Section 28.4 The Relativity of Length: Length Contraction

 17. Complete the following statement: To measure the proper length of an object moving relative to the surface of the earth, one must note the coordinates of points on the front and back ends

(a) at the same time with respect to a clock at rest on the earth.

(b) at different times with respect to a clock on the moving object.

(c) at the same time with respect to a clock on the moving object.

(d) at different times with respect to a clock at rest on the earth.

(e) at the same time with respect to a clock moving at the same speed on the surface of the earth.

 18. Which one of the following statements concerning the proper length of a meter stick is true?

(a) The proper length is always one meter.

(b) The proper length depends upon the speed of the observer.

(c) The proper length depends upon the acceleration of the observer.

(d) The proper length depends upon the reference frame in which it is measured.

(e) The proper length is the length measured by an observer who is moving with respect to the meter stick.

 19. A meter stick is observed to be only 0.900 meters long to an inertial observer. At what speed, relative to the observer, must the meter stick be moving?

(a) 0.44  10⁸ m/s (c) 0.95  10⁸ m/s (e) 2.70  10⁸ m/s

(b) 0.57  10⁸ m/s (d) 1.31  10⁸ m/s

 20. A UFO flies directly over a football stadium at a speed of 0.50c. If the proper length of the field is 100 yards, what field length is measured by the crew of the UFO?

(a) 59 yards (c) 87 yards (e) 121 yards

(b) 75 yards (d) 113 yards

 21. A spaceship leaves our solar system at a constant speed of 0.900c and travels to a point in the Andromeda galaxy. According to astronomers in an inertial reference frame on Earth, the distance to the galaxy is 2.081  10²² m. What distance does the crew on the ship measure on its journey?

(a) 9.07  10²¹ m (c) 1.91  10²² m (e) 4.77  10²² m

(b) 9.85  10²¹ m (d) 2.83  10²² m

 22. The Milky Way galaxy is a part of a group of galaxies called the Local Group. The proper distance from the Milky Way, on one side of the Local Group, to the M31 galaxy on the other side is approximately 2.4  10⁶ light-years. How long (in years) would it take a spaceship traveling at 0.999c to travel this distance according to travelers onboard?

(a) 2.4  10⁶ years (c) 1.1  10⁵ years (e) 2.0  10⁴ years

(b) 8.4  10⁵ years (d) 5.6  10⁴ years

Section 28.5 Relativistic Momentum

 23. A proton has a mass of 1.673  10^27 kg. If the proton is accelerated to a speed of 0.93c, what is the magnitude of the relativistic momentum of the proton?

(a) 6.2  10^–17 kg  m/s (c) 4.7  10^–19 kg  m/s (e) 1.6  10^–27 kg  m/s

(b) 1.3  10^–18 kg  m/s (d) 5.9  10^–24 kg  m/s

 24. An electron gun inside a computer monitor sends an electron toward the screen at a speed of 1.20  10⁸ m/s. If the mass of the electron is 9.109  10^31 kg, what is the magnitude of its relativistic momentum?

(a) 9.88  10^23 kg  m/s (c) 1.19  10^22 kg  m/s (e) 3.25  10^22 kg  m/s

(b) 1.09  10^22 kg  m/s (d) 1.41  10^22 kg  m/s

 25. In the distant future, a 5.40  10⁵-kg intergalactic ship leaves Earth orbit and accelerates to a constant speed of 0.92c. Determine the difference, p – p₀, between the relativistic and classical momenta of the ship.

(a) 3.9  10¹⁴ kg  m/s (c) 8.0  10¹³ kg  m/s (e) 1.2  10¹³ kg  m/s

(b) 2.3  10¹⁴ kg  m/s (d) 5.8  10¹³ kg  m/s

 26. The momentum of an electron is 1.60 times larger than the value computed non-relativistically.

What is the speed of the electron?

(a) 2.94  10⁸ m/s (c) 2.61  10⁸ m/s (e) 1.83  10⁸ m/s

(b) 2.76  10⁸ m/s (d) 2.34  10⁸ m/s