Question

Find the total energy of a moving object of mass 6.3 𝑘𝑔 and momentum

11.5 × 106 𝑘𝑔𝑚𝑠

−1

.

Answer 1

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

$$E=\gamma mc^2=\dfrac{mc^2}{\sqrt{1-\dfrac{v^2}{c^2}}}.$$

We can find the velocity of the object as follows:

$$p=mv,$$ $$v=\dfrac{p}{m}=\dfrac{11.5\times10^6\ \dfrac{kg\times m}{s}}{6.3\ kg}=18.25\times10^5\ \dfrac{m}{s}.$$

Then, we have:

$$E=\dfrac{6.3\ kg\times(3\times10^8\ \dfrac{m}{s})^2}{\sqrt{1-\dfrac{(18.25\times10^5\ \dfrac{m}{s})^2}{(3\times10^8\ \dfrac{m}{s})^2}}}=5.67\times10^{17}\ J.$$