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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.
Who first showed that Newton's Theory of Gravity was not as correct as another theory?
{ "text": [ "Albert Einstein", "Albert Einstein", "Albert Einstein", "Albert Einstein" ], "answer_start": [ 293, 293, 293, 293 ] }
Who [MASK] showed that [MASK] 's Theory of Gravity was not as correct as another theory?
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57378c9b1c456719005744a8
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:
What is the time rate of change of electric charge?
{ "text": [ "electric current", "electric current", "electric current", "electric current" ], "answer_start": [ 36, 36, 36, 36 ] }
What is the time rate of change of electric charge?
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57378c9b1c456719005744a9
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:
What magnetic and electric force acts on a charge?
{ "text": [ "unified electromagnetic", "unified electromagnetic force", "electromagnetic", "unified electromagnetic force" ], "answer_start": [ 294, 294, 302, 294 ] }
What magnetic and electric force acts on a charge?
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57378c9b1c456719005744a7
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:
What is the law named that defines a charge moving through a magnetic field?
{ "text": [ "Lorentz's Law", "Lorentz's Law", "Lorentz's Law", "Lorentz's Law" ], "answer_start": [ 139, 139, 139, 139 ] }
What is the law named that defines a charge moving through a magnetic field?
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57378c9b1c456719005744aa
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:
Whatare the electrostatic and magnetic force awritten as the sum of?
{ "text": [ "electrostatic force", "the electrostatic force (due to the electric field) and the magnetic force (due to the magnetic field).", "electrostatic force (due to the electric field) and the magnetic force", "the electrostatic force (due to the electric field) and the magnetic force" ], "answer_start": [ 389, 385, 389, 385 ] }
Whatare the electrostatic and magnetic force awritten as the sum of?
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57378e311c456719005744af
Force
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.
Who first fully explained the origins of magnetic and electric fields?
{ "text": [ "James Clerk Maxwell", "James Clerk Maxwell", "James Clerk Maxwell", "James Clerk Maxwell" ], "answer_start": [ 88, 88, 88, 88 ] }
Who [MASK] fully explained the origins of magnetic and electric fields?
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57378e311c456719005744b0
Force
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.
When did the origins of magnetic and electric fields occur?
{ "text": [ "1864", "1864", "1864", "1864" ], "answer_start": [ 78, 78, 78, 78 ] }
When did the origins of magnetic and electric fields occur?
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57378e311c456719005744b1
Force
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.
How many scalar equations were formed into a set by James Maxwell?
{ "text": [ "20", "20", "20", "20" ], "answer_start": [ 159, 159, 159, 159 ] }
How many scalar equations were formed into a set by [MASK]?
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57378e311c456719005744b2
Force
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.
How many vector equations did Heaviside and Gibbs reformilate Maxwell's 20 scalar equtions into?
{ "text": [ "4", "4", "4", "4" ], "answer_start": [ 215, 215, 215, 215 ] }
How many vector equations did [MASK] and Gibbs reformilate [MASK] 's [MASK] scalar equtions into?
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57378e311c456719005744b3
Force
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.
Who discovered that magnetic and electric could self-generate?
{ "text": [ "Maxwell", "James Clerk Maxwell", "Maxwell", "Maxwell" ], "answer_start": [ 444, 88, 444, 444 ] }
Who discovered that magnetic and electric could self-generate?
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573792ee1c456719005744b9
Force
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]
What was dificult to reconcile the photoelectric effect and the missing ultraviolet catastrophe?
{ "text": [ "electromagnetic theory", "electromagnetic theory", "electromagnetic theory", "electromagnetic theory" ], "answer_start": [ 33, 33, 33, 33 ] }
What was dificult to reconcile the photoelectric effect and the missing ultraviolet catastrophe?
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573792ee1c456719005744ba
Force
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]
What was used to create a new electromagnetic theory to reconcile the troubles with electromagnetic theory as it used to stand?
{ "text": [ "quantum mechanics", "quantum mechanics", "quantum mechanics", "the work of leading theoretical physicists" ], "answer_start": [ 283, 283, 283, 186 ] }
What was used to create a new electromagnetic theory to reconcile the troubles with electromagnetic theory as it used to stand?
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573792ee1c456719005744bb
Force
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]
What did electromagnetic theory finally lead to?
{ "text": [ "quantum electrodynamics", "quantum electrodynamics (or QED)", "quantum electrodynamics", "quantum electrodynamics" ], "answer_start": [ 370, 370, 370, 370 ] }
What did electromagnetic theory finally lead to?
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573792ee1c456719005744bc
Force
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]
What are the wave-particles called that mediate all electromagnetic phenomena?
{ "text": [ "photons", "photons", "photons", "photons" ], "answer_start": [ 501, 501, 501, 501 ] }
What are the wave-particles called that mediate all electromagnetic phenomena?
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5737958ac3c5551400e51f29
Force
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.
What is often misunderstood as the cause of matter rigidity?
{ "text": [ "repulsion of like charges", "repulsion of like charges under the influence of the electromagnetic force", "repulsion of like charges", "the repulsion of like charges under the influence of the electromagnetic force" ], "answer_start": [ 90, 90, 90, 86 ] }
What is often misunderstood as the cause of matter rigidity?
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5737958ac3c5551400e51f2a
Force
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.
What actually causes rigidity in matter?
{ "text": [ "the Pauli exclusion principle", "the Pauli exclusion principle", "Pauli exclusion principle", "Pauli exclusion principle" ], "answer_start": [ 218, 218, 222, 222 ] }
What actually causes rigidity in matter?
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5737958ac3c5551400e51f2b
Force
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.
What is needed to pack electrons densely together?
{ "text": [ "energy", "energy", "energy", "energy" ], "answer_start": [ 579, 579, 579, 579 ] }
What is needed to pack electrons densely together?
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5737958ac3c5551400e51f2c
Force
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.
How is the Pauli exclusion priciple manifested in the macro world?
{ "text": [ "as a structural force", "as a structural force", "a structural force", "macroscopically as a structural force" ], "answer_start": [ 657, 657, 660, 641 ] }
How is the Pauli exclusion priciple manifested in the macro world?
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573796edc3c5551400e51f33
Force
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.
What does stong force act upon?
{ "text": [ "elementary particles", "elementary particles", "elementary particles", "elementary particles" ], "answer_start": [ 41, 41, 41, 41 ] }
What does stong force act upon?
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573796edc3c5551400e51f34
Force
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.
What can be seen between hadrons?
{ "text": [ "residual of the force", "residual of the force", "nucleons in atomic nuclei", "a residual of the force" ], "answer_start": [ 74, 74, 182, 72 ] }
What can be seen between hadrons?
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573796edc3c5551400e51f35
Force
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.
What is the force between nucleons?
{ "text": [ "nuclear", "nuclear force.", "nuclear", "nuclear force" ], "answer_start": [ 216, 216, 216, 216 ] }
What is the force between nucleons?
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573796edc3c5551400e51f36
Force
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.
How are nuclear forces transmitted?
{ "text": [ "as gluons", "as gluons", "as gluons", "as gluons" ], "answer_start": [ 282, 282, 282, 282 ] }
How are nuclear forces transmitted?
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573796edc3c5551400e51f37
Force
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.
What is the term for the lack of obsevable free quarks?
{ "text": [ "color confinement", "color confinement", "color confinement", "color confinement" ], "answer_start": [ 564, 564, 564, 564 ] }
What is the term for the lack of obsevable free quarks?
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57379829c3c5551400e51f3d
Force
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.
What does the W and Z boson exchange create?
{ "text": [ "weak force", "weak force", "weak force", "weak force" ], "answer_start": [ 4, 4, 4, 4 ] }
What does the W and Z boson exchange create?
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57379829c3c5551400e51f3e
Force
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.
What is the observable effect of W and Z boson exchange?
{ "text": [ "beta decay", "beta decay (of neutrons in atomic nuclei)", "beta decay", "beta decay" ], "answer_start": [ 95, 95, 95, 95 ] }
What is the observable effect of W and Z boson exchange?
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57379829c3c5551400e51f3f
Force
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.
What is the effect of beta decay?
{ "text": [ "radioactivity", "radioactivity", "radioactivity", "radioactivity" ], "answer_start": [ 156, 156, 156, 156 ] }
What is the effect of beta decay?
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57379829c3c5551400e51f40
Force
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.
How many times less is the strenght of the weak field compared to the strong?
{ "text": [ "1013", "1013", "1013", "1013" ], "answer_start": [ 241, 241, 241, 241 ] }
How many times less is the strenght of the weak field compared to the strong?
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57379829c3c5551400e51f41
Force
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.
At what temperature do weak and electromagnetic forces appear the same?
{ "text": [ "approximately 1015 kelvins", "in excess of approximately 1015 kelvins", "1015 kelvins", "in excess of approximately 1015 kelvins" ], "answer_start": [ 514, 501, 528, 501 ] }
At what temperature do weak and electromagnetic forces appear the same?
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57379a4b1c456719005744cd
Force
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.
What is the repulsive force of close range atom interaction?
{ "text": [ "normal force", "normal force", "normal force", "normal force" ], "answer_start": [ 4, 4, 4, 4 ] }
What is the repulsive force of close range atom interaction?
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57379a4b1c456719005744ce
Force
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.
What occurs when electron clouds overlap from different atoms?
{ "text": [ "Pauli repulsion", "Pauli repulsion", "Pauli repulsion", "Pauli repulsion" ], "answer_start": [ 127, 127, 127, 127 ] }
What occurs when electron clouds overlap from different atoms?
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57379a4b1c456719005744cf
Force
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.
What causes Pauli repulsion?
{ "text": [ "fermionic nature of electrons", "fermionic nature of electrons", "fermionic nature of electrons", "fermionic nature of electrons" ], "answer_start": [ 151, 151, 151, 151 ] }
What causes Pauli repulsion?
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57379a4b1c456719005744d0
Force
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.
What is the force that causes rigid strength in structures?
{ "text": [ "normal", "normal force", "normal force", "normal force" ], "answer_start": [ 298, 298, 298, 298 ] }
What is the force that causes rigid strength in structures?
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5737a0acc3c5551400e51f47
Force
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:
What did Newton's mechanics affect?
{ "text": [ "idealized point particles", "idealized point particles rather than three-dimensional objects", "idealized point particles", "idealized point particles" ], "answer_start": [ 100, 100, 100, 100 ] }
What did [MASK] 's mechanics affect?
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5737a0acc3c5551400e51f48
Force
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:
What didn't Newton's mechanics affext?
{ "text": [ "three-dimensional objects", "three-dimensional objects", "three-dimensional objects" ], "answer_start": [ 138, 138, 138 ] }
What did n't [MASK] 's mechanics affext?
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5737a0acc3c5551400e51f49
Force
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:
In what kind of fluid are pressure differences caused by direction of forces over gradients?
{ "text": [ "extended", "extended", "extended" ], "answer_start": [ 530, 530, 530 ] }
In what kind of fluid are pressure differences caused by direction of forces over gradients?
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5737a0acc3c5551400e51f4a
Force
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:
What may a force on one part of an object affect?
{ "text": [ "other parts", "other parts of an object", "other parts of an object", "other parts of an object" ], "answer_start": [ 276, 276, 276, 276 ] }
What may a force on [MASK] part of an object affect?
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5737a0acc3c5551400e51f4b
Force
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:
What does matter actually have that Newtonian mechanics doesn't address?
{ "text": [ "extended structure", "extended structure", "extended structure", "extended structure and forces that act on one part of an object might affect other parts of an object" ], "answer_start": [ 199, 199, 199, 199 ] }
What does matter actually have that Newtonian mechanics doesn't address?
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5737a25ac3c5551400e51f51
Force
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
What causes strain in structures?
{ "text": [ "stress tensor", "stress tensor", "deformations", "The stress tensor" ], "answer_start": [ 376, 376, 434, 372 ] }
What causes strain in structures?
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5737a25ac3c5551400e51f52
Force
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
What is used to calculate cross section area in the volume of an object?
{ "text": [ "pressure terms", "stress tensor", "pressure terms associated with forces that act normal to the cross-sectional area (the matrix diagonals of the tensor) as well as shear terms" ], "answer_start": [ 132, 376, 132 ] }
What is used to calculate cross section area in the volume of an object?
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5737a25ac3c5551400e51f53
Force
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
What are associated with normal forces?
{ "text": [ "pressure terms", "matrix diagonals of the tensor)", "pressure terms" ], "answer_start": [ 132, 219, 132 ] }
What are associated with normal forces?
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5737a25ac3c5551400e51f54
Force
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
What includes pressure terms when calculating area in volume?
{ "text": [ "formalism", "the relevant cross-sectional area for the volume for which the stress-tensor is being calculated", "formalism", "This formalism" ], "answer_start": [ 113, 10, 113, 108 ] }
What includes pressure terms when calculating area in volume?
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5737a4511c456719005744df
Force
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:
What is the force equivalent of torque compared to angular momentum?
{ "text": [ "rotational equivalent for position", "rotation", "rotational inertia", "angle is the rotational equivalent for position" ], "answer_start": [ 77, 14, 242, 64 ] }
What is the force equivalent of torque compared to angular momentum?
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5737a4511c456719005744e0
Force
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:
What would change the rotational inertia of a body under Newton's First Law of Motion?
{ "text": [ "unbalanced torque", "unbalanced torque", "unbalanced torque", "an unbalanced torque" ], "answer_start": [ 346, 346, 346, 343 ] }
What would change the rotational inertia of a body under [MASK] 's [MASK] Law of Motion?
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5737a4511c456719005744e1
Force
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:
To calculate instant angular acceleration of a rigid body what would you use?
{ "text": [ "Newton's Second Law of Motion", "Newton's Second Law of Motion", "Newton's Second Law of Motion", "Newton's Second Law of Motion" ], "answer_start": [ 375, 375, 375, 375 ] }
To calculate instant angular acceleration of a rigid body what would you use?
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5737a7351c456719005744f1
Force
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.
What is the only form potential energy can change into?
{ "text": [ "kinetic", "kinetic", "kinetic", "kinetic" ], "answer_start": [ 127, 127, 127, 127 ] }
What is the only form potential energy can change into?
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5737a7351c456719005744f2
Force
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.
What is the only form kinetic energy can change into?
{ "text": [ "potential", "potential", "potential", "potential" ], "answer_start": [ 138, 138, 138, 138 ] }
What is the only form kinetic energy can change into?
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5737a7351c456719005744f3
Force
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.
What is preserved in a closed system of forces when acted upon?
{ "text": [ "net mechanical energy", "net mechanical energy", "net mechanical energy", "net mechanical energy" ], "answer_start": [ 196, 196, 196, 196 ] }
What is preserved in a closed system of forces when acted upon?
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5737a7351c456719005744f4
Force
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.
What is the force between two locations related to?
{ "text": [ "difference in potential energy", "the difference in potential energy", "the difference in potential energy", "the difference in potential energy between two different locations in space" ], "answer_start": [ 330, 326, 326, 326 ] }
What is the force between [MASK] locations related to?
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5737a7351c456719005744f5
Force
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.
What is the force called rgarding a potential field between two locations?
{ "text": [ "artifact", "artifact of the potential field", "an artifact" ], "answer_start": [ 434, 434, 431 ] }
What is the force called rgarding a potential field between [MASK] locations?
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5737a84dc3c5551400e51f59
Force
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.
What is sometimes impossible to model?
{ "text": [ "forces", "forces as being due to gradient of potentials", "forces", "forces as being due to gradient of potentials" ], "answer_start": [ 58, 58, 58, 58 ] }
What is sometimes impossible to model?
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5737a84dc3c5551400e51f5a
Force
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.
Why are some forces due to that are impossible to model?
{ "text": [ "gradient of potentials", "macrophysical considerations that yield forces as arising from a macroscopic statistical average of microstates", "gradient of potentials.", "gradient of potentials" ], "answer_start": [ 81, 126, 81, 81 ] }
Why are some forces due to that are impossible to model?
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5737a84dc3c5551400e51f5b
Force
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.
What do electrostatic gradiient potentials create?
{ "text": [ "friction", "friction", "friction", "friction" ], "answer_start": [ 252, 252, 252, 252 ] }
What do electrostatic gradiient potentials create?
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5737a84dc3c5551400e51f5c
Force
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.
Tension, compression, and drag are what kind of forces?
{ "text": [ "Nonconservative", "Nonconservative forces other than friction", "Nonconservative", "Nonconservative forces" ], "answer_start": [ 430, 430, 430, 430 ] }
Tension, compression, and drag are what kind of forces?
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5737a9afc3c5551400e51f61
Force
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.
In what treatment are nonconservative and conservative forces described?
{ "text": [ "statistical mechanics", "statistical mechanics", "detailed", "detailed treatment with statistical mechanics" ], "answer_start": [ 134, 134, 110, 110 ] }
In what treatment are nonconservative and conservative forces described?
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5737a9afc3c5551400e51f62
Force
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.
What changes macroscopic closed system energies?
{ "text": [ "nonconservative forces", "internal energies of the system", "nonconservative forces", "nonconservative forces" ], "answer_start": [ 188, 229, 188, 188 ] }
What changes macroscopic closed system energies?
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5737a9afc3c5551400e51f63
Force
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.
What is the exchange of heat associated with?
{ "text": [ "nonconservative forces", "nonconservative forces", "nonconservative forces", "nonconservative forces" ], "answer_start": [ 188, 188, 188, 188 ] }
What is the exchange of heat associated with?
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5737a9afc3c5551400e51f64
Force
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.
What is the law of thermodynamics associated with closed system heat exchange?
{ "text": [ "Second", "Second law of thermodynamics", "Second law", "Second" ], "answer_start": [ 331, 331, 331, 331 ] }
What is the law of thermodynamics associated with closed system heat exchange?
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5737a9afc3c5551400e51f65
Force
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.
What makes energy changes in a closed system?
{ "text": [ "nonconservative forces", "nonconservative forces", "nonconservative forces", "nonconservative forces" ], "answer_start": [ 361, 361, 361, 361 ] }
What makes energy changes in a closed system?
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5737aafd1c456719005744fb
Force
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.
What is the metric term less used than the Newton?
{ "text": [ "kilogram-force", "pound-force", "kilogram-force (kgf)", "kilogram-force", "the kilogram-force (" ], "answer_start": [ 82, 4, 82, 82, 78 ] }
What is the metric term less used than the [MASK]?
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5737aafd1c456719005744fc
Force
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.
What is the kilogram-force sometimes reffered to as?
{ "text": [ "kilopond", "kilopond", "kilopond", "kilopond", "kilopond" ], "answer_start": [ 114, 114, 114, 114, 114 ] }
What is the kilogram-force sometimes reffered to as?
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5737aafd1c456719005744fd
Force
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.
What is a very seldom used unit of mass in the metric system?
{ "text": [ "slug", "metric slug", "metric slug", "metric slug", "the metric slug" ], "answer_start": [ 274, 267, 267, 267, 263 ] }
What is a very seldom used unit of mass in the metric system?
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5737aafd1c456719005744fe
Force
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.
What seldom used term of a unit of force equal to 1000 pound s of force?
{ "text": [ "kip", "kip", "kip", "kip", "kip" ], "answer_start": [ 712, 712, 712, 712, 712 ] }
What seldom used term of a unit of force equal to [MASK] of force?
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5737aafd1c456719005744ff
Force
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.
What is the seldom used force unit equal to one thousand newtons?
{ "text": [ "sthène", "sthène", "sthène", "sthène", "sthène" ], "answer_start": [ 665, 665, 665, 665, 665 ] }
What is the seldom used force unit equal to [MASK]?
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