Chapter 36: Q. 35 (page 1060)

What is the speed, as a fraction of $c$ , of a particle whose momentum is $m c$ ?

Short Answer

Expert verified

$v = \frac{c}{\sqrt{2}}$

Step by step solution

Given Information

We have to find the speed as a fraction of $c$ , of a particle whose momentum is $m c$ .

Simplify

We will use the below formula

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

From the above formula we will find the speed value,

$p = \frac{m v}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} m c = \frac{m v}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} \sqrt{(1 - \frac{v^{2}}{c^{2}})} \cdot m c = \sqrt{(1 - \frac{v^{2}}{c^{2}})} \cdot \frac{m v}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} \sqrt{(1 - \frac{v^{2}}{c^{2}})} \cdot m c = m v \frac{\sqrt{(1 - \frac{v^{2}}{c^{2}})} \cdot m c}{m} = \frac{m v}{m} \sqrt{(1 - \frac{v^{2}}{c^{2}})} \cdot c = v^{2} c^{2} - v^{2} = v^{2} c^{2} = 2 v^{2} v^{2} = \frac{c^{2}}{2} v = \frac{c}{\sqrt{2}}$

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What is the speed, as a fraction of $c$ , of a particle whose momentum is $m c$ ?

Short Answer

Step by step solution

Given Information

Simplify

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What is the speed, as a fraction of c, of a particle whose momentum is mc?

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

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Waves Physics

Study anywhere. Anytime. Across all devices.

What is the speed, as a fraction of $c$ , of a particle whose momentum is $m c$ ?