Concept & Calculations

| 27 | ssm How much work must be done on an electron to accelerate it from rest to a speed of 0.990c?

* | 28 | Multiple-Concept Example 6 explores the approach taken in problems such as this one. Quasars are believed to be the nuclei of galaxies in the early stages of their formation. Suppose a quasar radiates electromagnetic energy at the rate of . At what rate (in kg/s) is the quasar losing mass as a result of this radiation?

* | 29 | How close would two stationary electrons have to be positioned so that their total mass is twice what it is when the electrons are very far apart? Section 28.7 The Relativistic Addition of Velocities

| 30 | The spaceship Enterprise 1 is moving directly away from earth at a velocity that an earth-based observer measures to be +0.65c. Asister ship, Enterprise 2, is ahead of Enterprise 1 and is also moving directly away from earth along the same line. The velocity of Enterprise 2 relative to Enterprise 1 is +0.31c. What is the velocity of Enterprise 2, as measured by the earth-based observer?

| 31 | ssm A spacecraft approaching the earth launches an exploration vehicle. After the launch, an observer on earth sees the spacecraft approaching at a speed of 0.50c and the exploration vehicle approaching at a speed of 0.70c. What is the speed of the exploration vehicle relative to the spaceship?

| 32 | Galaxy A is moving away from us with a speed of 0.75c relative to the earth. Galaxy B is moving away from us in the opposite direction with a relative speed of 0.55c. Assume that the earth and constant velocities, so they are inertial reference frames. How fast is galaxy A moving according to an observer in galaxy B?

| 33 | ssm www The crew of a rocket that is moving away from the earth launches an escape pod, which they measure to be 45 m long. The pod is launched toward the earth with a speed of 0.55c relative to the rocket. After the launch, the rocket’s speed relative to the earth is 0.75c. What is the length of the escape pod as determined by an observer on earth?

* | 34 | A person on earth notices a rocket approaching from the right at a speed of 0.75c and another rocket approaching from the left at 0.65c. What is the relative speed between the two rockets, as measured by a passenger on one of them?

** | 35 | Two atomic particles approach each other in a head-on collision. Each particle has a mass of . The speed of each particle is when measured by an observer standing in the laboratory. (a) What is the speed of one particle as seen by the other particle? (b) Determine the relativistic momentum of one particle, as it would be observed by the other.

| 36 | An electron and a positron have masses of . They collide and both vanish, with only electromagnetic radiation appearing after the collision. If each particle is moving at a speed of 0.20c relative to the laboratory before the collision, determine the energy of the electromagnetic radiation.

| 37 | ssm www How fast must a meter stick be moving if its length is observed to shrink to one-half of a meter?

| 38 | Suppose that you are traveling on board a spacecraft that is moving with respect to the earth at a speed of 0.975c. You are breathing at a rate of 8.0 breaths per minute. As monitored on earth, what is your breathing rate?

| 39 | At what speed is the magnitude of the relativistic momentum of a particle three times the magnitude of the nonrelativistic momentum?

* | 40 | Refer to Conceptual Example 11 as an aid in solving this problem. An intergalactic cruiser has two types of guns: a photon cannon that fires a beam of laser light and an ion gun that shoots ions at a velocity of 0.950c relative to the cruiser. The cruiser closes in on an alien spacecraft at a velocity of 0.800c relative to this spacecraft, The captain fires both types of guns. At what velocity do the aliens see (a) the laser light and (b) the ions approach them? At what velocity do the alien s see (c) the laser and (d) the ions move away from the cruiser?

* | 41 | Starting from rest, two skaters “push off” against each other on smooth level ice, where friction is negligible. One is a woman and one is a man. The woman moves away with a velocity of +2.5 m/s relative to the ice. The mass of the woman is 54 kg, and the mass of the man is 88 kg. Assuming that the speed of light is 3.0 m/s, so that the relativistic momentum must be used, find the recoil velocity of the man relative to the ice. (Hint: This problem is similar to Example 6 in Chapter 7.)

* | 42 | An object has a total energy of and a kinetic energy of . What is the magnitude of the object’s relativistic momentum?

** | 43 | ssm www A rectangle has the dimensions of when viewed by someone at rest with respect to it. When you move past the rectangle along one of its sides, the rectangle looks like a square. What dimensions do you observe when you move at the same speed along the adjacent side of the rectangle?

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.