Answer to Question #275983 in Physics for mynol

Question #275983

Find the total energy of a moving object of mass 6.3 π‘˜π‘” and momentum


11.5 Γ— 106 π‘˜π‘”π‘šπ‘ 


βˆ’1


.

1
Expert's answer
2021-12-06T09:48:55-0500

Since the object has a relativistic velocity we need to find the relativistic total energy as follows:


E=Ξ³mc2=mc21βˆ’v2c2.E=\gamma mc^2=\dfrac{mc^2}{\sqrt{1-\dfrac{v^2}{c^2}}}.

We can find the velocity of the object as follows:


p=mv,p=mv,v=pm=11.5Γ—106 kgΓ—ms6.3 kg=18.25Γ—105 ms.v=\dfrac{p}{m}=\dfrac{11.5\times10^6\ \dfrac{kg\times m}{s}}{6.3\ kg}=18.25\times10^5\ \dfrac{m}{s}.

Then, we have:


E=6.3 kgΓ—(3Γ—108 ms)21βˆ’(18.25Γ—105 ms)2(3Γ—108 ms)2=5.67Γ—1017 J.E=\dfrac{6.3\ kg\times(3\times10^8\ \dfrac{m}{s})^2}{\sqrt{1-\dfrac{(18.25\times10^5\ \dfrac{m}{s})^2}{(3\times10^8\ \dfrac{m}{s})^2}}}=5.67\times10^{17}\ J.

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