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?
temperature is the measure of degree of hotness or coldness of a body. measured in kelvin
Ahmad
a characteristic which tells hotness or coldness of a body
babar
Average kinetic energy of an object
Kym
average kinetic energy of the particles in an object
Kym
A measure of the quantity of heat contained in an object which arises from the average kinetic energy of the constituent particles of that object. It can be measured using thermometers. It has a unit of kelvin in the thermodynamic scale and degree Celsius in the Celsius scale.
ibrahim
Mass of air bubble in material medium is negative. why?
how did the value of gravitational constant 6.67×10°-11Nm2kg-2
Varun
A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.45 m. (a) Calculate its velocity just before it strikes the floor.
you could construct an aparatus that might have a slightly higher 'energy profit' than energy used, but you would havw to maintain the machine, and most likely keep it in a vacuum, for no air resistance, and cool it, so chances are quite slim.
Mr.
calculate the force, p, required to just make a 6kg object move along the horizontal surface where the coefficient of friction is 0.25
Gbolahan
Yes ask
Albert
if a man travel 7km 30degree east of North then 10km east find the resultant displacement
disagree. Displacement is the hypotenuse length of the final position to the starting position. Find x,y components of each leg of journey to determine final position, then use final components to calculate the displacement.