Chapter 41, Problem 16SP

Determine γ when the speed of a spacecraft is 3c/5. [Hint: Take a look at Table 41-1.]

To determine

The value of $\gamma$ if the speed of a spacecraft is $\frac{3c}{5}$.

Answer to Problem 16SP

Solution:

$1.25$

Explanation of Solution

Given data:

The speed of a spacecraft is $\frac{3c}{5}$.

Formula used:

Write the expression for $\gamma$.

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

Here, $c$ is the speed of light and $v$ is the speed of the object.

Explanation:

Recall the expression for $\gamma$.

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

Substitute $\frac{3c}{5}$ for $v$

$\begin{array}{c}\gamma =\frac{1}{\sqrt{1-\frac{{\left(\frac{3c}{5}\right)}^2}{c^2}}}\\ =\frac{1}{\sqrt{1-0.36}}\\ =1.25\end{array}$

Determine the value of $\frac{v}{c}$.

$\begin{array}{c}\frac{v}{c}=\frac{\left(\frac{3c}{5}\right)}{c}\\ =0.6\end{array}$

Refer the Table 41-1 for the value of $\frac{v}{c}$ as $0.6$, the corresponding value of the $\gamma$ is $1.25$. The same value is obtained with the help of calculation as well.

Conclusion:

The value of $\gamma$ is $1.25$.