Deck 39: Relativity

Question 1

Boat 1 goes directly across a stream a distance L and back taking a time t₁. Boat 2 goes down stream a distance L and back taking a time t₂. If both boats had the same speed relative to the water, which of the following statements is true?

A) t₂ > t₁
B) t₂ < t₁
C) t₂ = t₁
D) t₂ = 2t₁
E) t₂ = 0.5t₁

Answer 1

t₂ > t₁

Question 2

A spaceship moving past the Earth with a speed of 0.800 c signals to the Earth with pulsed laser photons emitted at 10.0-second intervals according to the spaceship's clock. According to observers on Earth who see the flashes, the time interval they measure is

A) 13.4 s
B) 16.7 s
C) 12.5 s
D) 9.70 s
E) 6.03 s

Answer 2

16.7 s

Question 3

Assume a gram of a substance marketed as "Pure Energy" is annihilated by a gram of a second substance "Anti-Pure Energy." How long would the energy released power a city which uses 10⁹ watts of power?

A) 40 hrs
B) 25 hrs
C) 50 hrs
D) 65 hrs
E) 50000 hrs

Answer 3

50 hrs

Question 4

The first intergalactic spaceship is headed toward the Magellanic Clouds at a speed of 0.8c. The spaceship is 1 000 m long. Clocks at the front and the rear of the spaceship both read 3:00 P.M. Can it be 3:00 P.M. simultaneously at the front and the back of the spaceship?

A) No, because
, where Δx is the length of the spaceship.
B) No, because one clock has to move after being synchronized with the other.
C) Yes, because Δx in (a) is zero for different points of the same spaceship.
D) Yes, because two clocks at rest relative to each other can be synchronized by means of light signals when the distance between them is known.
E) The question cannot be answered unless we know the object relative to which the spaceship's velocity is 0.8c.

Question 5

Fireworks go off at the same time according to Earth clocks in two cities, Alum and Boron, that are 300 km apart. The people in a spaceship that is flying in a straight line from Alum to Boron at 0.80 c also observe the fireworks. Do they see the fireworks in the two cities simultaneously? If the people in the spaceship say the fireworks were not simultaneous in Alum and Boron, how long before or after the fireworks flashed at Alum did the fireworks flash at Boron according to their calculations? (The spaceship is directly over Alum when the fireworks flash.)

A) Yes; 0
B) Before; 1.0 × 10−³ s
C) After; 1.0 × 10−³ s
D) Before; 1.3 × 10−³ s
E) After; 1.3 × 10−³ s

Question 6

A 1000-kg automobile moving with a speed of 24 m/s relative to the road collides with a 500-kg automobile initially at rest. If the two stick together, what is the velocity in m/s of the two cars after the collision according to an observer in a truck moving 10 m/s in the same direction as the moving cars?

A) 6
B) 11
C) 24
D) 26
E) 31

Question 7

A boat has an initial velocity of 2 m/s in the y direction on a stream which is moving in the x direction at 1 m/s. The boat is accelerating in its direction of motion at 1 m/s². What is the acceleration of the boat (in m/s²) relative to the water?

A) 1

B) 2

C) 3
+

D) 3
−

E) 1

Question 8

A jet plane travels around the world at 2 000 mi/hr (894 m/s). Two accurate atomic clocks measure the times of flight, one on board the plane and the second on Earth. If it takes 12 hours to complete the journey, what will the time difference (in μs) be?

A) 0.75
B) 0.50
C) 0.25
D) 1.0
E) 0.19

Question 9

A spaceship moves at a speed of 0.95 c away from the Earth. It shoots a star wars torpedo toward the Earth at a speed of 0.90 c relative to the ship. What is the velocity of the torpedo relative to the Earth? (The direction in which the spaceship moves is the positive direction.)

A) −0.34 c
B) 0.34 c
C) 0.060 c
D) −0.060 c
E) 0

Question 10

A satellite moves east, taken as the positive x axis direction, at a speed of 0.5 c and a spaceship moves toward it (to the west) at a speed of 0.8 c as measured by an observer on the Earth. The speed of the satellite measured by an observer in the spaceship is

A) 8.7 c
B) 0.21 c
C) −0.21 c
D) 0.93 c
E) −0.93 c

Question 11

The half-life of a muon is 2.20 μs as measured in a stationary reference frame. What is the half life of the muon (in μs) when it is moving with a speed of v = 0.800 c?

A) 8.13
B) 2.75
C) 3.67
D) 15.8
E) 1.32

Question 12

An electron has a kinetic energy that is twice its rest energy. Determine its speed.

A) 0.76 c
B) 0.81 c
C) 0.94 c
D) 0.54 c
E) 0.87 c

Question 13

A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth. (We measure that distance to be 1.5 × 10¹¹ m.) On Earth, the spaceship is observed to be traveling at a speed of 0.80 c, for which γ = 5/3. As measured on Earth it takes the spaceship 625 seconds to travel from the sun to Earth. When a scientist in the spaceship measures the Earth-sun distance and the time it takes her to travel that distance, she finds the results are respectively

A) 9.0 × 10¹⁰ m; 375 s.
B) 9.0 × 10¹⁰ m; 625 s.
C) 1.5 × 10¹¹ m; 625 s.
D) 2.5 × 10¹¹ m; 625 s.
E) 2.5 × 10¹¹ m; 1042 s.

Question 14

A proton has a total energy of 2.5 × 10−¹⁰ J. How fast is it moving? (M = 1.67 × 10−²⁷ kg)

A) 0.90 c
B) 0.80 c
C) 0.70 c
D) 0.60 c
E) 0.40 c

Question 15

The half-life of a muon is 2.2 μs. How fast is it moving relative to an observer who says its half-life is 4.4 μs?

A) 0.87 c
B) 0.75 c
C) 0.97 c
D) 0.72 c
E) 0.50 c

Question 16

An astronaut traveling with a speed v = 0.90 c holds a meterstick in his hand. If he measures its length, he will obtain a value of

A) 1.0 m
B) 2.3 m
C) 0.19 m
D) 0.43 m
E) 0.81 m

Question 17

A starship navigator measures the distance between the Earth and the sun. If the ship is moving at a speed of 0.90 c, instead of obtaining 93 million miles, the navigator measures a distance (in millions of miles) of

A) 41.
B) 30.
C) 80.
D) 215.
E) 90.

Question 18

A 1000-kg automobile moving with a speed of 24 m/s collides with a 500-kg car initially at rest. If the two stick together, what is the velocity (in m/s) of the two cars after the collision relative to an automobile moving in the same direction at 15 m/s?

A) 14
B) 16
C) 24
D) 48
E) 1.0

Question 19

A 30-year-old woman takes a trip on a rocket, leaving her 20-year-old brother behind. She travels at a speed of 0.8 c, and is gone 20 years, according to the younger brother. When she returns, how many years older/younger is she than her brother?

A) 2 years younger
B) 2 years older
C) 3 years older
D) 10 years older
E) 8 years older

Question 20

Energy is released during a nuclear reaction due to a conversion between mass and energy. Mass is not conserved. The initial and final amounts are different. If a total of 1.0 gram of mass is "missing", how much energy has been released?

A) 9.0 × 10¹¹ J
B) 9.0 × 10¹⁷ J
C) 9.0 × 10¹⁵ J
D) 9.0 × 10¹³ J
E) 9.0 × 10¹⁶ J

Question 21

A supertrain (rest-length = 100 m) travels at a speed of 0.950 c as it passes through a tunnel (rest-length 50.0 m). As seen by a trackside observer, is the train ever completely within the tunnel? If so, by how much?

Question 22

When at rest, a spacecraft has the same height as length. When moving at relativistic speeds in the direction of its length, which one of the following describes its length and height to an observer at rest?

A) Its length is decreased and its height is increased.
B) Its length is decreased and its height is decreased.
C) Its length is decreased and its height is unchanged.
D) Its length is unchanged and its height is increased.
E) Its length is increased and its height is decreased.

Question 23

In a classroom on the first spaceship to an extrasolar planet--there are children because the trip will take 200 years--a teacher is showing charge Q uniformly distributed along a conducting rod of length L₀ to produce linear charge density λ₀. As observed on Pluto when the spaceship passes it at 0.800 c, the linear charge density is

A) 0.360 λ₀.
B) 0.600 λ₀.
C) 0.800 λ₀.
D) 1.00 λ₀.
E) 1.67 λ₀.

Question 24

Find the momentum and speed of a proton whose kinetic energy equals its rest energy. (The mass of a proton is 938.3 MeV/c²).

Question 25

Two spaceships traveling in opposite directions along parallel lines measure their own and the other spaceship's length while passing one another. The crew on spaceship A says that their ship is 1000 m long and that ship B is 800 m long. The crew on ship B says that their ship is 1000 m long and that ship A is 800 m long. At what speed does each crew say that the other ship is traveling relative to their own ship?

A) 0.36 c
B) 0.60 c
C) 0.64 c
D) 0.80 c
E) 1.25 c

Question 26

Hanna, at rest in her spaceship which is moving past Earth at 0.800 c, observes a neutron at rest relative to her spaceship decay into a proton, an electron and a neutrino. She notes that the total momentum, , of the decay products is zero after the decay. According to an observer on Earth, the magnitude of the total momentum of the decay products, , is

A) 0.
B) 0.600m_n(0.800c)
C) 0.800m_n(0.800c).
D) 1.00m_n(0.800c).
E) 1.67m_n(0.800c).

Question 27

When 1.0 gram of hydrogen combines with 8.0 grams of oxygen, 9.0 grams of water is formed. But is this true? During the reaction 2.86 × 10⁵ J of energy is released. How much mass is actually lost in this reaction?

Question 28

The period of a pendulum is 2.0 s in a stationary inertial frame of reference. What is its period when measured by an observer moving at a speed of 0.60 c with respect to the inertial frame of reference?

Question 29

The 500 m-long spaceship Springbrake is at rest on the planet Hitest for refueling. Another spaceship, Summerbrake, passes parallel to Springbrake at 0.600c. The crew on Springbrake measure the length of Summerbrake as it passes and find that the length they measure is exactly the same as the known 500 m rest length of Springbrake. If Summerbrake were at rest next to Springbrake, its length would then be measured to be

A) 180 m.
B) 320 m.
C) 500 m.
D) 625 m.
E) 781 m.

Question 30

In a color television tube, electrons are accelerated through a potential difference of 20000 volts. With what velocity do the electrons strike the screen?

Question 31

A spaceship leaves Earth and maintains a constant force by means of a nuclear engine. As the speed of the spaceship increases, an observer on Earth finds that relative to her the magnitude of the spaceship's acceleration is

A) 0.
B) decreasing.
C) constant.
D) increasing.
E) proportional to the kinetic energy of the spaceship.

Question 32

The quantity which does not change in magnitude from that observed in system S when observed in system S' moving away from system S at speed v is

A) m
.
B) m
.
C) (γ − 1)mc².
D) E² − p²c².
E) x² + y² + z².

Question 33

Captain Jirk reports to headquarters that he left the planet Senesca 1.88 × 10⁴ seconds earlier. Headquarters sends back the message: "Was that spaceship proper time?" It will be spaceship proper time if it was

A) measured by one clock fixed at one spot on Senesca.
B) measured by one clock fixed at one spot on the spaceship.
C) measured by a clock on Senesca at departure and by a clock on the spaceship when reporting.
D) measured by a clock on the spaceship when departing and by a clock on Senesca when reporting.
E) calculated by dividing the distance from Senesca according to Senesca by the speed of the spaceship.

Question 34

Captain Ray, on the Galactic Explorer, sets off bright signal lights at the two ends of his spaceship so that they are seen as flashing simultaneously by General Kay, who is watch the ship go by. General Kay concludes that she was next to the midpoint of the ship at the instant when the lights flashed in her reference frame. This can only happen if Captain Ray, at the center of the Galactic Explorer,

A) sees the lights flash simultaneously in his coordinate system.
B) sees the bow (front) light flash before the aft (rear) light.
C) sees the aft (rear) light flash before the bow(front light.
D) can calculate that the light flashes reach General Kay so that the flash from the bow light reaches her before the flash from the aft light.
E) can calculate that the light flashes reach General Kay so that the flash from the aft light reaches her before the flash from the bow light.