Deck 36: The Theory of Special Relativity

Question 1

Suppose an airliner can travel at 300 km/hr in still air. If the airliner is traveling due east with a tailwind (a wind directed eastward) of 15 km/hr, the ground speed of the craft is

A) 285 km/hr.
B) 294 km/hr.
C) 300 km/hr.
D) 306 km/hr.
E) 315 km/hr.

Answer 1

315 km/hr.

Question 2

Suppose an airliner can travel at 300 km/hr in still air. If the airliner is traveling due east with a headwind (a wind directed westward) of 15 km/hr, the ground speed of the craft is

A) 285 km/hr.
B) 294 km/hr.
C) 300 km/hr.
D) 306 km/hr.
E) 315 km/hr.

Answer 2

285 km/hr.

Question 3

Suppose an airliner can travel at 300 km/hr in still air. If the airliner is traveling due east with a crosswind (a wind directed toward the south) of 60 km/hr, the ground speed of the craft is

A) 285 km/hr.
B) 294 km/hr.
C) 300 km/hr.
D) 306 km/hr.
E) 315 km/hr.

Answer 3

294 km/hr.

Question 4

The Michelson-Morley experiment demonstrated that

A) inertial frames exist.
B) noninertial frames exist.
C) the motion of the Earth has no effect on the propagation of light.
D) all of the above answers are correct.

Question 5

In special relativity time dilation occurs when

A) an object is standing still.
B) an object is moving.
C) an object is either standing still or moving.
D) an object is moving near the speed of light.

Question 6

A subatomic particle moving at 0.95 c is measured in the laboratory to live 1.5 $\mu$ s before decaying. The lifetime of the particle in a rest frame is

A) 0.47 $\mu$ s.
B) 1.5 $\mu$ s
C) 4.8 $\mu$ s.
D) 15 $\mu$ s.

Question 7

For a time dilation to increase the "time" by a factor of 2, the speed of the object is

A) 0.50 c.
B) 0.87 c.
C) 1.0 c.
D) 1.2 c.

Question 8

A pendulum is noted to swing once every second on Earth. Onboard a spacecraft traveling at 0.89 c the pendulum is noted to swing once every

A) 5 s.
B) 3 s.
C) 1 s.
D) 0.2 s.

Question 9

The space shuttle orbits the Earth at a speed of 7.5 km/s for one week. The time difference due to time dilation the astronauts experience is

A) 0.4 ms.
B) 4.0 ms.
C) 40 ms.
D) 0.4 s.

Question 10

A distant source of light is emitting one of the Balmer lines at 656 nm. The light is observed to be at a wavelength of 680 nm due to a motion of the source. The velocity of the source is

A) 0.036 c away from the observer.
B) 0.036 c toward the observer.
C) 0.36 c away from the observer.
D) 0.36 c toward the observer.

Question 11

A distant source of light is emitting the Balmer series, and the source of light is moving toward the Earth at a rate of 10 km/s. The wavelength of the 656.28-nm line will be observed at

A) 656.24 nm.
B) 656.26 nm.
C) 656.28 nm.
D) 656.30 nm.
E) 656.32 nm.

Question 12

Pepper, the space cat, travels to the Centauri star system 4.5 light-years away (one light-year is the distance light travels in one year) at a speed of 0.90 c. Relative to the Earth's frame of reference, the time it takes Pepper to reach the star system is

A) 5.0 years.
B) 4.5 years.
C) 10. years.
D) 4.0 years.

Question 13

Pepper, the space cat, travels to the Centauri star system 4.5 light-years away (one light-year is the distance light travels in one year) at a speed of 0.90 c. Relative to Pepper's frame of reference, the time it takes him to reach the star system is

A) 5.0 years.
B) 4.5 years.
C) 4.0 years.
D) 2.2 years.

Question 14

Pepper, the space cat, travels toward the Centauri star system 4.5 light-years away at a speed of 0.90 c. He sends back a transmission on his transmitter at a frequency of 31.20 MHz. The frequency received on Earth is

A) 7.158 MHz.
B) 31.20 MHz.
C) 68.00 MHz.
D) 136.0 MHz.

Question 15

Pepper, the space cat, travels back from the Centauri star system 4.5 light-years away at a speed of 0.90 c. He sends back a transmission on his transmitter at a frequency of 31.20 MHz. The frequency received on Earth is

A) 7.158 MHz.
B) 31.20 MHz.
C) 68.00 MHz.
D) 136.0 MHz.

Question 16

A meter stick on a spaceship is measured in the reference frame of the Earth to have a length of 80.0 cm. The velocity of the spaceship is

A) 1.0 c.
B) 0.80 c.
C) 0.60 c.
D) 0.50 c.

Question 17

A meter stick on a spaceship lies at a 45º angle perpendicular to the motion of travel. When the ship is moving at 0.80 c, the length of the meter stick, relative to a stationary observer, is

A) 0.42 m.
B) 0.82 m.
C) 0.87 m.
D) 1.00 m.

Question 18

A meter stick on a spaceship lies at a 45° angle perpendicular to the motion of travel. When the ship is moving at 0.80 c, the angle the meter stick appears to make with respect to a stationary observer is

A) 45°.
B) 59°.
C) 37°.
D) 63°.

Question 19

A simple harmonic oscillator has a period of 2.00 s on Earth. The harmonic oscillator is taken on a spacecraft, and its period is measured on Earth to be 2.50 s. The velocity of the spacecraft is

A) 0.40 c.
B) 0.60 c.
C) 0.80 c.
D) 1.00 c.

Question 20

The speed at which a clock has to travel to run at a rate that is one-third the rate of a stationary clock is

A) 0.912 c.
B) 0.943 c.
C) 0.955 c.
D) 1.00 c.

Question 21

The length contraction effect applies

A) to the spatial coordinate along the path of motion.
B) to the spatial coordinate perpendicular to the path of motion.
C) to the spatial coordinates both parallel and perpendicular to the path of the motion.
D) Hold on. Length contraction doesn't really exist.

Question 22

A meter stick is aligned perpendicularly to the direction of its motion. The length of the stick, as measured by a stationary observer when it is moving 0.60 c, is

A) 1.0 m.
B) 0.80 m.
C) 0.60 m.
D) 0.40 m.

Question 23

A meter stick is aligned parallel to the direction of its motion. The length of the stick, as measured by a stationary observer when it is moving at 0.60 c, is

A) 1.0 m.
B) 0.80 m.
C) 0.60 m.
D) 0.40 m.

Question 24

A particle has a lifetime of 25 ns in a stationary reference frame. If the particle is created with a velocity of 0.95 c, the distance it will travel is

A) 3.4 m.
B) 7.1 m.
C) 14 m.
D) 23 m.

Question 25

A particle has a lifetime of 25 ns in a stationary reference frame. The particle is moving with a constant speed and travels a distance of 10.0 m. The speed of the particle is

A) 0.50 c.
B) 0.60 c.
C) 0.70 c.
D) 0.80 c.

Question 26

A particle has a lifetime of 25 ns in a stationary reference frame. The particle is moving with a constant speed and travels a distance of 10.0 m. The time elapsed in the stationary frame is

A) 62 ns.
B) 42 ns.
C) 25 ns.
D) 23 ns.

Question 27

A spacecraft traveling at 0.75 c ejects a missile at a speed of 0.25 c (relative to the spacecraft) in the direction of travel. The speed of the missile relative to a stationary observer is

A) 0.50 c.
B) 0.61 c.
C) 0.84 c.
D) 1.0 c.

Question 28

Two spacecraft are traveling toward each other each with a speed of 0.60 c. The speed at which they are approaching each is

A) 1.2 c.
B) 0.88 c.
C) 0.78 c.
D) 0.60 c.

Question 29

Spacecraft A is traveling at a speed of 0.80 c toward spacecraft B, which is traveling in the same direction at a speed of 0.75 c. Spacecraft A shoots a projectile at a speed of 0.90 c toward spacecraft B. The speed of spacecraft B relative to the projectile is

A) 0.90 c.
B) 0.92 c.
C) 0.95 c.
D) 0.99 c.

Question 30

Spacecraft A is traveling at a speed of 0.80 c relative to Earth. Spacecraft B is traveling in the same direction as spacecraft A but at a speed of 0.40 c relative to spacecraft A. The speed of spacecraft B relative to Earth is

A) 0.08 c.
B) 0.80 c.
C) 0.85 c.
D) 0.91 c.

Question 31

An electron, initially at rest, is accelerated through a potential difference of 2.5 MeV, thereby increasing its total energy by 2.5 MeV. The mass of the electron is

A) $5.4 \times 10 ^ { - 30 } \mathrm {~kg}$
B) $9.1 \times 10 ^ { - 31 } \mathrm {~kg}$
C) $4.5 \times 10 ^ { - 30 } \mathrm {~kg}$
D) $4.5 \times 10 ^ { - 31 } \mathrm {~kg}$

Question 32

An electron, initially at rest, is accelerated through a potential difference of 2.50 MeV, thereby increasing its total energy by 2.50 MeV. The speed of the electron is

A) 0.912 c.
B) 0.972 c.
C) 0.986 c.
D) 0.995 c.

Question 33

An electron, initially at rest, is accelerated through a potential difference of 2.50 MeV, thereby increasing its total energy by 2.50 MeV. The momentum of the electron is

A) 2.12 MeV/c.
B) 2.52 MeV/c.
C) 2.97 MeV/c.
D) 3.21 MeV/c.

Question 34

The potential difference required to accelerate an electron from rest to a speed of 0.930 c is

A) 3.27 MeV.
B) 1.39 MeV.
C) 0.88 MeV.
D) 2.27 MeV.

Question 35

The energy produced from the conversion of 50 micrograms of matter into energy is

A) $4.5 \times 10 ^ { 8 } \mathrm {~J}$
B) $4.5 \times 10 ^ { 10 } \mathrm {~J}$
C) $4.5 \times 10 ^ { - 10 } \mathrm {~J}$
D) $4.5 \times 10 ^ { 12 } \mathrm {~J}$

Question 36

The speed at which a particle must be accelerated to triple its mass is

A) $1.24 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$
B) $2.62 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$
C) $2.83 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$
D) $2.99 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$

Question 37

The rest-mass energy of an electron is

A) zero.
B) $9.1 \times 10 ^ { - 31 } \mathrm {~kg}$
C) $8.2 \times 10 ^ { - 14 } \mathrm {~J}$
D) $0.511 \mathrm { MJ }$

Question 38

During a fission process, $1.5 \times 10 ^ { 11 } \mathrm {~J}$ of energy is created by a mass loss. The amount of mass converted to energy during the process is

A) $1.7 \times 10 ^ { - 6 } \mathrm {~g}$
B) $1.7 \mathrm { mg }$
C) $1.7 \mu \mathrm { g }$
D) $1.7 \mathrm {~kg}$

Question 39

The total energy of an electron that has a momentum of 0.86 MeV/c is

A) 0.35 MeV.
B) 0.86 MeV.
C) 1.00 MeV.
D) 1.16 MeV.

Question 40

The kinetic energy of an electron that has a momentum of 0.86 MeV/c is

A) 0.49 MeV.
B) 0.86 MeV.
C) 1.00 MeV.
D) 1.16 MeV.

Question 41

The velocity of an electron that has a momentum of 0.86 MeV/c is

A) 0.35 c.
B) 0.86 c.
C) 1.00 c.
D) 1.16 c.

Question 42

An electron has a momentum of 0.86 MeV/c. The momentum in SI units is

A) $0.86 \mathrm { MeV } / \mathrm { c }$
B) $4.6 \times 10 ^ { - 22 } \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$
C) $2.5 \times 10 ^ { - 22 } \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$
D) $1.2 \times 10 ^ { - 22 } \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$

Question 43

An electron has a momentum of 0.86 MeV/c. The fraction of the electron's kinetic energy compared to its total energy is

A) 46%.
B) 49%.
C) 52%.
D) 56%.

Question 44

An electron has a total energy that is four times its rest energy. The speed of the electron is

A) 0.998 c.
B) 0.988 c.
C) 0.978 c.
D) 0.968 c.

Question 45

The kinetic energy of an electron is four times its rest energy. The speed of the electron is

A) 0.998 c.
B) 0.990 c.
C) 0.985 c.
D) 0.980 c.

Question 46

A meter stick moving at a speed of 0.75 c moves past a stationary observer. The time it takes to pass by the stationary observer is

A) 5.02 ns.
B) 4.44 ns.
C) 2.94 ns.
D) 3.49 ns.

Question 47

The principle of relativity states that

A) all the laws of physics are the same in noninertial frames.
B) all the laws of physics are the same in inertial frames.
C) all the laws of physics are the same in both inertial and noninertial frames.

Question 48

A relativistic car is 4.5 m in length. The car is measured to be 4.0 m in length when it speeds at a velocity of

A) 0.33 c.
B) 0.46 c.
C) 0.57 c.
D) 0.89 c.

Question 49

An object moving with a constant velocity of 0.80 c has a mass of $2.78 \times 10 ^ { - 27 } \mathrm {~kg}$ . The rest mass of the object is

A) $3.87 \times 10 ^ { - 27 } \mathrm {~kg}$
B) $2.78 \times 10 ^ { - 27 } \mathrm {~kg}$
C) $1.67 \times 10 ^ { - 27 } \mathrm {~kg}$
D) $0.67 \times 10 ^ { - 27 } \mathrm {~kg}$

Question 50

The energy required to accelerate a 1.0-kg mass to 0.50 c is

A) $2.8 \times 10 ^ { 16 } \mathrm {~J}$
B) $1.4 \times 10 ^ { 16 } \mathrm {~J}$
C) $2.8 \times 10 ^ { 16 } \mathrm {~kJ}$
D) $1.4 \times 10 ^ { 16 } \mathrm {~kJ}$

Question 51

A nuclear-powered generator aboard a satellite is expected to deliver 25 W for at least 1 year. The amount of matter converted to energy during the lifetime of the satellite is

A) 9 g.
B) 9 ng
C) 900 $\mu$ g.
D) 9 $\mu$ g.