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Relativity QUESTION 1 Two spaceships, A and B, are both travelling relative to an inertial frame of reference at 0.8 c in the same direction. Spaceship A shines a light beam forward towards B as shown in the following diagram.

Light Beam A

B

What is the speed of the light beam according to the captain on spaceship B? A. B. C. D.

0.2 c 0.8 c c 1.8 c

QUESTION 2 In a particle accelerator, an alpha particle of mass 6.64 × 10 –27 kg is accelerated to high speed from rest. The total amount of work done on the alpha particle is equal to 7.71 × 10 –10 J. Which one of the following is closest to its final speed? A. B. C. D.

0.80c 0.90c 0.85c 0.95c

QUESTION 3 A stationary proton has a rest mass energy of 1.50 x 10-10J. When a proton is accelerated from a speed of γ = 1.05 to a speed of γ = 1.10, which of the following is closest to the amount of work done on the proton during its acceleration? A. B. C. D.

4.2 x 102 J 4.2 x 10-9 J 8.6 x 10-15 J 7.5 x 10-12 J

QUESTION 4 Which of the following statements best explains why it is impossible to accelerate particles to the speed of light? A. B. C. D.

The kinetic energy of particles tends towards an infinite value as they approach light speed. It is directly forbidden by one of Einstein’s postulates. As particles increase in speed their rest mass tends towards an infinite value. The length of the path taken increases to infinity.

QUESTION 5 According to Einstein’s theory of special relativity, which one of the following does not depend on the motion of the observer? A. B. C. D.

The order of occurrence of two events. The time interval between two events. The distance between two points. The speed of light. Use the following information given in the passage to answer questions from 6 to 9

A meteor is heading directly towards the surface of a planet at a constant speed of 0.85c. Observers on the surface of the planet observe it at a time when it is a distance x above the surface in their reference frame. The observers calculate the time that the meteor will take to reach the surface of the planet as 784 microseconds. Use these information to answer questions 6 to 8. QUESTION 6 Which one of the following is closest to the distance x? A. B. C. D.

105 km 200 km 235 km 380 km

QUESTION 7 Which one of the following is the best estimate of the time, as measured by the meteor, for it to reach the surface of the planet? A. B. C. D.

1488 microseconds 784 microseconds 666 microseconds 413 microseconds

QUESTION 8 Which one of the following best describes the time of the meteor’s descent to the planet surface as measured by the meteor, and the time as measured by the observers on the surface of the planet? A. B. C. D.

Only the meteor measures the proper time. They are both measurements of proper time in their own reference frames. Neither are measures of proper time. Only the observers measure the proper time.

QUESTION 9 Which of the following is closest to Einstein’s first postulate? A. B. C. D.

Light always travels at 3 × 108 m s–1. There is no way to tell how fast you are going unless you can see what’s around you. Velocities can only be measured relative to something else. Absolute velocity is that measured with respect to the Sun.

For Questions 10 and 11 use the following description. A spacecraft takes off on a trip to a distant star system 25 light years away at a speed, relative to earth of 0.995 c. Upon arrival it returns to Earth at a similar speed. QUESTION 10 What is the value of gamma? (the Lorentz factor) A. γ = 1.0 B. γ = 5.0 C. γ = 10.0 D. γ = 20.0 QUESTION 11 How long in Earth’s frame did it take the craft to reach the star system? A. B. C. D.

25.1 yrs 25.0 yrs 24.5 yrs 50 yrs