Chapter SH, Problem 20.11APP

To determine

To calculate: Velocity when mass increases.

Answer to Problem 20.11APP

Velocity of the car is $\underset{\_}{0.03c}$ .

Explanation of Solution

Given:

Mass of car = $1500\text{ kg}$

Increase in mass = $1\text{ kg}$

Formula used:

Mass increase is given by,

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

where $m_0$ is rest mass, v is velocity and c is speed of light.

Calculation:

Increased mass = $1500+1=1501\text{ kg}$

Velocity is calculated as:

  $\begin{array}{l}m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}\\ 1501=\frac{1500}{\sqrt{1-\frac{v^2}{c^2}}}\\ \sqrt{1-\frac{v^2}{c^2}}=\frac{1500}{1501}\\ 1-\frac{v^2}{c^2}={\left(\frac{1500}{1501}\right)}^2\\ \frac{v^2}{c^2}=1-{\left(\frac{1500}{1501}\right)}^2\\ \frac{v}{c}=\sqrt{1-{\left(\frac{1500}{1501}\right)}^2}\\ v=0.03c\end{array}$

Conclusion:

Velocity of the car is $\underset{\_}{0.03c}$ .