Chapter 36: Q. 40 (page 1060)

At what speed, as a fraction of $c$ , is a particle’s total energy twice its rest energy?

Short Answer

Expert verified

$v = \sqrt{\frac{3}{2}} c$

Step by step solution

Given Information

We have to find the speed, as a fraction of $c$ , is a particle’s total energy twice its rest energy?

Simplify

Total energy formula is

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

The rest of energy formula is

$E = m c^{2}$

Now we will find the total energy twice its rest energy.

$E_{ο} = 2 E \frac{m c^{2}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = 2 m c^{2} m c^{2} = \sqrt{1 - \frac{v^{2}}{c^{2}}} \cdot 2 m c^{2} \frac{c^{2}}{2 c^{2}} = \sqrt{1 - \frac{v^{2}}{c^{2}}} \frac{1}{2} = \sqrt{1 - \frac{v^{2}}{c^{2}}} \frac{1}{4} = 1 - \frac{v^{2}}{c^{2}} 4 v^{2} = 3 c^{2} v^{2} = \frac{3}{4} c^{2} v = \sqrt{\frac{3}{2}} c$

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At what speed, as a fraction of $c$ , is a particle’s total energy twice its rest energy?

Short Answer

Step by step solution

Given Information

Simplify

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At what speed, as a fraction of c, is a particle’s total energy twice its rest energy?

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

Astrophysics

Conservation of Energy and Momentum

Nuclear Physics

Scientific Method Physics

Rotational Dynamics

Dynamics

Study anywhere. Anytime. Across all devices.

At what speed, as a fraction of $c$ , is a particle’s total energy twice its rest energy?