Instruct: Given a question, retrieve relevant documents that answer the question.
Query: How is mass measured?
The basic SI unit of mass 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 is the property that (along with gravity) determines the strength of this force.
In everyday usage, mass and "weight" are often used interchangeably. For instance, a person's weight may be stated as 75kg. 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 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 natural course of free fall, which can be influenced by the nearby gravitational field. No matter how strong the gravitational field, objects in free fall are weightless, though they still have mass.[6]
There are several distinct phenomena which can be used to measure mass. Although some theorists have speculated that some of these phenomena could be independent of each other,[2] current experiments have found no difference in results regardless of how it is measured:
The operation of thermal dispersion mass flow meters is attributed to L.V. King who, in 1914, published his famous King's Law revealing how a heated wire immersed in a fluid flow measures the mass velocity at a point in the flow. King called his instrument a "hot-wire anemometer". However, it was not until the 1960s and 1970s that industrial-grade thermal dispersion mass flow meters finally emerged.
The coefficients are calculated by fitting to experimentally measured masses of nuclei. Their values can vary depending on how they are fitted to the data. Several examples are as shown below, with units of megaelectronvolts.
Dynamic vapor sorption (DVS) is a gravimetric technique that measures how quickly and how much of a solvent is absorbed by a sample: such as a dry powder absorbing water. It does this by varying the vapor concentration surrounding the sample and measuring the change in mass which this produces. Water vapor is most commonly used, but it is also possible to use a wide range of organic solvents.
The theorem is very important in extending the ideas of probability theory from probability masses and probability densities defined over real numbers to probability measures defined over arbitrary sets. It tells if and how it is possible to change from one probability measure to another. Specifically, the probability density function of a random variable is the Radon–Nikodym derivative of the induced measure with respect to some base measure (usually the Lebesgue measure for continuous random variables).
The distinction between mass and weight is unimportant for many practical purposes because the strength of gravity does not vary too much on the surface of the Earth. In a uniform gravitational field, the gravitational force exerted on an object (its weight) is directly proportional to its mass. For example, object A weighs 10 times as much as object B, so therefore the mass of object A is 10 times greater than that of object B. This means that an object's mass can be measured indirectly by its weight, and so, for everyday purposes, weighing (using a weighing scale) is an entirely acceptable way of measuring mass. Similarly, a balance measures mass indirectly by comparing the weight of the measured item to that of an object(s) of known mass. Since the measured item and the comparison mass are in virtually the same location, so experiencing the same gravitational field, the effect of varying gravity does not affect the comparison or the resulting measurement.
Note that this set of small measure need not be contiguous; a probability distribution can have several concentrations of mass in intervals of small measure, and the entropy may still be low no matter how widely scattered those intervals are. This is not the case with the variance: variance measures the concentration of mass about the mean of the distribution, and a low variance means that a considerable mass of the probability distribution is concentrated in a "contiguous interval" of small measure.
An accelerometer, in its simplest form, is a damped mass on the end of a spring, with some way of measuring how far the mass has moved on the spring in a particular direction, called an 'axis'.
These different definitions have true physical meaning because different techniques in physical polymer chemistry often measure just one of them. For instance, osmometry measures number average molar mass and small-angle laser light scattering measures mass average molar mass. M is obtained from viscosimetry and M by sedimentation in an analytical ultra-centrifuge. The quantity a in the expression for the viscosity average molar mass varies from 0.5 to 0.8 and depends on the interaction between solvent and polymer in a dilute solution. In a typical distribution curve, the average values are related to each other as follows: M < M < M < M. The dispersity (also known as the "polydispersity index") of a sample is defined as M divided by M and gives an indication just how narrow a distribution is.
In aerospace engineering, mass ratio is a measure of the efficiency of a rocket. It describes how much more massive the vehicle is with propellant than without; that is, the ratio of the rocket's "wet mass" (vehicle plus contents plus propellant) to its "dry mass" (vehicle plus contents). A more efficient rocket design requires less propellant to achieve a given goal, and would therefore have a lower mass ratio; however, for any given efficiency a higher mass ratio typically permits the vehicle to achieve higher delta-v.
The primary difficulty with Mach's definition of mass is that it fails to take into account the potential energy (or binding energy) needed to bring two masses sufficiently close to one another to perform the measurement of mass.[18] This is most vividly demonstrated by comparing the mass of the proton in the nucleus of deuterium, to the mass of the proton in free space (which is greater by about 0.239%—this is due to the binding energy of deuterium.). Thus, for example, if the reference weight m2 is taken to be the mass of the neutron in free space, and the relative accelerations for the proton and neutron in deuterium are computed, then the above formula over-estimates the mass m1 (by 0.239%) for the proton in deuterium. At best, Mach's formula can only be used to obtain ratios of masses, that is, as m1 /m2 = |a2| / |a1|. An additional difficulty was pointed out by Henri Poincaré, which is that the measurement of instantaneous acceleration is impossible: unlike the measurement of time or distance, there is no way to measure acceleration with a single measurement; one must make multiple measurements (of position, time, etc.) and perform a computation to obtain the acceleration. Poincaré termed this to be an "insurmountable flaw" in the Mach definition of mass.[21]
The mass-energy relation can be used to predict how much energy will be released or consumed by nuclear reactions; one simply measures the mass of all constituents and the mass of all the products and multiplies the difference between the two by . The result shows how much energy will be released or consumed, usually in the form of light or heat. When applied to certain nuclear reactions, the equation shows that an extraordinarily large amount of energy will be released, millions of times as much as in the combustion of chemical explosives, where mass is conserved. This explains why nuclear weapons and nuclear reactors produce such phenomenal amounts of energy, as they release binding energy during nuclear fission and nuclear fusion, and convert a portion of subatomic mass to energy.
In relativity, all the energy that moves with an object (that is, all the energy present in the object's rest frame) contributes to the total mass of the body, which measures how much it resists acceleration. Each bit of potential and kinetic energy makes a proportional contribution to the mass. As noted above, even if a box of ideal mirrors "contains" light, then the individually massless photons still contribute to the total mass of the box, by the amount of their energy divided by .
Geoeffectiveness is a measure of how strongly space weather magnetic fields, such as coronal mass ejections, couple with the Earth's magnetic field. This is determined by the direction of the magnetic field held within the plasma that originates from the Sun. New techniques measuring Faraday Rotation in radio waves are in development to measure field direction.
Because of changes in historic measurement systems, it is impossible to make meaningful and accurate comparisons of ship sizes over time beyond length. Three alternative forms of measurement are ship "volume", "weight", and weight of water it "displaces". A fourth, "deadweight tonnage" (DWT), is a measure of how much mass a ship can safely carry, and is thus more relevant to measuring cargo vessels than passenger ships.
In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a "force" that results from the action of gravity on matter: it measures how strongly the force of gravity pulls on that matter. However, in most practical everyday situations the word "weight" is used when, strictly, "mass" is meant. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass.
An air flow meter is a device that measures air flow, i.e. how much air is flowing through a tube. It does not measure the volume of the air passing through the tube, it measures the mass of air flowing through the device per unit time. Thus air flow meters are simply an application of mass flow meters for a special medium. Typically, mass air flow measurements are expressed in the units of kilograms per second (kg/s).
The majority of patented methods for noninvasive monitoring of ICP are based on an assumption that changes in ICP affect the physical dimensions and/or acoustic properties of the cranial vault or intracranial structures (dura, brain tissue, brain ventricles, and/or intracranial vessels). The common drawback of all these methods is that they measure only relative changes of ICP as referenced to a baseline measurement during which absolute ICP is known, i.e. the ultrasound readouts need to be calibrated on each subject against an invasive measurement. Ultrasound ‘time of the flight’ methods for non-invasive ICP monitoring have not been extensively validated and currently, the majority of them do not seem to be accurate enough for a routine clinical use. Their original formulations usually do not specify locations for the transducer's placement and do not address how the intentional or accidental use of different locations and/or angles of the transducers will affect the reliability of ICP estimates. It has also remained unexplored how the measurements are affected by the presence of intracranial pathological masses on the path of the ultrasound wave, or by brain masses shifts.
Measurements demand the use of "operational definitions" of relevant quantities. That is, a scientific quantity is described or defined by how it is measured, as opposed to some more vague, inexact or "idealized" definition. For example, electric current, measured in amperes, may be operationally defined in terms of the mass of silver deposited in a certain time on an electrode in an electrochemical device that is described in some detail. The operational definition of a thing often relies on comparisons with standards: the operational definition of "mass" ultimately relies on the use of an artifact, such as a particular kilogram of platinum-iridium kept in a laboratory in France.
In mathematics, the curvature of a measure defined on the Euclidean plane R is a quantification of how much the measure's "distribution of mass" is "curved". It is related to notions of curvature in geometry. In the form presented below, the concept was introduced in 1995 by the mathematician Mark S. Melnikov; accordingly, it may be referred to as the Melnikov curvature or Menger-Melnikov curvature. Melnikov and Verdera (1995) established a powerful connection between the curvature of measures and the Cauchy kernel.
Planetary mass is a measure of the mass of a planet-like object. Within the Solar System, planets are usually measured in the astronomical system of units, where the unit of mass is the solar mass (), the mass of the Sun. In the study of extrasolar planets, the unit of measure is typically the mass of Jupiter () for large gas giant planets, and the mass of Earth () for smaller rocky terrestrial planets.
In the standard model, neutrinos have exactly zero mass. This is a consequence of the standard model containing only left-handed neutrinos. With no suitable right-handed partner, it is impossible to add a renormalizable mass term to the standard model. Measurements however indicated that neutrinos spontaneously change flavour, which implies that neutrinos have a mass. These measurements only give the mass differences between the different flavours. The best constraint on the absolute mass of the neutrinos comes from precision measurements of tritium decay, providing an upper limit 2 eV, which makes them at least five orders of magnitude lighter than the other particles in the standard model. This necessitates an extension of the standard model, which not only needs to explain how neutrinos get their mass, but also why the mass is so small.
Inertial mass is a measure of an object's resistance to acceleration when a force is applied. It is determined by applying a force to an object and measuring the acceleration that results from that force. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says the body of greater mass has greater inertia. Active gravitational mass[note 3] is a measure of the strength of an object's gravitational flux (gravitational flux is equal to the surface integral of gravitational field over an enclosing surface). Gravitational field can be measured by allowing a small "test object" to fall freely and measuring its free-fall acceleration. For example, an object in free fall near the Moon is subject to a smaller gravitational field, and hence accelerates more slowly, than the same object would if it were in free fall near the Earth. The gravitational field near the Moon is weaker because the Moon has less active gravitational mass. Passive gravitational mass is a measure of the strength of an object's interaction with a gravitational field. Passive gravitational mass is determined by dividing an object's weight by its free-fall acceleration. Two objects within the same gravitational field will experience the same acceleration; however, the object with a smaller passive gravitational mass will experience a smaller force (less weight) than the object with a larger passive gravitational mass. Energy also has mass according to the principle of mass–energy equivalence. This equivalence is exemplified in a large number of physical processes including pair production, nuclear fusion, and the gravitational bending of light. Pair production and nuclear fusion are processes in which measurable amounts of mass are converted to energy, or vice versa. In the gravitational bending of light, photons of pure energy are shown to exhibit a behavior similar to passive gravitational mass. Curvature of spacetime is a relativistic manifestation of the existence of mass. Such curvature is extremely weak and difficult to measure. For this reason, curvature was not discovered until after it was predicted by Einstein's theory of general relativity. Extremely precise atomic clocks on the surface of the Earth, for example, are found to measure less time (run slower) when compared to similar clocks in space. This difference in elapsed time is a form of curvature called gravitational time dilation. Other forms of curvature have been measured using the Gravity Probe B satellite. Quantum mass manifests itself as a difference between an object's quantum frequency and its wave number. The quantum mass of an electron, the Compton wavelength, can be determined through various forms of spectroscopy and is closely related to the Rydberg constant, the Bohr radius, and the classical electron radius. The quantum mass of larger objects can be directly measured using a Kibble balance. In relativistic quantum mechanics, mass is one of the irreducible representation labels of the Poincaré group.