We are given:
- The mass of the particle, m
The total energy or relativistic energy of an object is given by the equation:
[tex]$E=\frac{m c^{2}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$[/tex], where:
- m is the mass of the object.
- [tex]$c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$[/tex] is the speed of light.
- v is the speed of the object.
According to the special theory of relativity, the rest-mass energy, [tex]$E_{0}$[/tex], of a mass, m, is given by the equation: [tex]$E_{0}=m c^{2}$[/tex]
Where, [tex]$c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$[/tex] is the speed of light.
Therefore, the ratio of the two is:
[tex]$\begin{aligned} \frac{E}{E_{0}} &=\frac{m c^{2} / \sqrt{1-\frac{v^{2}}{c^{2}}}}{m c^{2}} \\ &=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}} \end{aligned}$[/tex]
If [tex]$v=0.240 c_{\text {r }}$[/tex] then the ratio of its total energy to its rest energy is:
[tex]$\begin{aligned}\frac{E}{E_{0}} &=\frac{1}{\sqrt{1-\frac{(0.240 c)^{2}}{c^{2}}}} \\&=\frac{1}{\sqrt{1-(0.240)^{2}}} \\&=\frac{1}{\sqrt{0.9424}} \\& \approx \mathbf{1 . 0 3}\end{aligned}$[/tex]
What is Relativistic Energy?
- The mass-energy equivalence concept states that mass and energy may be converted into one another. Its rest-mass energy is the quantity of energy that corresponds to an object's mass while it is at rest.
- The entire energy of an object travelling at relativistic speed is referred to as relativistic energy (speed comparable to the speed of light). It is described as the total of an object's kinetic energy and rest mass.
Correct question : Find the ratio of the total energy to the rest energy of a particle of mass m moving with the following speeds.
(a)0.240 c
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