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Chapter 36: Q. 37 (page 1060)

What are the rest energy, the kinetic energy, and the total energy of a 1.0g particle with a speed of 0.80c?

Short Answer

Expert verified

KE=2.88×1013JEο=9.0×1013JEtotal=1.188×1014J

Step by step solution

01

Given Information

We have given that

m=1.0g→0.001kgv=0.80c
02

Simplify

Kinetic Energy formula is

KE=12mv2

Therefore substituting values in equation we get

KE=12mv2KE=12(0.001kg)(0.8)2(3×108)2 KE=2.88×1013J

Now, to find rest energy we use the below formula

Eο=mc2

Substituting values in rest energy formula we get

Eο=mc2Eο=(0.001kg)(3×108)2 Eο=9.0×1013J

Lastly, to find the total energy we will use the below formula

Etotal=KE+Eο

Substitute the given values in the total energy formula

Etotal=KE+EοEtotal=2.88×1013J+9.0×1013JEtotal=1.188×1014J

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Most popular questions from this chapter

A rocket fires a projectile at a speed of 0.95cwhile traveling past the earth. Does an earthbound scientist measure the projectile’s speed to be 0.90cWhat was the rocket’s speed as a fraction of c?

Two rockets approach each other. Each is traveling at0.75cin the earth’s reference frame. What is the speed, as a fraction of c, of one rocket relative to the other?

An out-of-control alien spacecraft is diving into a star at a speed of 1.0×108m/s. At what speed, relative to the spacecraft, is the starlight approaching?

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?

Let’s examine whether or not the law of conservation of momentum is true in all reference frames if we use the Newtonian definition of momentum: px=mux. Consider an object A of mass 3m at rest in reference frame S. Object A explodes into two pieces: object B, of mass m, that is shot to the left at a speed of c/2 and object C, of mass 2m, that, to conserve momentum, is shot to the right at a speed of c/4. Suppose this explosion is observed in reference frame S′ that is moving to the right at half the speed of light.

a. Use the Lorentz velocity transformation to find the velocity and the Newtonian momentum of A in S′.

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d. Newtonian momentum was conserved in frame S. Is it conserved in frame S′?
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