Chapter 26, Problem 71GP

To determine

The spaceship’s kinetic energy.

To compare: The obtained energy with totalannual energy consumption.

Answer to Problem 71GP

The spaceship’s kinetic energy is $\text{6}{\text{.8×10}}^{\text{21}}\text{J}$ and spaceship’s kinetic energy is about 68 times of total energy consumption.

Explanation of Solution

Given:

Rest mass is $\text{12,500}\text{kg}$

Speed is $\text{0}\text{.99}\text{c}$

Formula used:

It is known that,

  $KE=\frac{m_0{c}^2}{\sqrt{1-\frac{v^2}{c^2}}}-m_0{c}^2$

Where,

  $m_0$ is rest mass

  $KE$ is Kinetic energy

  $v$ is velocity

  $c$ is speed of light, $3.00\times {10}^{8}m/s$

Calculation:

The kinetic energyis $KE=\frac{\left(12,500kg\right){\left(3.00\times {10}^{8}m/s\right)}^2}{\sqrt{1-{\left(0.99\right)}^2}}-\left(12,500kg\right){\left(3.00\times {10}^{8}m/s\right)}^2=6.8\times {10}^{21}J$

Now, compare the value with annual energy consumption:

  $\frac{6.8\times {10}^{21}J}{{10}^{20}J}=68$

So, spaceship’s kinetic energy is about $68$ times the total energy consumption.