Chapter 20, Problem 1PE

Interpretation Introduction

Interpretation:

The mass of the tennis ball travelling at 53.6 m s^-1 is to be determined.

Concept Introduction:

Relativistic effect is defined as the difference in values in the models which consider and cannot consider the relativity.

Relativistic effect is very crucial for a heavy element having high atomic number.

The mass of the particle $\left(\text{m}\right)$, velocity of the particle $\left(\text{v}\right)$, rest mass of the particle $\left({\text{m}}_{\circ }\right)$, and the velocity of the light $\left(\text{c}\right)$ can be related by the following equation.

$\text{m}=\frac{{\text{m}}_{\circ }}{\sqrt{1-{\left(\frac{\text{v}}{\text{c}}\right)}^2}}$.

Answer to Problem 1PE

Solution: $57.7$ g.

Explanation of Solution

Given information: The rest mass of tennis ball is $57.7$ g.

The mass of the tennis ball is calculated as:

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

Here, $\text{m}$ is the mass of the object, ${\text{m}}_{\circ }$ is the rest mass of the object, $\text{v}$ is the speed of the object and $\text{c}$ is the speed of light.

Substitute rest mass of the object as $57.7\text{ g}$, velocity of the object as $53.6{\text{ ms}}^{-1}$ and the speed of light as $3\times {10}^8{\text{ ms}}^{-1}$.

$\text{m}=\frac{57.7\text{ g}}{\begin{array}{c}\sqrt{1-{\left(\frac{53.6{\text{ ms}}^{-1}}{3\times {10}^8{\text{ ms}}^{-1}}\right)}^2}\\ =57.7\text{ g}\end{array}}$

Thus, the mass of tennis ball is $57.7\text{ g}$.

Therefore, the tennis ball cannot have any relativistic effect due to its large size and slow speed.

Conclusion

The mass of the tennis ball is $57.7$ g.