Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Two fixed navigation beacons mark the approach lane to a star. The beacons are in line with the star and are 59 Mm apart. A spaceship approaches the star with a relative velocity of 0.60 c and passes the beacons. The passage of the ship between the beacons is timed by observers on the beacons. The time interval of the passage is closest to: A) 410 ms B) 330 ms C) 260 ms D) 160 ms E) 100 ms 1) 2) Two fixed navigation beacons mark the approach lane to a star. The beacons are in line with the star and are 60 Mm apart. A spaceship approaches the star with a relative velocity of 0.90 c and passes the beacons. The passage of the ship between the beacons is timed by an observer on the ship. The time interval of the passage is closest to: A) 510 ms B) 97 ms C) 220 ms D) 39 ms E) 58 ms 2) 3) Two fixed navigation beacons mark the approach lane to a star. The beacons are in line with the star and are 57 Mm apart. A spaceship approaches the star with a relative velocity of 0.60 c and passes the beacons. As the ship passes the first beacon the ship emits a short radar pulse toward the second beacon, and the radar echo is received at the ship. The time interval between the emission of the radar pulse and the reception of the radar echo is closest to: A) 300 ms B) 240 ms C) 190 ms D) 290 ms E) 110 ms 3) Figure 37.1a 4) A right-angled construction frame ABC, when measured at rest, has dimensions as follows: AB = 17.00 m, AC = 10.00 m, and BC = 13.75 m. The frame is given a velocity of 0.64c, relative to the space platform, in a direction parallel to AC. The dimensions of the moving frame are measured simultaneously by observers on the platform. In Fig. 37.1a, the length BC measured by these observers is closest to: A) 12 m B) 8 m C) 14 m D) 16 m E) 10 m 4) 1
Figure 37.1b 5) A right-angled construction frame ABC, when measured at rest, has dimensions as follows: AB = 18.00 m, AC = 10.00 m, and BC = 14.97 m. The frame is given a velocity of 0.59c, relative to the space platform, in a direction parallel to AC. The dimensions of the moving frame are measured simultaneously by observers on the platform. In Fig. 37.1b, the length AB measured by these observers is closest to: A) 16.5 m B) 16.0 m C) 17.5 m D) 17.0 m E) 18.0 m 5) Figure 37.2a 6) System S' has a velocity u = +0.45c relative to system S, as shown. The clocks of S and S' are synchronized at t = t' = 0 s when the origins O and O' coincide. An event is observed in both systems. The event takes place at x = 600 m and at time t = 1.9 µs, as measured by an observer in S. In Fig. 37.2a, the x'-coordinate of the event, measured by an observer in S' is closest to: A) 350 B) 380 C) 310 D) 340 E) 360 6) Figure 37.2b 7) System S' has a velocity u = +0.56c relative to system S, as shown. The clocks of S and S' are synchronized at t = t' = 0 s when the origins O and O' coincide. An event is observed in both systems. The event takes place at x = 800 m and at time t = 3.0 µs, as measured by an observer in S. In Fig. 37.2b, the time t' of the event, measured by an observer in S' is closest to: A) -4.9 µs B) 1.5 µs C) 1.3 µs D) 1.7 µs E) 1.8 µs 7) 2
Figure 37.2c 8) System S' has a velocity u = +0.77c relative to system S, as shown. The clocks of S and S' are synchronized at t = t' = 0 s when the origins O and O' coincide. An event is observed in both systems. The event takes place at x = 400 m and at time t = 8.7 µs, as measured by an observer in S. In Fig. 37.2c, a rod which is stationary in S has a proper length of 137 m. The length of the rod measured by an observer in S' is closest to: A) 210 m B) 79 m C) 87 m D) 61 m E) 54 m 8) Figure 37.3a 9) The captain of spaceship A observes enemy spaceship E escaping with a relative velocity of 0.48c. A missile M is fired from ship A, with a velocity of 0.72c relative to ship A. In Fig. 37.3a, the relative velocity of approach of missile M, observed by the crew on ship E, is closest to: A) 0.30c B) 0.37c C) 0.24c D) 0.34c E) 0.27c 9) Figure 37.3b 10) The captain of spaceship A observes enemy spaceship E escaping with a relative velocity of 0.52c. A missile M is fired from ship A, with a velocity of 0.72c relative to ship A. In Fig. 37.3b, the captain of ship A observes missile M closing in on ship E with a relative velocity that is closest to: A) 0.23c B) 0.32c C) 0.29c D) 0.26c E) 0.20c 10) 11) If you were in a spaceship traveling at a speed close to the speed of light (with respect to earth) you would notice that A) your pulse rate is different than normal. B) your mass is different than normal. C) some of your physical dimensions were smaller than normal. D) None of these effects occur. E) More than one of these effects occur. 11) 12) A spaceship approaching an asteroid at a speed of 0.6c launches a scout rocket with speed 0.4c. At what speed is the scout rocket approaching the asteroid? A) 0.76c B) 0.96c C) 1.00c D) 0.81c E) 0.64c 12) 3
Figure 37.4a 13) Three spaceships A, B, and C are in motion. The commander on ship B observes ship C approaching with a relative velocity of 0.78c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.31c. In Fig. 37.4a, the velocity of ship C, relative to an observer on ship A, is closest to: A) 0.62c B) 1.1c C) 0.88c D) 0.38c E) 1.4c 13) Figure 37.4b 14) Three spaceships A, B, and C are in motion. The commander on ship B observes ship C approaching with a relative velocity of 0.83c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.48c. In Fig. 37.4b, the commander on ship B observes ship A and ship C approaching each other, with a relative velocity that is closest to: A) 1.3c B) 0.58c C) 0.25c D) 2.2c E) 0.94c 14) Situation 37.1 A navigational beacon in deep space broadcasts at a radio frequency of 50 MHz. A spaceship approaches the beacon with a relative velocity of 0.40c. 15) In Situation 37.1, the frequency of the beacon radio signal that is detected on the ship is closest to: A) 60 MHz B) 66 MHz C) 76 MHz D) 71 MHz E) 55 MHz 15) 16) In Situation 37.1, the spaceship passes the beacon and departs from it with a different relative velocity. The beacon signal is now detected at a frequency of 40 MHz. The new velocity of the spaceship, relative to the beacon, is closest to: A) 0.24c B) 0.26c C) 0.22c D) 0.20c E) 0.28c 16) Situation 37.2 An electron (of mass 9.11 10-31 kg and charge 1.60 10-19 C) is accelerated from rest through a potential difference of 50.0 kv. 17) In Situation 37.2, the speed of the electron is closest to: A) 8.00 10-15 J B) 8.00 10-12 J C) 4.00 10-15 J D) 8.20 10-14 J E) 4.00 10-12 J 17) 4
18) In Situation 37.2, the speed of the electron is closest to: A) 1.33 10 8 m/s B) 3.24 10 8 m/s C) 4.12 10 8 m/s D) 3.33 10 8 m/s E) 1.24 10 8 m/s 18) 19) In Situation 37.2, the total energy of the electron is closest to: A) 8.00 10-15 J B) 9.00 10-14 J C) 8.20 10-14 J D) 16.2 10-15 J E) 16.2 10-14 J 19) Situation 37.3 A proton (of mass 1.67 10-27 kg and charge 1.60 10-19 C) has a kinetic energy that is equal to its rest mass energy. 20) In Situation 37.3, the speed of the proton is closest to: A) 0.50c B) 0.87c C) 0.75c D) 0.71c E) 0.25c 20) 21) In Situation 37.3, the total energy of the proton is closest to: A) 5.69 10-11 J B) 2.07 10-10 J C) 8.77 10-10 J D) 1.50 10-10 J E) 3.01 10-10 J 21) 22) In Situation 37.3, the momentum of the proton is closest to: A) 5.01 10-19 kg m/s B) 2.51 10-19 kg m/s C) 8.68 10-19 kg m/s D) 2.89 10-19 kg m/s E) 4.34 10-19 kg m/s 22) 23) Consider three galaxies, Alpha, Beta and Gamma. An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 0.7c. At what speed would an observer in Alpha see the galaxy Beta moving? A) 0.35c B) 0.57c C) 0.70c D) 0.82c E) 0.94c 23) 5
24) Consider three galaxies, Alpha, Beta and Gamma. An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 0.7c. At what speed would an observer in Alpha see the galaxy Gamma moving? A) 0.7c B) 0.98c C) 0.94c D) 1.4c E) 0.82c 24) Situation 37.4 A relativistic proton has a momentum of 1.0 10-18 kg m/s. The rest energy of a proton is 0.150 nj. 25) In Situation 37.4, the kinetic energy of the proton, in nj, is closest to: A) 0.16 B) 0.25 C) 0.22 D) 0.19 E) 0.13 25) 26) In Situation 37.4, the speed of the proton is closest to: A) 0.93c B) 0.87c C) 0.95c D) 0.89c E) 0.91c 26) 27) The special theory of relativity predicts that there is an upper limit to the speed of a particle. It thus follows that there is also an upper limit on the following property of a particle: A) the total energy B) the kinetic energy C) the linear momentum D) more than one of these E) none of these 27) Situation 37.5 A spaceship moves with velocity 0.6c with respect to the Earth. At midnight it passes Earth, and observers on both the spaceship and on Earth agree that their clocks read midnight. At 12:50 A.M. (spaceship time) the spaceship passes an interplanetary navigational station and sends a radio signal back to Earth. The receiving antenna on Earth, immediately on receiving this signal, responds by sending a signal back to the spaceship. The following questions refer to this series of events. 28) In Situation 37.5, how far from Earth (as measured by an Earth-based observer) is the navigational station? A) 6.75 10-11 m B) 6.50 10-11 m C) 8.44 10-11 m D) 7.25 10-11 m E) 5.40 10-11 m 28) 29) In Situation 37.5, at what time (Earth-based clock) did the spaceship pass the navigational station? A) 12:45:30 A.M. B) 12:40 A.M. C) 1:02:30 A.M. D) 12:50 A.M. E) 1:10 A.M. 29) 6
30) In Situation 37.5, at what time does the receiver on Earth detect the signal from the spaceship (Earth-based time)? A) 1:40 A.M. B) 1:36 A.M. C) 1:42 A.M. D) 1:48 A.M. E) 1:30 A.M. 30) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 31) An unstable particle is moving at a speed of 2.6 10 8 m/s relative to a laboratory. Its lifetime is measured by a stationary observer in the laboratory to be 4.7 10-6 seconds. What is the lifetime of the particle, measured in the rest frame of the particle? (Use 3.00 10 8 m/s for the speed of light.) 32) A spacecraft is measured by an observer on the ground to have a length of 53 m as it flies overhead with a speed 1.7 10 8 m/s. The spacecraft then lands and its length is again measured by the observer on the ground, this time while the spacecraft is at rest relative to him. What result does he now get for the length? (Use 3.00 10 8 m/s for the speed of light.) 33) An experimenter is observing the inelastic collision of two rather rapid objects in order to test the predictions of relativistic momentum conservation. Particle A has a known rest mass of 7.5 10-25 kg and moves with speed (in the lab) 2.4 10 8 m/s. Particle B's mass is unknown, but it moves with speed (also in the lab) 1.9 10 8 m/s. Initially the particles are moving in precisely opposite directions. After the collision (a near miss), the particles, to the experimenter's amazement, are each moving perpendicular to the original direction of motion. For this to happen, what must be the rest mass of particle B? (Like the experimenter, you should use 3.00 10 8 m/s as the speed of light.) 31) 32) 33) 34) How much work must be done to accelerate a particle of mass 2.7 10-14 kg (rest mass) from a speed of 1.1 10 8 m/s to a speed of 1.9 10 8 m/s? (Use c = 3.00 10 8 m/s for the speed of light.) 35) Two spaceships are approaching one another, each at a speed of 0.68c relative to a stationary observer on Earth. What speed does an observer on one spaceship record for the other approaching spaceship? 34) 35) 36) As a rocket is moving past Earth, an Earthling measures its length to be 325 m, while the captain on board radios that her rocket s length is 1150 m. (a) How fast is the rocket moving relative to Earth? (b) What is the total energy of a 75.0-kg crewman as measured by (i) an observer at rest in the rocket and (ii) an observer at rest on Earth? 36) 7
Answer Key Testname: UNTITLED1 1) B 2) B 3) B 4) C 5) D 6) B 7) E 8) C 9) B 10) E 11) D 12) D 13) C 14) A 15) C 16) C 17) A 18) E 19) B 20) B 21) E 22) C 23) C 24) C 25) D 26) D 27) E 28) A 29) C 30) A 31) 2.3 10-6 seconds 32) 6.4 10 1 m 33) 1.2 10-24 kg 34) 530 J 35) 0.93 c 36) (a) 0.959c = 2.88 10 8 m/s (b) (i) 6.75 10 18 J, (ii) 2.39 10 19 J 8