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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

01

Given Information

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

02

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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Most popular questions from this chapter

Consider the inelastic collision $e^{-} + e^{-} \to e^{-} + e^{-} + e^{-} + e^{+}$ in which an electron-positron pair is produced in a head-on collision between two electrons moving in opposite directions at the same speed. This is similar to Figure 36.39, but both of the initial electrons are moving.

a. What is the threshold kinetic energy? That is, what minimum kinetic energy must each electron have to allow this process to occur?

b. What is the speed of an electron with this kinetic energy?

Particle A has half the mass and twice the speed of particle B. Is the momentum $p_{A}$ less than, greater than, or equal to $p_{B}$ ? Explain.

You are standing at $x = 9.0 k m .$ Lightning bolt $1$ strikes at $x = 0 k m$ and lightning bolt $2$ strikes at $x = 12.0 k m .$ Both flashes reach your eye at the same time. Your assistant is standing at $x = 3.0 k m .$ Does your assistant see the flashes at the same time? If not, which does she see first, and what is the time difference between the two?

The star Alpha goes supernova. Ten years later and $100 l y$ away, as measured by astronomers in the galaxy, star Beta explodes.

a. Is it possible that the explosion of Alpha is in any way responsible for the explosion of Beta? Explain.

b. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is $120 l y$ . According to the aliens, what is the time between the explosions?

You are standing at $x = 9.0 k m$ and your assistant is standing a $x = 3.0 k m$ Lightning bolt $1$ strikes at $x = 0 k m$ and a lightning bolt $2$ strikes at $x = 12.0 k m$ . You see the flash from bolt $2$ at $t = 10 m s$ and the flash from bolt $1 a t t = 50 m s$ According to your assistant, were the lightning strikes simultaneous? If not, which occurred first, and what was the time difference between the two?

See all solutions

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