rest mass

Examples of rest mass in the following topics:

• Relativistic Kinetic Energy

  • Relativistic kinetic energy can be expressed as: $E_{k} = \frac{mc^{2}}{\sqrt{1 - (v/c)^{2})}} - mc^{2}$ where $m$ is rest mass, $v$ is velocity, $c$ is speed of light.
  • Using $m$ for rest mass, $v$ and $\nu$ for the object's velocity and speed respectively, and $c$ for the speed of light in vacuum, the relativistic expression for linear momentum is:
  • The body at rest must have energy content equal to:
  • $KE = mc^2-m_0c^2$, where m is the relativistic mass of the object and m0 is the rest mass of the object.
  • Thus, the total energy can be partitioned into the energy of the rest mass plus the traditional classical kinetic energy at low speeds.

• Relativistic Energy and Mass

  • 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.
  • Relativistic energy ($E_{r} = \sqrt{(m_{0}c^{2})^{2} + (pc)^{^{2}}}$) is connected with rest mass via the following equation: $m = \frac{\sqrt{(E^{2} - (pc)^{^{2}}}}{c^{2}}$.

• Energy, Mass, and Momentum of Photon

  • It has no rest mass and has no electric charge.
  • Momentum of photon: According to the theory of Special Relativity, energy and momentum (p) of a particle with rest mass m has the following relationship: $E^2 = (mc^2)^2+p^2c^2$, where c is the speed of light.
  • In the case of a photon with zero rest mass, we get $E = pc$.
  • You may wonder how an object with zero rest mass can have nonzero momentum.

• Relativistic Shocks

  • It is most clear to use the rest-mass energy density for $n_\mathrm{prop}$.
  • where $w=\epsilon + p$ and $\epsilon$ includes the rest-mass energy of the particles.
  • Here $w$ is the enthalpy per unit volume whereas in previous sections it denoted the enthalpy per unit mass, $w_\mathrm{mass}=w_\mathrm{volume} V$.
  • The first term cancels in the previous equation, leaving the middle term which equals twice the enthalpy per unit mass.

• Photon Interactions and Pair Production

  • ., the total rest mass energy of the two particles) and that the situation allows both energy and momentum to be conserved.
  • The energy of this photon can be converted into mass through Einstein's equation $E=mc^2$ where $E$ is energy, $m$ is mass and $c$ is the speed of light.
  • The photon must have enough energy to create the mass of an electron plus a positron.
  • The mass of an electron is $9.11 \cdot 10^{-31}$ kg (equivalent to 0.511 MeV in energy), the same as a positron.

• Fusion Reactors

  • If two light nuclei fuse, they will generally form a single nucleus with a slightly smaller mass than the sum of their original masses; this is not true in every case, though.
  • The difference in mass is released as energy according to Albert Einstein's mass-energy equivalence formula, E = mc2.
  • Above this atomic mass, energy will generally be released by nuclear fission reactions; below this mass, energy will be released by fusion.
  • Helium has an extremely low mass per nucleon and therefore is energetically favored as a fusion product.
  • This is because the rest of mass of helium and a neutron combined is less than the rest mass of deuterium and tritium combined, providing energy according to E=mc2.

• Normal Forces

  • A more complex example of a situation in which a normal force exists is when a mass rests on an inclined plane.
  • In this case, the normal force is not in the exact opposite direction as the force due to the weight of the mass.
  • This is because the mass contacts the surface at an angle.
  • A mass rests on an inclined plane that is at an angle $\theta$ to the horizontal.
  • The following forces act on the mass: the weight of the mass ($m \cdot g$),the force due to friction ($F_r$),and the normal force ($F_n$).

• Rocket Propulsion, Changing Mass, and Momentum

  • The remainder of the mass (m−m) now has a greater velocity (v+Δv).
  • The third factor is the mass m of the rocket.
  • It can be shown that, in the absence of air resistance and neglecting gravity, the final velocity of a one-stage rocket initially at rest is
  • If we start from rest, the change in velocity equals the final velocity. )
  • (a) This rocket has a mass m and an upward velocity v.

• Measurements of Microbial Mass

  • Changes in the number of bacteria can be calculated by a variety of methods that focus on microbial mass.
  • There are several methods for measuring cell mass, including the gravimeter method which uses ordinary balances to weigh a sample (dry weight/ml) after the water has been removed.
  • An indirect method for calculating cell mass is turbidimetry.
  • Cell cultures are turbid: they absorb some of the light and let the rest of it pass through.
  • An additional method for the measurement of microbial mass is the quantification of cells in a culture by plating the cells on a petri dish.

• Relationship Between Torque and Angular Acceleration

  • Just like Newton's Second Law, which is force is equal to the mass times the acceleration, torque obeys a similar law.
  • If you replace torque with force and rotational inertia with mass and angular acceleration with linear acceleration, you get Newton's Second Law back out.
  • If no outside forces act on an object, an object in motion remains in motion and an object at rest remains at rest.
  • With rotating objects, we can say that unless an outside torque is applied, a rotating object will stay rotating and an object at rest will not begin rotating.