also agreed that navigation on the Mississippi River was to be open to vessels of all nations. |
Britain gained control of French Canada and Acadia, colonies containing approximately 80,000 primarily French-speaking Roman Catholic residents. The deportation of Acadians beginning in 1755 resulted in land made available to migrants from Europe and the colonies further south. The British resettled many Acadians throughout its North American provinces, but many went to France, and some went to New Orleans, which they had expected to remain French. Some were sent to colonize places as diverse as French Guiana and the Falkland Islands; these latter efforts were unsuccessful. Others migrated to places like Saint-Domingue, and fled to New Orleans after the Haitian Revolution. The Louisiana population contributed to the founding of the modern Cajun population. (The French word "Acadien" evolved to "Cadien", then to "Cajun".) |
Following the treaty, King George III issued the Royal Proclamation of 1763 on October 7, 1763, which outlined the division and administration of the newly conquered territory, and to some extent continues to govern relations between the government of modern Canada and the First Nations. Included in its provisions was the reservation of lands west of the Appalachian Mountains to its Indian population, a demarcation that was at best a temporary impediment to a rising tide of westward-bound settlers. The proclamation also contained provisions that prevented civic participation by the Roman Catholic Canadians. When accommodations were made in the Quebec Act in 1774 to address this and other issues, religious concerns were raised in the largely Protestant Thirteen Colonies over the advance of "popery"; the Act maintained French Civil law, including the seigneurial system, a medieval code soon to be removed from France within a generation by the French Revolution. |
For many native populations, the elimination of French power in North America meant the disappearance of a strong ally and counterweight to British expansion, leading to their ultimate dispossession. The Ohio Country was particularly vulnerable to legal and illegal settlement due to the construction of military roads to the area by Braddock and Forbes. Although the Spanish takeover of the Louisiana territory (which was not completed until 1769) had modest repercussions, the British takeover of Spanish Florida resulted in the westward migration of tribes that did not want to do business with the British, and a rise in tensions between the Choctaw and the Creek, historic enemies whose divisions the British at times exploited. The change of control in Florida also prompted most of its Spanish Catholic population to leave. Most went to Cuba, including the entire governmental records from St. Augustine, although some Christianized Yamasee were resettled to the coast of Mexico. |
Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part this was due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years. By the early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light, and also provided insight into the forces produced by gravitation and inertia. |
With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised a Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational.:2–10:79 High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. |
Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground and that they will stay that way if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force. This theory, based on the everyday experience of how objects move, such as the constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles, such as the flight of arrows. The place where the archer moves the projectile was at the start of the flight, and while the projectile sailed through the air, no discernible efficient cause acts on it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries the projectile to its target. This explanation demands a continuum like air for change of place in general. |
The shortcomings of Aristotelian physics would not be fully corrected until the 17th century work of Galileo Galilei, who was influenced by the late Medieval idea that objects in forced motion carried an innate force of impetus. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the Aristotelian theory of motion early in the 17th century. He showed that the bodies were accelerated by gravity to an extent that was independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction. |
Newton's First Law of Motion states that objects continue to move in a state of constant velocity unless acted upon by an external net force or resultant force. This law is an extension of Galileo's insight that constant velocity was associated with a lack of net force (see a more detailed description of this below). Newton proposed that every object with mass has an innate inertia that functions as the fundamental equilibrium "natural state" in place of the Aristotelian idea of the "natural state of rest". That is, the first law contradicts the intuitive Aristotelian belief that a net force is required to keep an object moving with constant velocity. By making rest physically indistinguishable from non-zero constant velocity, Newton's First Law directly connects inertia with the concept of relative velocities. Specifically, in systems where objects are moving with different velocities, it is impossible to determine which object is "in motion" and which object is "at rest". In other words, to phrase matters more technically, the laws of physics are the same in every inertial frame of reference, that is, in all frames related by a Galilean transformation. |
For instance, while traveling in a moving vehicle at a constant velocity, the laws of physics do not change from being at rest. A person can throw a ball straight up in the air and catch it as it falls down without worrying about applying a force in the direction the vehicle is moving. This is true even though another person who is observing the moving vehicle pass by also observes the ball follow a curving parabolic path in the same direction as the motion of the vehicle. It is the inertia of the ball associated with its constant velocity in the direction of the vehicle's motion that ensures the ball continues to move forward even as it is thrown up and falls back down. From the perspective of the person in the car, the vehicle and everything inside of it is at rest: It is the outside world that is moving with a constant speed in the opposite direction. Since there is no experiment that can distinguish whether it is the vehicle that is at rest or the outside world that is at rest, the two situations are considered to be physically indistinguishable. Inertia therefore applies equally well to constant velocity motion as it does to rest. |
The concept of inertia can be further generalized to explain the tendency of objects to continue in many different forms of constant motion, even those that are not strictly constant velocity. The rotational inertia of planet Earth is what fixes the constancy of the length of a day and the length of a year. Albert Einstein extended the principle of inertia further when he explained that reference frames subject to constant acceleration, such as those free-falling toward a gravitating object, were physically equivalent to inertial reference frames. This is why, for example, astronauts experience weightlessness when in free-fall orbit around the Earth, and why Newton's Laws of Motion are more easily discernible in such environments. If an astronaut places an object with mass in mid-air next to himself, it will remain stationary with respect to the astronaut due to its inertia. This is the same thing that would occur if the astronaut and the object were in intergalactic space with no net force of gravity acting on their shared reference frame. This principle of equivalence was one of the foundational underpinnings for the development of the general theory of relativity. |
Newton's Second Law asserts the direct proportionality of acceleration to force and the inverse proportionality of acceleration to mass. Accelerations can be defined through kinematic measurements. However, while kinematics are well-described through reference frame analysis in advanced physics, there are still deep questions that remain as to what is the proper definition of mass. General relativity offers an equivalence between space-time and mass, but lacking a coherent theory of quantum gravity, it is unclear as to how or whether this connection is relevant on microscales. With some justification, Newton's second law can be taken as a quantitative definition of mass by writing the law as an equality; the relative units of force and mass then are fixed. |
Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies,[Note 3] and thus that there is no such thing as a unidirectional force or a force that acts on only one body. Whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction. This law is sometimes referred to as the action-reaction law, with F called the "action" and −F the "reaction". The action and the reaction are simultaneous: |
This means that in a closed system of particles, there are no internal forces that are unbalanced. That is, the action-reaction force shared between any two objects in a closed system will not cause the center of mass of the system to accelerate. The constituent objects only accelerate with respect to each other, the system itself remains unaccelerated. Alternatively, if an external force acts on the system, then the center of mass will experience an acceleration proportional to the magnitude of the external force divided by the mass of the system.:19-1 |
Since forces are perceived as pushes or pulls, this can provide an intuitive understanding for describing forces. As with other physical concepts (e.g. temperature), the intuitive understanding of forces is quantified using precise operational definitions that are consistent with direct observations and compared to a standard measurement scale. Through experimentation, it is determined that laboratory measurements of forces are fully consistent with the conceptual definition of force offered by Newtonian mechanics. |
Forces act in a particular direction and have sizes dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as "vector quantities". This means that forces follow a different set of mathematical rules than physical quantities that do not have direction (denoted scalar quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result. If both of these pieces of information are not known for each force, the situation is ambiguous. For example, if you know that two people are pulling on the same rope with known magnitudes of force but you do not know which direction either person is pulling, it is impossible to determine what the acceleration of the rope will be. The two people could be pulling against each other as in tug of war or the two people could be pulling in the same direction. In this simple one-dimensional example, without knowing the direction of the forces it is impossible to decide whether the net force is the result of adding the two force magnitudes or subtracting one from the other. Associating forces with vectors avoids such problems. |
Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces canceled each other out. Such experiments demonstrate the crucial properties that forces are additive vector quantities: they have magnitude and direction. When two forces act on a point particle, the resulting force, the resultant (also called the net force), can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. However, if the forces are acting on an extended body, their respective lines of application must also be specified in order to account for their effects on the motion of the body. |
As well as being added, forces can also be resolved into independent components at right angles to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on the magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right-angles to the other two. |
Pushing against an object on a frictional surface can result in a situation where the object does not move because the applied force is opposed by static friction, generated between the object and the table surface. For a situation with no movement, the static friction force exactly balances the applied force resulting in no acceleration. The static friction increases or decreases in response to the applied force up to an upper limit determined by the characteristics of the contact between the surface and the object. |
A static equilibrium between two forces is the most usual way of measuring forces, using simple devices such as weighing scales and spring balances. For example, an object suspended on a vertical spring scale experiences the force of gravity acting on the object balanced by a force applied by the "spring reaction force", which equals the object's weight. Using such tools, some quantitative force laws were discovered: that the force of gravity is proportional to volume for objects of constant density (widely exploited for millennia to define standard weights); Archimedes' principle for buoyancy; Archimedes' analysis of the lever; Boyle's law for gas pressure; and Hooke's law for springs. These were all formulated and experimentally verified before Isaac Newton expounded his Three Laws of Motion. |
Dynamic equilibrium was first described by Galileo who noticed that certain assumptions of Aristotelian physics were contradicted by observations and logic. Galileo realized that simple velocity addition demands that the concept of an "absolute rest frame" did not exist. Galileo concluded that motion in a constant velocity was completely equivalent to rest. This was contrary to Aristotle's notion of a "natural state" of rest that objects with mass naturally approached. Simple experiments showed that Galileo's understanding of the equivalence of constant velocity and rest were correct. For example, if a mariner dropped a cannonball from the crow's nest of a ship moving at a constant velocity, Aristotelian physics would have the cannonball fall straight down while the ship moved beneath it. Thus, in an Aristotelian universe, the falling cannonball would land behind the foot of the mast of a moving ship. However, when this experiment is actually conducted, the cannonball always falls at the foot of the mast, as if the cannonball knows to travel with the ship despite being separated from it. Since there is no forward horizontal force being applied on the cannonball as it falls, the only conclusion left is that the cannonball continues to move with the same velocity as the boat as it falls. Thus, no force is required to keep the cannonball moving at the constant forward velocity. |
A simple case of dynamic equilibrium occurs in constant velocity motion across a surface with kinetic friction. In such a situation, a force is applied in the direction of motion while the kinetic friction force exactly opposes the applied force. This results in zero net force, but since the object started with a non-zero velocity, it continues to move with a non-zero velocity. Aristotle misinterpreted this motion as being caused by the applied force. However, when kinetic friction is taken into consideration it is clear that there is no net force causing constant velocity motion. |
The notion "force" keeps its meaning in quantum mechanics, though one is now dealing with operators instead of classical variables and though the physics is now described by the Schrödinger equation instead of Newtonian equations. This has the consequence that the results of a measurement are now sometimes "quantized", i.e. they appear in discrete portions. This is, of course, difficult to imagine in the context of "forces". However, the potentials V(x,y,z) or fields, from which the forces generally can be derived, are treated similar to classical position variables, i.e., . |
However, already in quantum mechanics there is one "caveat", namely the particles acting onto each other do not only possess the spatial variable, but also a discrete intrinsic angular momentum-like variable called the "spin", and there is the Pauli principle relating the space and the spin variables. Depending on the value of the spin, identical particles split into two different classes, fermions and bosons. If two identical fermions (e.g. electrons) have a symmetric spin function (e.g. parallel spins) the spatial variables must be antisymmetric (i.e. they exclude each other from their places much as if there was a repulsive force), and vice versa, i.e. for antiparallel spins the position variables must be symmetric (i.e. the apparent force must be attractive). Thus in the case of two fermions there is a strictly negative correlation between spatial and spin variables, whereas for two bosons (e.g. quanta of electromagnetic waves, photons) the correlation is strictly positive. |
In modern particle physics, forces and the acceleration of particles are explained as a mathematical by-product of exchange of momentum-carrying gauge bosons. With the development of quantum field theory and general relativity, it was realized that force is a redundant concept arising from conservation of momentum (4-momentum in relativity and momentum of virtual particles in quantum electrodynamics). The conservation of momentum can be directly derived from the homogeneity or symmetry of space and so is usually considered more fundamental than the concept of a force. Thus the currently known fundamental forces are considered more accurately to be "fundamental interactions".:199–128 When particle A emits (creates) or absorbs (annihilates) virtual particle B, a momentum conservation results in recoil of particle A making impression of repulsion or attraction between particles A A' exchanging by B. This description applies to all forces arising from fundamental interactions. While sophisticated mathematical descriptions are needed to predict, in full detail, the accurate result of such interactions, there is a conceptually simple way to describe such interactions through the use of Feynman diagrams. In a Feynman diagram, each matter particle is represented as a straight line (see world line) traveling through time, which normally increases up or to the right in the diagram. Matter and anti-matter particles are identical except for their direction of propagation through the Feynman diagram. World lines of particles intersect at interaction vertices, and the Feynman diagram represents any force arising from an interaction as occurring at the vertex with an associated instantaneous change in the direction of the particle world lines. Gauge bosons are emitted away from the vertex as wavy lines and, in the case of virtual particle exchange, are absorbed at an adjacent vertex. |
All of the forces in the universe are based on four fundamental interactions. The strong and weak forces are nuclear forces that act only at very short distances, and are responsible for the interactions between subatomic particles, including nucleons and compound nuclei. The electromagnetic force acts between electric charges, and the gravitational force acts between masses. All other forces in nature derive from these four fundamental interactions. For example, friction is a manifestation of the electromagnetic force acting between the atoms of two surfaces, and the Pauli exclusion principle, which does not permit atoms to pass through each other. Similarly, the forces in springs, modeled by Hooke's law, are the result of electromagnetic forces and the Exclusion Principle acting together to return an object to its equilibrium position. Centrifugal forces are acceleration forces that arise simply from the acceleration of rotating frames of reference.:12-11:359 |
The development of fundamental theories for forces proceeded along the lines of unification of disparate ideas. For example, Isaac Newton unified the force responsible for objects falling at the surface of the Earth with the force responsible for the orbits of celestial mechanics in his universal theory of gravitation. Michael Faraday and James Clerk Maxwell demonstrated that electric and magnetic forces were unified through one consistent theory of electromagnetism. In the 20th century, the development of quantum mechanics led to a modern understanding that the first three fundamental forces (all except gravity) are manifestations of matter (fermions) interacting by exchanging virtual particles called gauge bosons. This standard model of particle physics posits a similarity between the forces and led scientists to predict the unification of the weak and electromagnetic forces in electroweak theory subsequently confirmed by observation. The complete formulation of the standard model predicts an as yet unobserved Higgs mechanism, but observations such as neutrino oscillations indicate that the standard model is incomplete. A Grand Unified Theory allowing for the combination of the electroweak interaction with the strong force is held out as a possibility with candidate theories such as supersymmetry proposed to accommodate some of the outstanding unsolved problems in physics. Physicists are still attempting to develop self-consistent unification models that would combine all four fundamental interactions into a theory of everything. Einstein tried and failed at this endeavor, but currently the most popular approach to answering this question is string theory.:212–219 |
What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as and has a magnitude of about 9.81 meters per second squared (this measurement is taken from sea level and may vary depending on location), and points toward the center of the Earth. This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of will experience a force: |
Newton came to realize that the effects of gravity might be observed in different ways at larger distances. In particular, Newton determined that the acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law. Further, Newton realized that the acceleration due to gravity is proportional to the mass of the attracting body. Combining these ideas gives a formula that relates the mass () and the radius () of the Earth to the gravitational acceleration: |
In this equation, a dimensional constant is used to describe the relative strength of gravity. This constant has come to be known as Newton's Universal Gravitation Constant, though its value was unknown in Newton's lifetime. Not until 1798 was Henry Cavendish able to make the first measurement of using a torsion balance; this was widely reported in the press as a measurement of the mass of the Earth since knowing could allow one to solve for the Earth's mass given the above equation. Newton, however, realized that since all celestial bodies followed the same laws of motion, his law of gravity had to be universal. Succinctly stated, Newton's Law of Gravitation states that the force on a spherical object of mass due to the gravitational pull of mass is |
It was only the orbit of the planet Mercury that Newton's Law of Gravitation seemed not to fully explain. Some astrophysicists predicted the existence of another planet (Vulcan) that would explain the discrepancies; however, despite some early indications, no such planet could be found. When Albert Einstein formulated his theory of general relativity (GR) he turned his attention to the problem of Mercury's orbit and found that his theory added a correction, which could account for the discrepancy. This was the first time that Newton's Theory of Gravity had been shown to be less correct than an alternative. |
Since then, and so far, general relativity has been acknowledged as the theory that best explains gravity. In GR, gravitation is not viewed as a force, but rather, objects moving freely in gravitational fields travel under their own inertia in straight lines through curved space-time – defined as the shortest space-time path between two space-time events. From the perspective of the object, all motion occurs as if there were no gravitation whatsoever. It is only when observing the motion in a global sense that the curvature of space-time can be observed and the force is inferred from the object's curved path. Thus, the straight line path in space-time is seen as a curved line in space, and it is called the ballistic trajectory of the object. For example, a basketball thrown from the ground moves in a parabola, as it is in a uniform gravitational field. Its space-time trajectory (when the extra ct dimension is added) is almost a straight line, slightly curved (with the radius of curvature of the order of few light-years). The time derivative of the changing momentum of the object is what we label as "gravitational force". |
Through combining the definition of electric current as the time rate of change of electric charge, a rule of vector multiplication called Lorentz's Law describes the force on a charge moving in a magnetic field. The connection between electricity and magnetism allows for the description of a unified electromagnetic force that acts on a charge. This force can be written as a sum of the electrostatic force (due to the electric field) and the magnetic force (due to the magnetic field). Fully stated, this is the law: |
The origin of electric and magnetic fields would not be fully explained until 1864 when James Clerk Maxwell unified a number of earlier theories into a set of 20 scalar equations, which were later reformulated into 4 vector equations by Oliver Heaviside and Josiah Willard Gibbs. These "Maxwell Equations" fully described the sources of the fields as being stationary and moving charges, and the interactions of the fields themselves. This led Maxwell to discover that electric and magnetic fields could be "self-generating" through a wave that traveled at a speed that he calculated to be the speed of light. This insight united the nascent fields of electromagnetic theory with optics and led directly to a complete description of the electromagnetic spectrum. |
However, attempting to reconcile electromagnetic theory with two observations, the photoelectric effect, and the nonexistence of the ultraviolet catastrophe, proved troublesome. Through the work of leading theoretical physicists, a new theory of electromagnetism was developed using quantum mechanics. This final modification to electromagnetic theory ultimately led to quantum electrodynamics (or QED), which fully describes all electromagnetic phenomena as being mediated by wave–particles known as photons. In QED, photons are the fundamental exchange particle, which described all interactions relating to electromagnetism including the electromagnetic force.[Note 4] |
It is a common misconception to ascribe the stiffness and rigidity of solid matter to the repulsion of like charges under the influence of the electromagnetic force. However, these characteristics actually result from the Pauli exclusion principle.[citation needed] Since electrons are fermions, they cannot occupy the same quantum mechanical state as other electrons. When the electrons in a material are densely packed together, there are not enough lower energy quantum mechanical states for them all, so some of them must be in higher energy states. This means that it takes energy to pack them together. While this effect is manifested macroscopically as a structural force, it is technically only the result of the existence of a finite set of electron states. |
The strong force only acts directly upon elementary particles. However, a residual of the force is observed between hadrons (the best known example being the force that acts between nucleons in atomic nuclei) as the nuclear force. Here the strong force acts indirectly, transmitted as gluons, which form part of the virtual pi and rho mesons, which classically transmit the nuclear force (see this topic for more). The failure of many searches for free quarks has shown that the elementary particles affected are not directly observable. This phenomenon is called color confinement. |
The weak force is due to the exchange of the heavy W and Z bosons. Its most familiar effect is beta decay (of neutrons in atomic nuclei) and the associated radioactivity. The word "weak" derives from the fact that the field strength is some 1013 times less than that of the strong force. Still, it is stronger than gravity over short distances. A consistent electroweak theory has also been developed, which shows that electromagnetic forces and the weak force are indistinguishable at a temperatures in excess of approximately 1015 kelvins. Such temperatures have been probed in modern particle accelerators and show the conditions of the universe in the early moments of the Big Bang. |
The normal force is due to repulsive forces of interaction between atoms at close contact. When their electron clouds overlap, Pauli repulsion (due to fermionic nature of electrons) follows resulting in the force that acts in a direction normal to the surface interface between two objects.:93 The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever an external force pushes on a solid object. An example of the normal force in action is the impact force on an object crashing into an immobile surface. |
Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and unstretchable. They can be combined with ideal pulleys, which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action-reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by the second object. By connecting the same string multiple times to the same object through the use of a set-up that uses movable pulleys, the tension force on a load can be multiplied. For every string that acts on a load, another factor of the tension force in the string acts on the load. However, even though such machines allow for an increase in force, there is a corresponding increase in the length of string that must be displaced in order to move the load. These tandem effects result ultimately in the conservation of mechanical energy since the work done on the load is the same no matter how complicated the machine. |
Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. However, in real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together the atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids, differences in pressure result in forces being directed along the pressure gradients as follows: |
where is the relevant cross-sectional area for the volume for which the stress-tensor is being calculated. This formalism includes pressure terms associated with forces that act normal to the cross-sectional area (the matrix diagonals of the tensor) as well as shear terms associated with forces that act parallel to the cross-sectional area (the off-diagonal elements). The stress tensor accounts for forces that cause all strains (deformations) including also tensile stresses and compressions.:133–134:38-1–38-11 |
Torque is the rotation equivalent of force in the same way that angle is the rotational equivalent for position, angular velocity for velocity, and angular momentum for momentum. As a consequence of Newton's First Law of Motion, there exists rotational inertia that ensures that all bodies maintain their angular momentum unless acted upon by an unbalanced torque. Likewise, Newton's Second Law of Motion can be used to derive an analogous equation for the instantaneous angular acceleration of the rigid body: |
where is the mass of the object, is the velocity of the object and is the distance to the center of the circular path and is the unit vector pointing in the radial direction outwards from the center. This means that the unbalanced centripetal force felt by any object is always directed toward the center of the curving path. Such forces act perpendicular to the velocity vector associated with the motion of an object, and therefore do not change the speed of the object (magnitude of the velocity), but only the direction of the velocity vector. The unbalanced force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates the object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction. |
A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms. This means that for a closed system, the net mechanical energy is conserved whenever a conservative force acts on the system. The force, therefore, is related directly to the difference in potential energy between two different locations in space, and can be considered to be an artifact of the potential field in the same way that the direction and amount of a flow of water can be considered to be an artifact of the contour map of the elevation of an area. |
For certain physical scenarios, it is impossible to model forces as being due to gradient of potentials. This is often due to macrophysical considerations that yield forces as arising from a macroscopic statistical average of microstates. For example, friction is caused by the gradients of numerous electrostatic potentials between the atoms, but manifests as a force model that is independent of any macroscale position vector. Nonconservative forces other than friction include other contact forces, tension, compression, and drag. However, for any sufficiently detailed description, all these forces are the results of conservative ones since each of these macroscopic forces are the net results of the gradients of microscopic potentials. |
The connection between macroscopic nonconservative forces and microscopic conservative forces is described by detailed treatment with statistical mechanics. In macroscopic closed systems, nonconservative forces act to change the internal energies of the system, and are often associated with the transfer of heat. According to the Second law of thermodynamics, nonconservative forces necessarily result in energy transformations within closed systems from ordered to more random conditions as entropy increases. |
The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass. The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass that accelerates at 1 m·s−2 when subjected to a force of 1 kgf. The kilogram-force is not a part of the modern SI system, and is generally deprecated; however it still sees use for some purposes as expressing aircraft weight, jet thrust, bicycle spoke tension, torque wrench settings and engine output torque. Other arcane units of force include the sthène, which is equivalent to 1000 N, and the kip, which is equivalent to 1000 lbf. |
Beyoncé Giselle Knowles-Carter (/biːˈjɒnseɪ/ bee-YON-say) (born September 4, 1981) is an American singer, songwriter, record producer and actress. Born and raised in Houston, Texas, she performed in various singing and dancing competitions as a child, and rose to fame in the late 1990s as lead singer of R&B girl-group Destiny's Child. Managed by her father, Mathew Knowles, the group became one of the world's best-selling girl groups of all time. Their hiatus saw the release of Beyoncé's debut album, Dangerously in Love (2003), which established her as a solo artist worldwide, earned five Grammy Awards and featured the Billboard Hot 100 number-one singles "Crazy in Love" and "Baby Boy". |
Following the disbandment of Destiny's Child in June 2005, she released her second solo album, B'Day (2006), which contained hits "Déjà Vu", "Irreplaceable", and "Beautiful Liar". Beyoncé also ventured into acting, with a Golden Globe-nominated performance in Dreamgirls (2006), and starring roles in The Pink Panther (2006) and Obsessed (2009). Her marriage to rapper Jay Z and portrayal of Etta James in Cadillac Records (2008) influenced her third album, I Am... Sasha Fierce (2008), which saw the birth of her alter-ego Sasha Fierce and earned a record-setting six Grammy Awards in 2010, including Song of the Year for "Single Ladies (Put a Ring on It)". Beyoncé took a hiatus from music in 2010 and took over management of her career; her fourth album 4 (2011) was subsequently mellower in tone, exploring 1970s funk, 1980s pop, and 1990s soul. Her critically acclaimed fifth studio album, Beyoncé (2013), was distinguished from previous releases by its experimental production and exploration of darker themes. |
A self-described "modern-day feminist", Beyoncé creates songs that are often characterized by themes of love, relationships, and monogamy, as well as female sexuality and empowerment. On stage, her dynamic, highly choreographed performances have led to critics hailing her as one of the best entertainers in contemporary popular music. Throughout a career spanning 19 years, she has sold over 118 million records as a solo artist, and a further 60 million with Destiny's Child, making her one of the best-selling music artists of all time. She has won 20 Grammy Awards and is the most nominated woman in the award's history. The Recording Industry Association of America recognized her as the Top Certified Artist in America during the 2000s decade. In 2009, Billboard named her the Top Radio Songs Artist of the Decade, the Top Female Artist of the 2000s and their Artist of the Millennium in 2011. Time listed her among the 100 most influential people in the world in 2013 and 2014. Forbes magazine also listed her as the most powerful female musician of 2015. |
Beyoncé Giselle Knowles was born in Houston, Texas, to Celestine Ann "Tina" Knowles (née Beyincé), a hairdresser and salon owner, and Mathew Knowles, a Xerox sales manager. Beyoncé's name is a tribute to her mother's maiden name. Beyoncé's younger sister Solange is also a singer and a former member of Destiny's Child. Mathew is African-American, while Tina is of Louisiana Creole descent (with African, Native American, French, Cajun, and distant Irish and Spanish ancestry). Through her mother, Beyoncé is a descendant of Acadian leader Joseph Broussard. She was raised in a Methodist household. |
Beyoncé attended St. Mary's Elementary School in Fredericksburg, Texas, where she enrolled in dance classes. Her singing talent was discovered when dance instructor Darlette Johnson began humming a song and she finished it, able to hit the high-pitched notes. Beyoncé's interest in music and performing continued after winning a school talent show at age seven, singing John Lennon's "Imagine" to beat 15/16-year-olds. In fall of 1990, Beyoncé enrolled in Parker Elementary School, a music magnet school in Houston, where she would perform with the school's choir. She also attended the High School for the Performing and Visual Arts and later Alief Elsik High School. Beyoncé was also a member of the choir at St. John's United Methodist Church as a soloist for two years. |
At age eight, Beyoncé and childhood friend Kelly Rowland met LaTavia Roberson while in an audition for an all-girl entertainment group. They were placed into a group with three other girls as Girl's Tyme, and rapped and danced on the talent show circuit in Houston. After seeing the group, R&B producer Arne Frager brought them to his Northern California studio and placed them in Star Search, the largest talent show on national TV at the time. Girl's Tyme failed to win, and Beyoncé later said the song they performed was not good. In 1995 Beyoncé's father resigned from his job to manage the group. The move reduced Beyoncé's family's income by half, and her parents were forced to move into separated apartments. Mathew cut the original line-up to four and the group continued performing as an opening act for other established R&B girl groups. The girls auditioned before record labels and were finally signed to Elektra Records, moving to Atlanta Records briefly to work on their first recording, only to be cut by the company. This put further strain on the family, and Beyoncé's parents separated. On October 5, 1995, Dwayne Wiggins's Grass Roots Entertainment signed the group. In 1996, the girls began recording their debut album under an agreement with Sony Music, the Knowles family reunited, and shortly after, the group got a contract with Columbia Records. |
The group changed their name to Destiny's Child in 1996, based upon a passage in the Book of Isaiah. In 1997, Destiny's Child released their major label debut song "Killing Time" on the soundtrack to the 1997 film, Men in Black. The following year, the group released their self-titled debut album, scoring their first major hit "No, No, No". The album established the group as a viable act in the music industry, with moderate sales and winning the group three Soul Train Lady of Soul Awards for Best R&B/Soul Album of the Year, Best R&B/Soul or Rap New Artist, and Best R&B/Soul Single for "No, No, No". The group released their multi-platinum second album The Writing's on the Wall in 1999. The record features some of the group's most widely known songs such as "Bills, Bills, Bills", the group's first number-one single, "Jumpin' Jumpin'" and "Say My Name", which became their most successful song at the time, and would remain one of their signature songs. "Say My Name" won the Best R&B Performance by a Duo or Group with Vocals and the Best R&B Song at the 43rd Annual Grammy Awards. The Writing's on the Wall sold more than eight million copies worldwide. During this time, Beyoncé recorded a duet with Marc Nelson, an original member of Boyz II Men, on the song "After All Is Said and Done" for the soundtrack to the 1999 film, The Best Man. |
LeToya Luckett and Roberson became unhappy with Mathew's managing of the band and eventually were replaced by Farrah Franklin and Michelle Williams. Beyoncé experienced depression following the split with Luckett and Roberson after being publicly blamed by the media, critics, and blogs for its cause. Her long-standing boyfriend left her at this time. The depression was so severe it lasted for a couple of years, during which she occasionally kept herself in her bedroom for days and refused to eat anything. Beyoncé stated that she struggled to speak about her depression because Destiny's Child had just won their first Grammy Award and she feared no one would take her seriously. Beyoncé would later speak of her mother as the person who helped her fight it. Franklin was dismissed, leaving just Beyoncé, Rowland, and Williams. |
The remaining band members recorded "Independent Women Part I", which appeared on the soundtrack to the 2000 film, Charlie's Angels. It became their best-charting single, topping the U.S. Billboard Hot 100 chart for eleven consecutive weeks. In early 2001, while Destiny's Child was completing their third album, Beyoncé landed a major role in the MTV made-for-television film, Carmen: A Hip Hopera, starring alongside American actor Mekhi Phifer. Set in Philadelphia, the film is a modern interpretation of the 19th century opera Carmen by French composer Georges Bizet. When the third album Survivor was released in May 2001, Luckett and Roberson filed a lawsuit claiming that the songs were aimed at them. The album debuted at number one on the U.S. Billboard 200, with first-week sales of 663,000 copies sold. The album spawned other number-one hits, "Bootylicious" and the title track, "Survivor", the latter of which earned the group a Grammy Award for Best R&B Performance by a Duo or Group with Vocals. After releasing their holiday album 8 Days of Christmas in October 2001, the group announced a hiatus to further pursue solo careers. |
In July 2002, Beyoncé continued her acting career playing Foxxy Cleopatra alongside Mike Myers in the comedy film, Austin Powers in Goldmember, which spent its first weekend atop the US box office and grossed $73 million. Beyoncé released "Work It Out" as the lead single from its soundtrack album which entered the top ten in the UK, Norway, and Belgium. In 2003, Beyoncé starred opposite Cuba Gooding, Jr., in the musical comedy The Fighting Temptations as Lilly, a single mother whom Gooding's character falls in love with. The film received mixed reviews from critics but grossed $30 million in the U.S. Beyoncé released "Fighting Temptation" as the lead single from the film's soundtrack album, with Missy Elliott, MC Lyte, and Free which was also used to promote the film. Another of Beyoncé's contributions to the soundtrack, "Summertime", fared better on the US charts. |
Beyoncé's first solo recording was a feature on Jay Z's "'03 Bonnie & Clyde" that was released in October 2002, peaking at number four on the U.S. Billboard Hot 100 chart. Her first solo album Dangerously in Love was released on June 24, 2003, after Michelle Williams and Kelly Rowland had released their solo efforts. The album sold 317,000 copies in its first week, debuted atop the Billboard 200, and has since sold 11 million copies worldwide. The album's lead single, "Crazy in Love", featuring Jay Z, became Beyoncé's first number-one single as a solo artist in the US. The single "Baby Boy" also reached number one, and singles, "Me, Myself and I" and "Naughty Girl", both reached the top-five. The album earned Beyoncé a then record-tying five awards at the 46th Annual Grammy Awards; Best Contemporary R&B Album, Best Female R&B Vocal Performance for "Dangerously in Love 2", Best R&B Song and Best Rap/Sung Collaboration for "Crazy in Love", and Best R&B Performance by a Duo or Group with Vocals for "The Closer I Get to You" with Luther Vandross. |
In November 2003, she embarked on the Dangerously in Love Tour in Europe and later toured alongside Missy Elliott and Alicia Keys for the Verizon Ladies First Tour in North America. On February 1, 2004, Beyoncé performed the American national anthem at Super Bowl XXXVIII, at the Reliant Stadium in Houston, Texas. After the release of Dangerously in Love, Beyoncé had planned to produce a follow-up album using several of the left-over tracks. However, this was put on hold so she could concentrate on recording Destiny Fulfilled, the final studio album by Destiny's Child. Released on November 15, 2004, in the US and peaking at number two on the Billboard 200, Destiny Fulfilled included the singles "Lose My Breath" and "Soldier", which reached the top five on the Billboard Hot 100 chart. Destiny's Child embarked on a worldwide concert tour, Destiny Fulfilled... and Lovin' It and during the last stop of their European tour, in Barcelona on June 11, 2005, Rowland announced that Destiny's Child would disband following the North American leg of the tour. The group released their first compilation album Number 1's on October 25, 2005, in the US and accepted a star on the Hollywood Walk of Fame in March 2006. |
Beyoncé's second solo album B'Day was released on September 5, 2006, in the US, to coincide with her twenty-fifth birthday. It sold 541,000 copies in its first week and debuted atop the Billboard 200, becoming Beyoncé's second consecutive number-one album in the United States. The album's lead single "Déjà Vu", featuring Jay Z, reached the top five on the Billboard Hot 100 chart. The second international single "Irreplaceable" was a commercial success worldwide, reaching number one in Australia, Hungary, Ireland, New Zealand and the United States. B'Day also produced three other singles; "Ring the Alarm", "Get Me Bodied", and "Green Light" (released in the United Kingdom only). |
Her first acting role of 2006 was in the comedy film The Pink Panther starring opposite Steve Martin, grossing $158.8 million at the box office worldwide. Her second film Dreamgirls, the film version of the 1981 Broadway musical loosely based on The Supremes, received acclaim from critics and grossed $154 million internationally. In it, she starred opposite Jennifer Hudson, Jamie Foxx, and Eddie Murphy playing a pop singer based on Diana Ross. To promote the film, Beyoncé released "Listen" as the lead single from the soundtrack album. In April 2007, Beyoncé embarked on The Beyoncé Experience, her first worldwide concert tour, visiting 97 venues and grossed over $24 million.[note 1] Beyoncé conducted pre-concert food donation drives during six major stops in conjunction with her pastor at St. John's and America's Second Harvest. At the same time, B'Day was re-released with five additional songs, including her duet with Shakira "Beautiful Liar". |
On April 4, 2008, Beyoncé married Jay Z. She publicly revealed their marriage in a video montage at the listening party for her third studio album, I Am... Sasha Fierce, in Manhattan's Sony Club on October 22, 2008. I Am... Sasha Fierce was released on November 18, 2008 in the United States. The album formally introduces Beyoncé's alter ego Sasha Fierce, conceived during the making of her 2003 single "Crazy in Love", selling 482,000 copies in its first week, debuting atop the Billboard 200, and giving Beyoncé her third consecutive number-one album in the US. The album featured the number-one song "Single Ladies (Put a Ring on It)" and the top-five songs "If I Were a Boy" and "Halo". Achieving the accomplishment of becoming her longest-running Hot 100 single in her career, "Halo"'s success in the US helped Beyoncé attain more top-ten singles on the list than any other woman during the 2000s. It also included the successful "Sweet Dreams", and singles "Diva", "Ego", "Broken-Hearted Girl" and "Video Phone". The music video for "Single Ladies" has been parodied and imitated around the world, spawning the "first major dance craze" of the Internet age according to the Toronto Star. The video has won several awards, including Best Video at the 2009 MTV Europe Music Awards, the 2009 Scottish MOBO Awards, and the 2009 BET Awards. At the 2009 MTV Video Music Awards, the video was nominated for nine awards, ultimately winning three including Video of the Year. Its failure to win the Best Female Video category, which went to American country pop singer Taylor Swift's "You Belong with Me", led to Kanye West interrupting the ceremony and Beyoncé improvising a re-presentation of Swift's award during her own acceptance speech. In March 2009, Beyoncé embarked on the I Am... World Tour, her second headlining worldwide concert tour, consisting of 108 shows, grossing $119.5 million. |
Beyoncé further expanded her acting career, starring as blues singer Etta James in the 2008 musical biopic, Cadillac Records. Her performance in the film received praise from critics, and she garnered several nominations for her portrayal of James, including a Satellite Award nomination for Best Supporting Actress, and a NAACP Image Award nomination for Outstanding Supporting Actress. Beyoncé donated her entire salary from the film to Phoenix House, an organization of rehabilitation centers for heroin addicts around the country. On January 20, 2009, Beyoncé performed James' "At Last" at the First Couple's first inaugural ball. Beyoncé starred opposite Ali Larter and Idris Elba in the thriller, Obsessed. She played Sharon Charles, a mother and wife who learns of a woman's obsessive behavior over her husband. Although the film received negative reviews from critics, the movie did well at the US box office, grossing $68 million—$60 million more than Cadillac Records—on a budget of $20 million. The fight scene finale between Sharon and the character played by Ali Larter also won the 2010 MTV Movie Award for Best Fight. |
At the 52nd Annual Grammy Awards, Beyoncé received ten nominations, including Album of the Year for I Am... Sasha Fierce, Record of the Year for "Halo", and Song of the Year for "Single Ladies (Put a Ring on It)", among others. She tied with Lauryn Hill for most Grammy nominations in a single year by a female artist. In 2010, Beyoncé was featured on Lady Gaga's single "Telephone" and its music video. The song topped the US Pop Songs chart, becoming the sixth number-one for both Beyoncé and Gaga, tying them with Mariah Carey for most number-ones since the Nielsen Top 40 airplay chart launched in 1992. "Telephone" received a Grammy Award nomination for Best Pop Collaboration with Vocals. |
Beyoncé announced a hiatus from her music career in January 2010, heeding her mother's advice, "to live life, to be inspired by things again". During the break she and her father parted ways as business partners. Beyoncé's musical break lasted nine months and saw her visit multiple European cities, the Great Wall of China, the Egyptian pyramids, Australia, English music festivals and various museums and ballet performances. |
In 2011, documents obtained by WikiLeaks revealed that Beyoncé was one of many entertainers who performed for the family of Libyan ruler Muammar Gaddafi. Rolling Stone reported that the music industry was urging them to return the money they earned for the concerts; a spokesperson for Beyoncé later confirmed to The Huffington Post that she donated the money to the Clinton Bush Haiti Fund. Later that year she became the first solo female artist to headline the main Pyramid stage at the 2011 Glastonbury Festival in over twenty years, and was named the highest-paid performer in the world per minute. |
Her fourth studio album 4 was released on June 28, 2011 in the US. 4 sold 310,000 copies in its first week and debuted atop the Billboard 200 chart, giving Beyoncé her fourth consecutive number-one album in the US. The album was preceded by two of its singles "Run the World (Girls)" and "Best Thing I Never Had", which both attained moderate success. The fourth single "Love on Top" was a commercial success in the US. 4 also produced four other singles; "Party", "Countdown", "I Care" and "End of Time". "Eat, Play, Love", a cover story written by Beyoncé for Essence that detailed her 2010 career break, won her a writing award from the New York Association of Black Journalists. In late 2011, she took the stage at New York's Roseland Ballroom for four nights of special performances: the 4 Intimate Nights with Beyoncé concerts saw the performance of her 4 album to a standing room only. |
On January 7, 2012, Beyoncé gave birth to her first child, a daughter, Blue Ivy Carter, at Lenox Hill Hospital in New York. Five months later, she performed for four nights at Revel Atlantic City's Ovation Hall to celebrate the resort's opening, her first performances since giving birth to Blue Ivy. |
In January 2013, Destiny's Child released Love Songs, a compilation album of the romance-themed songs from their previous albums and a newly recorded track, "Nuclear". Beyoncé performed the American national anthem singing along with a pre-recorded track at President Obama's second inauguration in Washington, D.C. The following month, Beyoncé performed at the Super Bowl XLVII halftime show, held at the Mercedes-Benz Superdome in New Orleans. The performance stands as the second most tweeted about moment in history at 268,000 tweets per minute. At the 55th Annual Grammy Awards, Beyoncé won for Best Traditional R&B Performance for "Love on Top". Her feature-length documentary film, Life Is But a Dream, first aired on HBO on February 16, 2013. The film, which she directed and produced herself, featured footage from her childhood, her as a mother and businesswoman, recording, rehearsing for live performances, and her return to the spotlight following Blue Ivy's birth. Its DVD release in November 2013 was accompanied by footage from the Revel Presents: Beyoncé Live concerts and a new song, "God Made You Beautiful". In February 2013, Beyoncé signed a global publishing agreement with Warner/Chappell Music, which would cover her future songwriting and then-upcoming studio album. |
Beyoncé embarked on The Mrs. Carter Show World Tour on April 15 in Belgrade, Serbia; the tour included 132 dates that ran through to March 2014. It became the most successful tour of her career and one of the most-successful tours of all time. In May, Beyoncé's cover of Amy Winehouse's "Back to Black" with André 3000 on The Great Gatsby soundtrack was released. She was also honorary chair of the 2013 Met Gala. Beyoncé voiced Queen Tara in the 3D CGI animated film, Epic, released by 20th Century Fox on May 24, and recorded an original song for the film, "Rise Up", co-written with Sia. |
On December 13, 2013, Beyoncé unexpectedly released her eponymous fifth studio album on the iTunes Store without any prior announcement or promotion. The album debuted atop the Billboard 200 chart, giving Beyoncé her fifth consecutive number-one album in the US. This made her the first woman in the chart's history to have her first five studio albums debut at number one. Beyoncé received critical acclaim and commercial success, selling one million digital copies worldwide in six days; The New York Times noted the album's unconventional, unexpected release as significant. Musically an electro-R&B album, it concerns darker themes previously unexplored in her work, such as "bulimia, postnatal depression [and] the fears and insecurities of marriage and motherhood". The single "Drunk in Love", featuring Jay Z, peaked at number two on the Billboard Hot 100 chart. In April 2014, after much speculation in the weeks before, Beyoncé and Jay Z officially announced their On the Run Tour. It served as the couple's first co-headlining stadium tour together. On August 24, 2014, she received the Video Vanguard Award at the 2014 MTV Video Music Awards. Knowles also took home three competitive awards: Best Video with a Social Message and Best Cinematography for "Pretty Hurts", as well as best collaboration for "Drunk in Love". In November, Forbes reported that Beyoncé was the top-earning woman in music for the second year in a row—earning $115 million in the year, more than double her earnings in 2013. Beyoncé was reissued with new material in three forms: as an extended play, a box set, as well as a full platinum edition. |
At the 57th Annual Grammy Awards in February 2015, Beyoncé was nominated for six awards, ultimately winning three: Best R&B Performance and Best R&B Song for "Drunk in Love", and Best Surround Sound Album for Beyoncé. She was nominated for Album of the Year but the award was won by Beck for his Morning Phase album. In August, the cover of the September issue of Vogue magazine was unveiled online, Beyoncé as the cover star, becoming the first African-American artist and third African-American woman in general to cover the September issue. She headlined the 2015 Made in America festival in early September and also the Global Citizen Festival later that month. Beyoncé made an uncredited featured appearance on the track "Hymn for the Weekend" by British rock band Coldplay, on their seventh studio album A Head Full of Dreams (2015), which saw release in December. On January 7, 2016, Pepsi announced Beyoncé would perform alongside Coldplay at Super Bowl 50 in February. Knowles has previously performed at four Super Bowl shows throughout her career, serving as the main headliner of the 47th Super Bowl halftime show in 2013. |
On February 6, 2016, one day before her performance at the Super Bowl, Beyoncé released a new single exclusively on music streaming service Tidal called "Formation". |
Beyoncé is believed to have first started a relationship with Jay Z after a collaboration on "'03 Bonnie & Clyde", which appeared on his seventh album The Blueprint 2: The Gift & The Curse (2002). Beyoncé appeared as Jay Z's girlfriend in the music video for the song, which would further fuel speculation of their relationship. On April 4, 2008, Beyoncé and Jay Z were married without publicity. As of April 2014, the couple have sold a combined 300 million records together. The couple are known for their private relationship, although they have appeared to become more relaxed in recent years. Beyoncé suffered a miscarriage in 2010 or 2011, describing it as "the saddest thing" she had ever endured. She returned to the studio and wrote music in order to cope with the loss. In April 2011, Beyoncé and Jay Z traveled to Paris in order to shoot the album cover for her 4, and unexpectedly became pregnant in Paris. |
In August, the couple attended the 2011 MTV Video Music Awards, at which Beyoncé performed "Love on Top" and started the performance saying "Tonight I want you to stand up on your feet, I want you to feel the love that's growing inside of me". At the end of the performance, she dropped her microphone, unbuttoned her blazer and rubbed her stomach, confirming her pregnancy she had alluded to earlier in the evening. Her appearance helped that year's MTV Video Music Awards become the most-watched broadcast in MTV history, pulling in 12.4 million viewers; the announcement was listed in Guinness World Records for "most tweets per second recorded for a single event" on Twitter, receiving 8,868 tweets per second and "Beyonce pregnant" was the most Googled term the week of August 29, 2011. |
On January 7, 2012, Beyoncé gave birth to a daughter, Blue Ivy Carter, at Lenox Hill Hospital in New York under heavy security. Two days later, Jay Z released "Glory", a song dedicated to their child, on his website Lifeandtimes.com. The song detailed the couple's pregnancy struggles, including a miscarriage Beyoncé suffered before becoming pregnant with Blue Ivy. Blue Ivy's cries are included at the end of the song, and she was officially credited as "B.I.C." on it. At two days old, she became the youngest person ever to appear on a Billboard chart when "Glory" debuted on the Hot R&B/Hip-Hop Songs chart. |
Beyoncé and husband Jay Z are friends with President Barack Obama and First Lady Michelle Obama. She performed "America the Beautiful" at the 2009 presidential inauguration, as well as "At Last" during the first inaugural dance at the Neighborhood Ball two days later. Beyoncé and Jay Z held a fundraiser at the latter's 40/40 Club in Manhattan for Obama's 2012 presidential campaign which raised $4 million. Beyoncé uploaded pictures of her paper ballot on Tumblr, confirming she had voted in support for the Democratic Party and to encourage others to do so. She also performed the American national anthem at his second inauguration, singing along with a pre-recorded track. She publicly endorsed same sex marriage on March 26, 2013, after the Supreme Court debate on California's Proposition 8. In July 2013, Beyoncé and Jay-Z attended a rally in response to the acquittal of George Zimmerman for the shooting of Trayvon Martin. |
In an interview published by Vogue in April 2013, Beyoncé was asked if she considers herself a feminist, to which she said, "that word can be very extreme... But I guess I am a modern-day feminist. I do believe in equality". She would later align herself more publicly with the movement, sampling "We should all be feminists", a speech delivered by Nigerian author Chimamanda Ngozi Adichie at a TEDxEuston conference in April 2013, in her song "Flawless", released later that year. She has also contributed to the Ban Bossy campaign, which uses television and social media to encourage leadership in girls. |
In 2015 Beyoncé signed an open letter which the ONE Campaign had been collecting signatures for; the letter was addressed to Angela Merkel and Nkosazana Dlamini-Zuma, urging them to focus on women as they serve as the head of the G7 in Germany and the AU in South Africa respectively, which will start to set the priorities in development funding before a main UN summit in September 2015 that will establish new development goals for the generation. |
Following the death of Freddie Gray, Beyoncé and Jay-Z, among other notable figures, met with his family. After the imprisonment of protesters of Gray's death, Beyoncé and Jay-Z donated thousands of dollars to bail them out. |
Forbes magazine began reporting on Beyoncé's earnings in 2008, calculating that the $80 million earned between June 2007 to June 2008, for her music, tour, films and clothing line made her the world's best-paid music personality at the time, above Madonna and Celine Dion. They placed her fourth on the Celebrity 100 list in 2009 and ninth on the "Most Powerful Women in the World" list in 2010. The following year, Forbes placed her eighth on the "Best-Paid Celebrities Under 30" list, having earned $35 million in the past year for her clothing line and endorsement deals. In 2012, Forbes placed Beyoncé at number 16 on the Celebrity 100 list, twelve places lower than three years ago yet still having earned $40 million in the past year for her album 4, clothing line and endorsement deals. In the same year, Beyoncé and Jay Z placed at number one on the "World's Highest-Paid Celebrity Couples", for collectively earning $78 million. The couple made it into the previous year's Guinness World Records as the "highest-earning power couple" for collectively earning $122 million in 2009. For the years 2009 to 2011, Beyoncé earned an average of $70 million per year, and earned $40 million in 2012. In 2013, Beyoncé's endorsements of Pepsi and H&M made her and Jay Z the world's first billion dollar couple in the music industry. That year, Beyoncé was published as the fourth most-powerful celebrity in the Forbes rankings. MTV estimated that by the end of 2014, Beyoncé would become the highest-paid black musician in history; she succeeded to do so in April 2014. In June 2014, Beyoncé ranked at #1 on the Forbes Celebrity 100 list, earning an estimated $115 million throughout June 2013 – June 2014. This in turn was the first time she had topped the Celebrity 100 list as well as being her highest yearly earnings to date. As of May 2015, her net worth is estimated to be $250 million. |
Beyoncé's vocal range spans four octaves. Jody Rosen highlights her tone and timbre as particularly distinctive, describing her voice as "one of the most compelling instruments in popular music". While another critic says she is a "Vocal acrobat, being able to sing long and complex melismas and vocal runs effortlessly, and in key. Her vocal abilities mean she is identified as the centerpiece of Destiny's Child. The Daily Mail calls Beyoncé's voice "versatile", capable of exploring power ballads, soul, rock belting, operatic flourishes, and hip hop. Jon Pareles of The New York Times commented that her voice is "velvety yet tart, with an insistent flutter and reserves of soul belting". Rosen notes that the hip hop era highly influenced Beyoncé's strange rhythmic vocal style, but also finds her quite traditionalist in her use of balladry, gospel and falsetto. Other critics praise her range and power, with Chris Richards of The Washington Post saying she was "capable of punctuating any beat with goose-bump-inducing whispers or full-bore diva-roars." |
Beyoncé's music is generally R&B, but she also incorporates pop, soul and funk into her songs. 4 demonstrated Beyoncé's exploration of 90s-style R&B, as well as further use of soul and hip hop than compared to previous releases. While she almost exclusively releases English songs, Beyoncé recorded several Spanish songs for Irreemplazable (re-recordings of songs from B'Day for a Spanish-language audience), and the re-release of B'Day. To record these, Beyoncé was coached phonetically by American record producer Rudy Perez. |
She has received co-writing credits for most of the songs recorded with Destiny's Child and her solo efforts. Her early songs were personally driven and female-empowerment themed compositions like "Independent Women" and "Survivor", but after the start of her relationship with Jay Z she transitioned to more man-tending anthems such as "Cater 2 U". Beyoncé has also received co-producing credits for most of the records in which she has been involved, especially during her solo efforts. However, she does not formulate beats herself, but typically comes up with melodies and ideas during production, sharing them with producers. |
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