Q. 39 At what speed, as a fraction of ... [FREE SOLUTION]

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Chapter 36: Q. 39 (page 1060)

At what speed, as a fraction of c, is a particle鈥檚 kinetic energy twice its rest energy?

Short Answer

Expert verified

The speed of particle is 0.943c.

Step by step solution

Given information

We have given that particle鈥檚 kinetic energy twice its rest energy.

Step 1.

The formula of total energy is $E = 违_{p} m c^{2}$ .

Here, m = mass of particle

c = speed of light

$违_{p}$ = Lorentz factor

We know that total energy is the sum of rest mass energy and kinetic energy.

$E = E_{0} + K$

Here, $E_{0}$ =rest mass energy

K = kinetic energy

Substituting both values of total energy in formula :

$违_{p} m c^{2} = E_{0} + K$

Step 2.

We have given that kinetic energy is twice of rest mass energy.

Substituting value in formula :

$违_{p} m c^{2} = E_{0} + 2 E_{0}$

We know that $E_{0} = m c^{2}$

Substituting the value of $E_{0}$ in formula :

$违_{p} m c^{2} = 3 m c^{2}$

$违_{p} = 3 m$

We know that $违_{p} = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

Substituting the value of $违_{p}$ in formula :

$\frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = 3$

$1 - \frac{v^{2}}{c^{2}} = \frac{1}{9}$

$v = \frac{\sqrt{8}}{3} c$

$v = 0.943 c$

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91影视

At what speed, as a fraction of c, is a particle鈥檚 kinetic energy twice its rest energy?

Short Answer

Step by step solution

Given information

Step 1.

Step 2.

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