mass

Examples of mass in the following topics:

• Mass

  • In theoretical physics, a mass generation mechanism is a theory which attempts to explain the origin of mass from the most fundamental laws of physics.
  • The physical property we are covering in this atom is called mass.
  • Weight is a different property of matter that, while related to mass, is not mass, but rather the amount of gravitational force acting on a given body of matter.
  • Mass is an intrinsic property that never changes.
  • The International System of Units (SI) measures mass in kilograms, or kg.

• Physics and Engeineering: Center of Mass

  • For a continuous mass distribution, the position of center of mass is given as $\mathbf R = \frac 1M \int_V\rho(\mathbf{r}) \mathbf{r} dV$ .
  • In physics, the center of mass (COM) of a mass or object in space is the unique point at which the weighted relative position of the distributed mass sums to zero.
  • In this case, the distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates.
  • where $M$ is the total mass in the volume.
  • The two objects are rotating around their center of mass.

• Locating the Center of Mass

  • The center of mass is a statement of spatial arrangement of mass (i.e. distribution of mass within the system).
  • where M is the total mass in the volume.
  • If a continuous mass distribution has uniform density, which means ρ is constant, then the center of mass is the same as the center of the volume.
  • Thus, the center of mass of a circular cylinder of constant density has its center of mass on the axis of the cylinder.
  • Identify the center of mass for an object with continuous mass distribution

• Molar Mass of Compounds

  • The molar mass of a particular substance is the mass of one mole of that substance.
  • The mass of one mole of atoms of a pure element in grams is equivalent to the atomic mass of that element in atomic mass units (amu) or in grams per mole (g/mol).
  • Molar mass is the mass of a given substance divided by the amount of that substance, measured in g/mol.
  • The characteristic molar mass of an element is simply the atomic mass in g/mol.
  • However, molar mass can also be calculated by multiplying the atomic mass in amu by the molar mass constant (1 g/mol).

• The Law of Conservation of Mass

  • The law of conservation of mass states that mass in an isolated system is neither created nor destroyed.
  • However, Antoine Lavoisier described the law of conservation of mass (or the principle of mass/matter conservation) as a fundamental principle of physics in 1789.
  • In other words, in a chemical reaction, the mass of the products will always be equal to the mass of the reactants.
  • This law was later amended by Einstein in the law of conservation of mass-energy, which describes the fact that the total mass and energy in a system remain constant.
  • However, the law of conservation of mass remains a useful concept in chemistry, since the energy produced or consumed in a typical chemical reaction accounts for a minute amount of mass.

• Average Atomic Mass

  • The average atomic mass of an element is the sum of the masses of its isotopes, each multiplied by its natural abundance.
  • These different types of helium atoms have different masses (3 or 4 atomic mass units), and they are called isotopes.
  • Then, calculate the mass numbers.
  • To calculate the average atomic mass, multiply the fraction by the mass number for each isotope, then add them together.
  • Whenever we do mass calculations involving elements or compounds (combinations of elements), we always use average atomic masses.

• High Resolution Spectra

  • In assigning mass values to atoms and molecules, we have assumed integral values for isotopic masses.
  • Thus, relative to 12C at 12.0000, the isotopic mass of 16O is 15.9949 amu (not 16) and 14N is 14.0031 amu (not 14).
  • By designing mass spectrometers that can determine m/z values accurately to four decimal places, it is possible to distinguish different formulas having the same nominal mass.
  • Mass spectrometry therefore not only provides a specific molecular mass value, but it may also establish the molecular formula of an unknown compound.
  • Tables of precise mass values for any molecule or ion are available in libraries; however, the mass calculator provided below serves the same purpose.

• Mass Spectrometer

  • Mass spectrometry (MS) is the art of displaying the spectra (singular spectrum) of the masses of a sample of material.
  • Mass spectrometers, as diagramed in , separate compounds based on a property known as the mass-to-charge ratio.
  • Since the acceleration of a charge is dependent on the mass and strength of the charge, a lighter mass-to-charge ratio will not travel as far as a high mass-to-charge ratio, allowing for comparison of the physical properties of different particles.
  • The elements or molecules are uniquely identified by correlating known masses by the identified masses.
  • Schematics of a simple mass spectrometer with sector type mass analyzer.

• Center of Mass and Inertia

  • The center of mass for a rigid body can be expressed as a triple integral.
  • where $M$ is the sum of the masses of all of the particles.
  • where $M$ is the total mass in the volume.
  • Two bodies orbiting around the center of mass inside one body
  • Use multiple integrals to find the center of mass of a distribution of mass

• Mass-to-Mole Conversions

  • Mass-to-mole conversions can be facilitated by employing the molar mass as a conversion ratio.
  • The relative atomic mass is a ratio between the average mass of an element and 1/12 of the mass of an atom of carbon-12.
  • From the relative atomic mass of each element, it is possible to determine each element's molar mass by multiplying the molar mass constant (1 g/mol) by the atomic weight of that particular element.
  • The molar mass value can be used as a conversion factor to facilitate mass-to-mole and mole-to-mass conversions.
  • The molar mass of water is 18 g/mol.