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.

• 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

• 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 Gravity

  • This center of mass's main characteristic is that it appears to carry the whole mass of the body.
  • The center of mass does not actually carry all the mass, despite appearances.
  • Specifically: 'the total mass x the position of the center of mass= ∑ the mass of the individual particle x the position of the particle. ' The center of mass is a geometric point in three-dimensional volume.
  • where r is the reference axis x, y, or z; m is individual mass; ri is the individual position; and M is the total mass.
  • When taking the center of mass of an oddly shaped object, it is helpful to break it down into smaller sections whose mass and properties are easier to evaluate, and then add the products of the individual masses and positions and divide by the total mass.

• Mass

  • Mass is the quantity of matter that an object contains, as measured by its resistance to acceleration.
  • Mass, specifically inertial mass, is a quantitative measure of an object's resistance to acceleration.
  • The SI unit of mass is the kilogram (kg).
  • The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water.
  • A graph of the relative change in mass of selected kilogram prototypes.

• Weight of the Earth

  • Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.
  • In modern language, the law states the following: Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.
  • where $F$ is the force between the masses, $G$ is the gravitational constant, $m_1$ is the first mass, $m_2$ is the second mass and $r$ is the distance between the centers of the masses.
  • The theorem tells us how different parts of the mass distribution affect the gravitational force measured at a point located a distance $r_0$ from the center of the mass distribution:
  • The portion of the mass that is located at radii $rmass enclosed within a sphere of radius $r_0$ was concentrated at the center of the mass distribution (as noted above).

• Gravitational Attraction of Spherical Bodies: A Uniform Sphere

  • That is, a mass $m$ within a spherically symmetric shell of mass $M$, will feel no net force (Statement 2 of Shell Theorem).
  • Only the mass of the sphere within the desired radius $M_{mass of the sphere inside $d$) is relevant, and can be considered as a point mass at the center of the sphere.
  • So, the gravitational force acting upon point mass $m$ is:
  • That is, the sphere's mass is uniformly distributed.)
  • which shows that mass $m$ feels a force that is linearly proportional to its distance, $d$, from the sphere's center of mass.

• Introduction to Two Coupled Masses

  • where $F_i$ is the total force acting on the i-th mass.
  • No matter how many springs and masses we have in the system, the force applied to a given mass must be transmitted by the two springs it is connected to.
  • For instance, suppose both masses are displaced to the right (positive $x_i$ ) with mass 1 being displaced more than mass 2.
  • Similarly, suppose both masses are displaced to the right, but now with mass 2 displaced more than mass 1, corresponding to spring 2 being stretched.
  • This should result in a force on mass 1 in the positive $x$ direction since the mass is being pulled away from its equilibrium position.

• The Law of Universal Gravitation

  • Objects with mass feel an attractive force that is proportional to their masses and inversely proportional to the square of the distance.
  • The Law of Universal Gravitation states that every point mass attracts every other point mass in the universe by a force pointing in a straight line between the centers-of-mass of both points, and this force is proportional to the masses of the objects and inversely proportional to their separation This attractive force always points inward, from one point to the other.
  • The Law applies to all objects with masses, big or small.
  • For these cases the mass of each object can be represented as a point mass located at its center-of-mass.
  • All masses are attracted to each other.

• Relativistic Energy and Mass

  • The conservation of mass and energy are well-accepted laws of physics.
  • Relativistic mass was defined by Richard C.
  • For a slower than light particle, a particle with a nonzero rest mass, the formula becomes where is the rest mass and is the Lorentz factor.
  • When the relative velocity is zero, is simply equal to 1, and the relativistic mass is reduced to the rest mass.
  • In the formula for momentum the mass that occurs is the relativistic mass.