Relativistic energy is conserved as long as we define it to include the possibility of mass changing to energy.
Total Energy is defined as:
$E={\mathrm{\gamma mc}}^{2}$ , where
$\gamma =\frac{1}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}$ .
Rest energy is
${E}_{0}={\mathrm{mc}}^{2}$ , meaning that mass is a form of energy. If energy is stored in an object, its mass increases. Mass can be destroyed to release energy.
We do not ordinarily notice the increase or decrease in mass of an object because the change in mass is so small for a large increase in energy.
The relativistic work-energy theorem is
${W}_{\text{net}}=E-{E}_{0}=\gamma {\mathrm{mc}}^{2}-{\mathrm{mc}}^{2}=\left(\gamma -1\right){\mathrm{mc}}^{2}$ .
Relativistically,
${W}_{\text{net}}={\text{KE}}_{\text{rel}}$ ,
where
${\text{KE}}_{\text{rel}}$ is the relativistic kinetic energy.
Relativistic kinetic energy is
${\text{KE}}_{\text{rel}}=\left(\gamma -1\right){\mathrm{mc}}^{2}$ , where
$\gamma =\frac{1}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}$ . At low velocities, relativistic kinetic energy reduces to classical kinetic energy.
No object with mass can attain the speed of light because an infinite amount of work and an infinite amount of energy input is required to accelerate a mass to the speed of light.
The equation
${E}^{2}=(\mathrm{pc}{)}^{2}+({\mathrm{mc}}^{2}{)}^{2}$ relates the relativistic total energy
$E$ and the relativistic momentum
$p$ . At extremely high velocities, the rest energy
${\mathrm{mc}}^{2}$ becomes negligible, and
$E=\mathrm{pc}$ .
Conceptual questions
How are the classical laws of conservation of energy and conservation of mass modified by modern relativity?
Consider a thought experiment. You place an expanded balloon of air on weighing scales outside in the early morning. The balloon stays on the scales and you are able to measure changes in its mass. Does the mass of the balloon change as the day progresses? Discuss the difficulties in carrying out this experiment.
The mass of the fuel in a nuclear reactor decreases by an observable amount as it puts out energy. Is the same true for the coal and oxygen combined in a conventional power plant? If so, is this observable in practice for the coal and oxygen? Explain.
If you use an Earth-based telescope to project a laser beam onto the Moon, you can move the spot across the Moon’s surface at a velocity greater than the speed of light. Does this violate modern relativity? (Note that light is being sent from the Earth to the Moon, not across the surface of the Moon.)
What is the rest energy of an electron, given its mass is
$9\text{.}\text{11}\times {\text{10}}^{-\text{31}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ ? Give your answer in joules and MeV.
Find the rest energy in joules and MeV of a proton, given its mass is
$1\text{.}\text{67}\times {\text{10}}^{-\text{27}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ .
If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6 MeV respectively, what is the difference in their masses in kilograms?
please explain; when a glass rod is rubbed with silk, it becomes positive and the silk becomes negative- yet both attracts dust. does dust have third types of charge that is attracted to both positive and negative
The Critical Angle Derivation
So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
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Chidalu
pls who can give the definition of relative density?
Temiloluwa
the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
Instantaneous velocity is defined as the rate of change of position for a time interval which is almost equal to zero
Astronomy
The potential in a region between x= 0 and x = 6.00 m
lis V= a+ bx, where a = 10.0 V and b = -7.00 V/m.
Determine (a) the potential atx=0, 3.00 m, and 6.00 m
and (b) the magnitude and direction of the electric
ficld at x =0, 3.00 m, and 6.00 m.