91Ó°ÊÓ

The mass of block is $m=1\text{kg}$

The speed of block is $v=0.8c$

The total energy of a particle moving at high speed consists of kinetic energy and rest energy. The rest energy is the energy same as produced due to complete conversion of mass of particle into energy. The momentum of moving particle is relativistic momentum.

The internal energy of block is given as:

$E_i=m{c}^2$

Here, c is the speed of light and its value is$3×{10}^8\text{m}/\text{s}$ .

Substitute all the values in the equation.

$$\begin{gathered} E_i=\left(1\text{kg}\right){\left(3×{10}^8\text{m}/\text{s}\right)}^2 \\ {E}_i=9×{10}^{16}\text{J} \end{gathered}$$

The total energy of block is given as:

$E=\frac{m{c}^2}{\sqrt{1-{\left(\frac{v}{c}\right)}^2}}$

Substitute all the values in the equation.

$$\begin{gathered} E=\frac{\left(1\text{kg}\right){\left(3×{10}^8\text{m}/\text{s}\right)}^2}{\sqrt{1-{\left(\frac{0.8c}{c}\right)}^2}} \\ E=15×{10}^{16}\text{J} \end{gathered}$$

The energy of block is given as:

$K=E-E_i$

Substitute all the values in the equation.

$$\begin{gathered} K=15×{10}^{16}\text{J}-9×{10}^{16}\text{J} \\ K=6×{10}^{16}\text{J} \end{gathered}$$

Therefore, the internal energy, kinetic energy and total energy of block are $9×{10}^{16}\text{J}$, $6×{10}^{16}\text{J}$ and $15×{10}^{16}\text{J}$.