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Chapter 36: Q. 33 (page 1060)

A 1.0 g particle has momentum 400,000 kgm/s. What is the particle’s speed in m/s?

Short Answer

Expert verified

The speed of particle is $2.4 \times 10^{8} m / s$ .

Step by step solution

01

Given information

We have given that, a 1.0 g particle has momentum 400,000 kgm/s.

02

Step 1.

We will use relativistic momentum formula to get the value of photon's velocity.

Formula of relativistic momentum is :

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

Here, m = mass of photon

v = velocity of photon

c = speed of light

$ρ$ = relativistic density

03

Step 2.

Substituting the values in the formula :

400, 000 k g m / s = \frac{(1.0 \times 10^{- 3} k g) \times v}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}

$\sqrt{1 - \frac{v^{2}}{c^{2}}} = \frac{1.0 \times 10^{- 3} k g}{400, 000 k g m / s} c (\frac{v}{c})$

$\sqrt{1 - \frac{v^{2}}{c^{2}}} = \frac{3}{4} (\frac{v}{c})$

$1 - \frac{v^{2}}{c^{2}} = \frac{9}{16} \frac{v^{2}}{c^{2}}$

$v = 2.4 \times 10^{8} m / s$

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Most popular questions from this chapter

A proton is accelerated to 0.999c.

a. What is the proton’s momentum?

b. By what factor does the proton’s momentum exceed its Newtonian momentum?

FIGURE Q36.1 shows two balls. What are the speed and direction of each (a) in a reference frame that moves with ball 1 and (b) in a reference frame that moves with ball 2?

FIGURE Q36.5 shows Peggy standing at the center of her railroad car as it passes Ryan on the ground. Firecrackers attached to the ends of the car explode. A short time later, the flashes from the two explosions arrive at Peggy at the same time.

a. Were the explosions simultaneous in Peggy’s reference frame? If not, which exploded first? Explain.

b. Were the explosions simultaneous in Ryan’s reference frame?

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

A baseball pitcher can throw a ball with a speed of $40 m / s$ . He is in the back of a pickup truck that is driving away from you. He throws the ball in your direction, and it floats toward you at a lazy $10 m / s$ . What is the speed of the truck?

See all solutions

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