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83-405: As a unit of mass , ton can mean: Its original use as a unit of volume has continued in the capacity of cargo ships and in units such as the freight ton and a number of other units, ranging from 35 to 100 cubic feet (0.99 to 2.83  m ) in size. Recent specialized uses include the ton as a means of truck classification . It can also be used as a unit of energy , or in refrigeration as

166-402: A displacement R AB , Newton's law of gravitation states that each object exerts a gravitational force on the other, of magnitude where G is the universal gravitational constant . The above statement may be reformulated in the following way: if g is the magnitude at a given location in a gravitational field, then the gravitational force on an object with gravitational mass M is This

249-466: A long assay ton is approximately 32.67 g (1.152 oz). These amounts bear the same ratio to a milligram as a short or long ton bears to a troy ounce . Therefore, the number of milligrams of a particular metal found in a sample weighing one assay ton gives the number of troy ounces of metal contained in a ton of ore. In documents that predate 1960 the word ton is sometimes spelled tonne , but in more recent documents tonne refers exclusively to

332-406: A bronze ball and a wooden ramp. The wooden ramp was "12 cubits long, half a cubit wide and three finger-breadths thick" with a straight, smooth, polished groove . The groove was lined with " parchment , also smooth and polished as possible". And into this groove was placed "a hard, smooth and very round bronze ball". The ramp was inclined at various angles to slow the acceleration enough so that

415-530: A curved path. "For a stone projected is by the pressure of its own weight forced out of the rectilinear path, which by the projection alone it should have pursued, and made to describe a curve line in the air; and through that crooked way is at last brought down to the ground. And the greater the velocity is with which it is projected, the farther it goes before it falls to the Earth." Newton further reasons that if an object were "projected in an horizontal direction from

498-505: A force from a scale or the surface of a planetary body such as the Earth or the Moon . This force keeps the object from going into free fall. Weight is the opposing force in such circumstances and is thus determined by the acceleration of free fall. On the surface of the Earth, for example, an object with a mass of 50 kilograms weighs 491 newtons, which means that 491 newtons is being applied to keep

581-399: A friend, Edmond Halley , that he had solved the problem of gravitational orbits, but had misplaced the solution in his office. After being encouraged by Halley, Newton decided to develop his ideas about gravity and publish all of his findings. In November 1684, Isaac Newton sent a document to Edmund Halley, now lost but presumed to have been titled De motu corporum in gyrum (Latin for "On

664-421: A gravitational field. Newton further assumed that the strength of each object's gravitational field would decrease according to the square of the distance to that object. If a large collection of small objects were formed into a giant spherical body such as the Earth or Sun, Newton calculated the collection would create a gravitational field proportional to the total mass of the body, and inversely proportional to

747-406: A hammer and a feather are dropped from the same height through the air on Earth, the feather will take much longer to reach the ground; the feather is not really in free -fall because the force of air resistance upwards against the feather is comparable to the downward force of gravity. On the other hand, if the experiment is performed in a vacuum , in which there is no air resistance, the hammer and

830-806: A ship is its weight . As the term indicates, it is measured indirectly, using Archimedes' principle , by first calculating the volume of water displaced by the ship, then converting that value into weight. Traditionally, various measurement rules have been in use, giving various measures in long tons . Today, tonnes are more commonly used. Ship displacement varies by a vessel's degree of load, from its empty weight as designed (known as "lightweight tonnage" ) to its maximum load. Numerous specific terms are used to describe varying levels of load and trim, detailed below. Ship displacement should not be confused with measurements of volume or capacity typically used for commercial vessels and measured by tonnage : net tonnage and gross tonnage . The process of determining

913-463: A string, does the combined system fall faster because it is now more massive, or does the lighter body in its slower fall hold back the heavier body? The only convincing resolution to this question is that all bodies must fall at the same rate. A later experiment was described in Galileo's Two New Sciences published in 1638. One of Galileo's fictional characters, Salviati, describes an experiment using

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996-410: A uniform acceleration and a uniform gravitational field. Thus, the theory postulates that the force acting on a massive object caused by a gravitational field is a result of the object's tendency to move in a straight line (in other words its inertia) and should therefore be a function of its inertial mass and the strength of the gravitational field. In theoretical physics , a mass generation mechanism

1079-407: A unit of power , sometimes called a ton of refrigeration . Because the ton (of any system of measuring weight) is usually the heaviest unit named in colloquial speech, its name also has figurative uses, singular and plural, informally meaning a large amount or quantity, or to a great degree, as in "There's a ton of bees in this hive," "We have tons of homework," and "I love you a ton." The ton

1162-455: A vacuum, as David Scott did on the surface of the Moon during Apollo 15 . A stronger version of the equivalence principle, known as the Einstein equivalence principle or the strong equivalence principle , lies at the heart of the general theory of relativity . Einstein's equivalence principle states that within sufficiently small regions of spacetime, it is impossible to distinguish between

1245-427: A vessel's displacement begins with measuring its draft . This is accomplished by means of its "draft marks". A merchant vessel has three matching sets: one mark each on the port and starboard sides forward, midships, and astern. These marks allow a ship's displacement to be determined to an accuracy of 0.5%. The draft observed at each set of marks is averaged to find a mean draft. The ship's hydrostatic tables show

1328-485: Is a balance scale , which balances the force of one object's weight against the force of another object's weight. The two sides of a balance scale are close enough that the objects experience similar gravitational fields. Hence, if they have similar masses then their weights will also be similar. This allows the scale, by comparing weights, to also compare masses. Consequently, historical weight standards were often defined in terms of amounts. The Romans, for example, used

1411-411: Is a conventional value, based on the amount of energy released by burning one tonne of coal. Plural name is tonnes of coal equivalent . The unit ton is used in refrigeration and air conditioning to measure the rate of heat absorption. Prior to the introduction of mechanical refrigeration, cooling was accomplished by delivering ice. Installing one ton of mechanical refrigeration capacity replaced

1494-541: Is a conventional value, based on the amount of energy released by burning one tonne of crude oil. The unit is used, for example, by the International Energy Agency (IEA), for the reported world energy consumption as TPES in millions of toe (Mtoe). Other sources convert 1 toe into 1.28 tonne of coal equivalent (tce). 1 toe is also standardized as 7.33 barrel of oil equivalent (boe). A tonne of coal equivalent ( tce ), sometimes ton of coal equivalent ,

1577-450: Is a theory which attempts to explain the origin of mass from the most fundamental laws of physics . To date, a number of different models have been proposed which advocate different views of the origin of mass. The problem is complicated by the fact that the notion of mass is strongly related to the gravitational interaction but a theory of the latter has not been yet reconciled with the currently popular model of particle physics , known as

1660-419: Is adequate for most of classical mechanics, and sometimes remains in use in basic education, if the priority is to teach the difference between mass from weight.) This traditional "amount of matter" belief was contradicted by the fact that different atoms (and, later, different elementary particles) can have different masses, and was further contradicted by Einstein's theory of relativity (1905), which showed that

1743-513: Is defined as 224 imperial gallons (35.96 cu ft; 1.018 m), the volume occupied by 1 long ton (2,240 lb; 1,016 kg) of water under the conditions that define the imperial gallon . These are small calories (cal). The large or dietary calorie (Cal) is equal to one kilocalorie (kcal), and is gradually being replaced by the latter correct term. Early values for the explosive energy released by trinitrotoluene (TNT) ranged from 900 to 1100 calories per gram. In order to standardise

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1826-413: Is derived from the tun , the term applied to a cask of the largest capacity. This could contain a volume between 175 and 213 imperial gallons (210 and 256  US gal ; 800 and 970  L ), which could weigh around 2,000 pounds (910  kg ) and occupy some 60 cubic feet (1.7  m ) of space. There are several similar units of mass or volume called the ton : The difference between

1909-472: Is equal to 40 cubic feet (1.133 m), but historically it has had several different definitions. It is used to determine the amount of money to be charged in loading, unloading, or carrying different sorts of cargo. In general if a cargo is heavier than salt water, the actual weight is used. If it is lighter than salt water, e.g. feathers, freight is calculated in measurement tons of 40 cubic feet. Gross tonnage and net tonnage are volumetric measures of

1992-546: Is equivalent to 20 hundredweight; however, they are long 51 kilograms (112 lb) or short hundredweight 45 kilograms (100 lb), respectively. Before the 20th century there were several definitions. Prior to the 15th century in England, the ton was 20 hundredweight, each of 108 lb, giving a ton of 2,160 pounds (980 kg). In the 19th century in different parts of Britain, definitions of 2,240, or 2,352, or 2,400 lb were used, with 2,000 lb for explosives;

2075-416: Is measured: The mass of an object determines its acceleration in the presence of an applied force. The inertia and the inertial mass describe this property of physical bodies at the qualitative and quantitative level respectively. According to Newton's second law of motion , if a body of fixed mass m is subjected to a single force F , its acceleration a is given by F / m . A body's mass also determines

2158-552: Is pronounced / t ɒ n / . In Ireland and most members of the Commonwealth of Nations, a ton is defined as 2,240 pounds (1,016.04691 kg). In the United States and Canada, a ton is defined as 2,000 pounds (907.18474 kg). Assay ton (abbreviation 'AT') is not a unit of measurement but a standard quantity used in assaying ores of precious metals. A short assay ton is approximately 29.17 g (1.029 oz) and

2241-459: Is the kilogram (kg). In physics , mass is not the same as weight , even though mass is often determined by measuring the object's weight using a spring scale , rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass

2324-408: Is the acceleration due to Earth's gravitational field , (expressed as the acceleration experienced by a free-falling object). For other situations, such as when objects are subjected to mechanical accelerations from forces other than the resistance of a planetary surface, the weight force is proportional to the mass of an object multiplied by the total acceleration away from free fall, which is called

2407-430: Is the basis by which masses are determined by weighing . In simple spring scales , for example, the force F is proportional to the displacement of the spring beneath the weighing pan, as per Hooke's law , and the scales are calibrated to take g into account, allowing the mass M to be read off. Assuming the gravitational field is equivalent on both sides of the balance, a balance measures relative weight, giving

2490-427: Is the gravitational mass ( standard gravitational parameter ) of the body causing gravitational fields, and R is the radial coordinate (the distance between the centers of the two bodies). By finding the exact relationship between a body's gravitational mass and its gravitational field, Newton provided a second method for measuring gravitational mass. The mass of the Earth can be determined using Kepler's method (from

2573-699: Is the property that (along with gravity) determines the strength of this force. In the Standard Model of physics, the mass of elementary particles is believed to be a result of their coupling with the Higgs boson in what is known as the Brout–Englert–Higgs mechanism . There are several distinct phenomena that can be used to measure mass. Although some theorists have speculated that some of these phenomena could be independent of each other, current experiments have found no difference in results regardless of how it

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2656-410: Is theoretically possible to collect an immense number of small objects and form them into an enormous gravitating sphere. However, from a practical standpoint, the gravitational fields of small objects are extremely weak and difficult to measure. Newton's books on universal gravitation were published in the 1680s, but the first successful measurement of the Earth's mass in terms of traditional mass units,

2739-462: The Cavendish experiment , did not occur until 1797, over a hundred years later. Henry Cavendish found that the Earth's density was 5.448 ± 0.033 times that of water. As of 2009, the Earth's mass in kilograms is only known to around five digits of accuracy, whereas its gravitational mass is known to over nine significant figures. Given two objects A and B, of masses M A and M B , separated by

2822-532: The Solar System . On 25 August 1609, Galileo Galilei demonstrated his first telescope to a group of Venetian merchants, and in early January 1610, Galileo observed four dim objects near Jupiter, which he mistook for stars. However, after a few days of observation, Galileo realized that these "stars" were in fact orbiting Jupiter. These four objects (later named the Galilean moons in honor of their discoverer) were

2905-550: The Standard Model . The concept of amount is very old and predates recorded history . The concept of "weight" would incorporate "amount" and acquire a double meaning that was not clearly recognized as such. What we now know as mass was until the time of Newton called “weight.” ... A goldsmith believed that an ounce of gold was a quantity of gold. ... But the ancients believed that a beam balance also measured “heaviness” which they recognized through their muscular senses. ... Mass and its associated downward force were believed to be

2988-405: The carob seed ( carat or siliqua ) as a measurement standard. If an object's weight was equivalent to 1728 carob seeds , then the object was said to weigh one Roman pound. If, on the other hand, the object's weight was equivalent to 144 carob seeds then the object was said to weigh one Roman ounce (uncia). The Roman pound and ounce were both defined in terms of different sized collections of

3071-492: The elementary charge . Non-SI units accepted for use with SI units include: Outside the SI system, other units of mass include: In physical science , one may distinguish conceptually between at least seven different aspects of mass , or seven physical notions that involve the concept of mass . Every experiment to date has shown these seven values to be proportional , and in some cases equal, and this proportionality gives rise to

3154-442: The melting point of ice. However, because precise measurement of a cubic decimetre of water at the specified temperature and pressure was difficult, in 1889 the kilogram was redefined as the mass of a metal object, and thus became independent of the metre and the properties of water, this being a copper prototype of the grave in 1793, the platinum Kilogramme des Archives in 1799, and the platinum–iridium International Prototype of

3237-421: The metric ton . In nuclear power plants tHM and MTHM mean tonnes of heavy metals , and MTU means tonnes of uranium . In the steel industry, the abbreviation THM means 'tons/tonnes hot metal', which refers to the amount of liquid iron or steel that is produced, particularly in the context of blast furnace production or specific consumption. A dry ton or dry tonne has the same mass value, but

3320-416: The proper acceleration . Through such mechanisms, objects in elevators, vehicles, centrifuges, and the like, may experience weight forces many times those caused by resistance to the effects of gravity on objects, resulting from planetary surfaces. In such cases, the generalized equation for weight W of an object is related to its mass m by the equation W = – ma , where a is the proper acceleration of

3403-453: The torsion balance pendulum, in 1889. As of 2008 , no deviation from universality, and thus from Galilean equivalence, has ever been found, at least to the precision 10 . More precise experimental efforts are still being carried out. The universality of free-fall only applies to systems in which gravity is the only acting force. All other forces, especially friction and air resistance , must be absent or at least negligible. For example, if

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3486-444: The "Galilean equivalence principle" or the " weak equivalence principle " has the most important consequence for freely falling objects. Suppose an object has inertial and gravitational masses m and M , respectively. If the only force acting on the object comes from a gravitational field g , the force on the object is: Given this force, the acceleration of the object can be determined by Newton's second law: Putting these together,

3569-400: The 17th century have demonstrated that inertial and gravitational mass are identical; since 1915, this observation has been incorporated a priori in the equivalence principle of general relativity . The International System of Units (SI) unit of mass is the kilogram (kg). The kilogram is 1000 grams (g), and was first defined in 1795 as the mass of one cubic decimetre of water at

3652-654: The Kilogram (IPK) in 1889. However, the mass of the IPK and its national copies have been found to drift over time. The re-definition of the kilogram and several other units came into effect on 20 May 2019, following a final vote by the CGPM in November 2018. The new definition uses only invariant quantities of nature: the speed of light , the caesium hyperfine frequency , the Planck constant and

3735-428: The abstract concept of mass. There are a number of ways mass can be measured or operationally defined : In everyday usage, mass and " weight " are often used interchangeably. For instance, a person's weight may be stated as 75 kg. In a constant gravitational field, the weight of an object is proportional to its mass, and it is unproblematic to use the same unit for both concepts. But because of slight differences in

3818-471: The cargo-carrying capacity of a ship. The Panama Canal/Universal Measurement System (PC/UMS) is based on net tonnage , modified for Panama Canal billing purposes. PC/UMS is based on a mathematical formula to calculate a vessel's total volume; a PC/UMS net ton is equivalent to 100 cubic feet of capacity. The water ton is used chiefly in Great Britain, in statistics dealing with petroleum products, and

3901-405: The classical theory offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact. Albert Einstein developed his general theory of relativity starting with the assumption that the inertial and passive gravitational masses are the same. This is known as the equivalence principle . The particular equivalence often referred to as

3984-420: The corresponding volume displaced. To calculate the weight of the displaced water, it is necessary to know its density. Seawater (1,025 kg/m ) is more dense than fresh water (1,000 kg/m ); so a ship will ride higher in salt water than in fresh. The density of water also varies with temperature. Devices akin to slide rules have been available since the 1950s to aid in these calculations. Presently, it

4067-403: The daily delivery of one ton of ice. The refrigeration ton is commonly abbreviated as RT . Unit of mass Mass is an intrinsic property of a body . It was traditionally believed to be related to the quantity of matter in a body, until the discovery of the atom and particle physics . It was found that different atoms and different elementary particles , theoretically with

4150-457: The degree to which it generates and is affected by a gravitational field . If a first body of mass m A is placed at a distance r (center of mass to center of mass) from a second body of mass m B , each body is subject to an attractive force F g = Gm A m B / r , where G = 6.67 × 10  N⋅kg ⋅m is the "universal gravitational constant ". This is sometimes referred to as gravitational mass. Repeated experiments since

4233-470: The double of the distance between the two bodies. Hooke urged Newton, who was a pioneer in the development of calculus , to work through the mathematical details of Keplerian orbits to determine if Hooke's hypothesis was correct. Newton's own investigations verified that Hooke was correct, but due to personal differences between the two men, Newton chose not to reveal this to Hooke. Isaac Newton kept quiet about his discoveries until 1684, at which time he told

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4316-434: The elapsed time could be measured. The ball was allowed to roll a known distance down the ramp, and the time taken for the ball to move the known distance was measured. The time was measured using a water clock described as follows: Galileo found that for an object in free fall, the distance that the object has fallen is always proportional to the square of the elapsed time: Galileo had shown that objects in free fall under

4399-497: The exact number of carob seeds that would be required to produce a gravitational field similar to that of the Earth or Sun. In fact, by unit conversion it is a simple matter of abstraction to realize that any traditional mass unit can theoretically be used to measure gravitational mass. Measuring gravitational mass in terms of traditional mass units is simple in principle, but extremely difficult in practice. According to Newton's theory, all objects produce gravitational fields and it

4482-410: The feather should hit the ground at exactly the same time (assuming the acceleration of both objects towards each other, and of the ground towards both objects, for its own part, is negligible). This can easily be done in a high school laboratory by dropping the objects in transparent tubes that have the air removed with a vacuum pump. It is even more dramatic when done in an environment that naturally has

4565-404: The first celestial bodies observed to orbit something other than the Earth or Sun. Galileo continued to observe these moons over the next eighteen months, and by the middle of 1611, he had obtained remarkably accurate estimates for their periods. Sometime prior to 1638, Galileo turned his attention to the phenomenon of objects in free fall, attempting to characterize these motions. Galileo was not

4648-402: The first paragraph of Principia , Newton defined quantity of matter as “density and bulk conjunctly”, and mass as quantity of matter. The quantity of matter is the measure of the same, arising from its density and bulk conjunctly. ... It is this quantity that I mean hereafter everywhere under the name of body or mass. And the same is known by the weight of each body; for it is proportional to

4731-436: The first to investigate Earth's gravitational field, nor was he the first to accurately describe its fundamental characteristics. However, Galileo's reliance on scientific experimentation to establish physical principles would have a profound effect on future generations of scientists. It is unclear if these were just hypothetical experiments used to illustrate a concept, or if they were real experiments performed by Galileo, but

4814-560: The gap between Galileo's gravitational acceleration and Kepler's elliptical orbits. It appeared in Newton's 1728 book A Treatise of the System of the World . According to Galileo's concept of gravitation, a dropped stone falls with constant acceleration down towards the Earth. However, Newton explains that when a stone is thrown horizontally (meaning sideways or perpendicular to Earth's gravity) it follows

4897-421: The gravitational acceleration is given by: This says that the ratio of gravitational to inertial mass of any object is equal to some constant K if and only if all objects fall at the same rate in a given gravitational field. This phenomenon is referred to as the "universality of free-fall". In addition, the constant K can be taken as 1 by defining our units appropriately. The first experiments demonstrating

4980-626: The influence of the Earth's gravitational field have a constant acceleration, and Galileo's contemporary, Johannes Kepler, had shown that the planets follow elliptical paths under the influence of the Sun's gravitational mass. However, Galileo's free fall motions and Kepler's planetary motions remained distinct during Galileo's lifetime. According to K. M. Browne: "Kepler formed a [distinct] concept of mass ('amount of matter' ( copia materiae )), but called it 'weight' as did everyone at that time." Finally, in 1686, Newton gave this distinct concept its own name. In

5063-460: The legal ton was usually 2,240 lb. In the United Kingdom, Canada, Australia, and other areas that had used the imperial system, the tonne is the form of ton legal in trade. The displacement , essentially the weight, of a ship is traditionally expressed in long tons . To simplify measurement it is determined by measuring the volume , rather than weight, of water displaced, and calculating

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5146-447: The material ( sludge , slurries, compost , and similar mixtures in which solid material is soaked with or suspended in water ) has been dried to a relatively low, consistent moisture level ( dry weight ). If the material is in its natural, wet state, it is called a wet ton or wet tonne . Both the UK definition of long ton and US definition of short ton have similar underlying bases. Each

5229-405: The measurable mass of an object increases when energy is added to it (for example, by increasing its temperature or forcing it near an object that electrically repels it.) This motivates a search for a different definition of mass that is more accurate than the traditional definition of "the amount of matter in an object". Displacement (ship) The displacement or displacement tonnage of

5312-544: The motion of bodies in an orbit"). Halley presented Newton's findings to the Royal Society of London, with a promise that a fuller presentation would follow. Newton later recorded his ideas in a three-book set, entitled Philosophiæ Naturalis Principia Mathematica (English: Mathematical Principles of Natural Philosophy ). The first was received by the Royal Society on 28 April 1685–86; the second on 2 March 1686–87; and

5395-403: The nearby gravitational field. No matter how strong the gravitational field, objects in free fall are weightless , though they still have mass. The force known as "weight" is proportional to mass and acceleration in all situations where the mass is accelerated away from free fall. For example, when a body is at rest in a gravitational field (rather than in free fall), it must be accelerated by

5478-509: The object caused by all influences other than gravity. (Again, if gravity is the only influence, such as occurs when an object falls freely, its weight will be zero). Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. In classical mechanics , Newton's third law implies that active and passive gravitational mass must always be identical (or at least proportional), but

5561-430: The object from going into free fall. By contrast, on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons, because only 81.5 newtons is required to keep this object from going into a free fall on the moon. Restated in mathematical terms, on the surface of the Earth, the weight W of an object is related to its mass m by W = mg , where g = 9.80665 m/s

5644-412: The orbit of Earth's Moon), or it can be determined by measuring the gravitational acceleration on the Earth's surface, and multiplying that by the square of the Earth's radius. The mass of the Earth is approximately three-millionths of the mass of the Sun. To date, no other accurate method for measuring gravitational mass has been discovered. Newton's cannonball was a thought experiment used to bridge

5727-409: The planets orbit the Sun. In Kepler's final planetary model, he described planetary orbits as following elliptical paths with the Sun at a focal point of the ellipse . Kepler discovered that the square of the orbital period of each planet is directly proportional to the cube of the semi-major axis of its orbit, or equivalently, that the ratio of these two values is constant for all planets in

5810-464: The relative gravitation mass of each object. Mass was traditionally believed to be a measure of the quantity of matter in a physical body, equal to the "amount of matter" in an object. For example, Barre´ de Saint-Venant argued in 1851 that every object contains a number of "points" (basically, interchangeable elementary particles), and that mass is proportional to the number of points the object contains. (In practice, this "amount of matter" definition

5893-547: The results obtained from these experiments were both realistic and compelling. A biography by Galileo's pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass. In support of this conclusion, Galileo had advanced the following theoretical argument: He asked if two bodies of different masses and different rates of fall are tied by

5976-471: The same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia , meaning the resistance to acceleration (change of velocity ) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass

6059-503: The same common mass standard, the carob seed. The ratio of a Roman ounce (144 carob seeds) to a Roman pound (1728 carob seeds) was: In 1600 AD, Johannes Kepler sought employment with Tycho Brahe , who had some of the most precise astronomical data available. Using Brahe's precise observations of the planet Mars, Kepler spent the next five years developing his own method for characterizing planetary motion. In 1609, Johannes Kepler published his three laws of planetary motion, explaining how

6142-407: The same thing. Humans, at some early era, realized that the weight of a collection of similar objects was directly proportional to the number of objects in the collection: where W is the weight of the collection of similar objects and n is the number of objects in the collection. Proportionality, by definition, implies that two values have a constant ratio : An early use of this relationship

6225-482: The short ton and the other common forms ("long" and "metric") is about 10%, while the metric and long tons differ by less than 2%. The metric tonne is usually distinguished by its spelling when written, but in the United States and United Kingdom, it is pronounced the same as ton, hence is often spoken as "metric ton" when it is necessary to make the distinction. In the United Kingdom the final "e" of "tonne" can also be pronounced ( / ˈ t ʌ n i / ). In Australia, it

6308-441: The square of the distance to the body's center. For example, according to Newton's theory of universal gravitation, each carob seed produces a gravitational field. Therefore, if one were to gather an immense number of carob seeds and form them into an enormous sphere, then the gravitational field of the sphere would be proportional to the number of carob seeds in the sphere. Hence, it should be theoretically possible to determine

6391-501: The strength of the Earth's gravitational field at different places, the distinction becomes important for measurements with a precision better than a few percent, and for places far from the surface of the Earth, such as in space or on other planets. Conceptually, "mass" (measured in kilograms ) refers to an intrinsic property of an object, whereas "weight" (measured in newtons ) measures an object's resistance to deviating from its current course of free fall , which can be influenced by

6474-497: The third on 6 April 1686–87. The Royal Society published Newton's entire collection at their own expense in May 1686–87. Isaac Newton had bridged the gap between Kepler's gravitational mass and Galileo's gravitational acceleration, resulting in the discovery of the following relationship which governed both of these: where g is the apparent acceleration of a body as it passes through a region of space where gravitational fields exist, μ

6557-492: The top of a high mountain" with sufficient velocity, "it would reach at last quite beyond the circumference of the Earth, and return to the mountain from which it was projected." In contrast to earlier theories (e.g. celestial spheres ) which stated that the heavens were made of entirely different material, Newton's theory of mass was groundbreaking partly because it introduced universal gravitational mass : every object has gravitational mass, and therefore, every object generates

6640-459: The universality of free-fall were—according to scientific 'folklore'—conducted by Galileo obtained by dropping objects from the Leaning Tower of Pisa . This is most likely apocryphal: he is more likely to have performed his experiments with balls rolling down nearly frictionless inclined planes to slow the motion and increase the timing accuracy. Increasingly precise experiments have been performed, such as those performed by Loránd Eötvös , using

6723-656: The use of the term TNT as a unit of energy, an arbitrary value was assigned based on 1,000 calories (1 kcal or 4.184  kJ ) per gram. Thus there is no longer a direct connection to the chemical TNT itself. It is now merely a unit of energy that happens to be expressed using words normally associated with mass (e.g., kilogram, tonne, pound). The definition applies for both spellings: ton of TNT and tonne of TNT . Measurements in tons of TNT have been used primarily to express nuclear weapon yields , though they have also been used since in seismology as well. A tonne of oil equivalent (toe), sometimes ton of oil equivalent ,

6806-413: The weight from the volume and density. For practical purposes the displacement ton (DT) is a unit of volume, 35 cubic feet (0.9911 m), the approximate volume occupied by one ton of seawater (the actual volume varies with salinity and temperature). It is slightly less than the 224 imperial gallons (1.018 m) of the water ton (based on distilled water ). One measurement ton or freight ton

6889-535: The weight. Robert Hooke had published his concept of gravitational forces in 1674, stating that all celestial bodies have an attraction or gravitating power towards their own centers, and also attract all the other celestial bodies that are within the sphere of their activity. He further stated that gravitational attraction increases by how much nearer the body wrought upon is to its own center. In correspondence with Isaac Newton from 1679 and 1680, Hooke conjectured that gravitational forces might decrease according to

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