Question 1

Relative to the frame of the observer making the measurement, at what speed parallel to its length is the length of a meterstick 60 cm?

Accepted Answer

A)  0.80c 
B)  0.60c 
C)  0.50c 
D)  0.70c 
E)  0.90c 
A)  0.80c 
B)  0.60c 
C)  0.50c 
D)  0.70c 
E)  0.90c

Question 2

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. What is the frequency of the beacon radio signal that is detected on the ship?

Accepted Answer

A)  55 MHz 
B)  60 MHz 
C)  66 MHz 
D)  71 MHz 
E)  76 MHz 
A)  55 MHz 
B)  60 MHz 
C)  66 MHz 
D)  71 MHz 
E)  76 MHz

Question 3

The special theory of relativity predicts that there is an upper limit to the speed of a particle. It therefore follows that there is also an upper limit on the following properties of a particle.

Accepted Answer

A)  the kinetic energy 
B)  the total energy 
C)  the linear momentum 
D)  more than one of these 
E)  none of these 
A)  the kinetic energy 
B)  the total energy 
C)  the linear momentum 
D)  more than one of these 
E)  none of these

Question 4

In the lab, a relativistic proton has a momentum of 1.00 × 10-19 kg ∙ m/s and a rest energy of 0.150 nJ. What is the speed of the proton in the lab? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

Accepted Answer

A)  0.170c 
B)  0.196c 
C)  0.911c 
D)  0.930c 
E)  0.951c 
A)  0.170c 
B)  0.196c 
C)  0.911c 
D)  0.930c 
E)  0.951c

Question 5

As measured in Earth's rest frame, a spaceship traveling at 0.964c takes 11.2 y to travel between planets. How long does the trip take as measured by someone on the spaceship?

Accepted Answer

A)  2.98 y 
B)  7.28 y 
C)  42.1 y 
D)  30.7 y 
A)  2.98 y 
B)  7.28 y 
C)  42.1 y 
D)  30.7 y

Question 6

An astronaut in an inertial reference frame measures a time interval Δt between her heartbeats. What will observers in all other inertial reference frames measure for the time interval between her heartbeats?

Accepted Answer

A)  Δt 
B)  more thanΔt 
C)  less than Δt 
D)  The answer depends on whether they are moving toward her or away from her. 
A)  Δt 
B)  more thanΔt 
C)  less than Δt 
D)  The answer depends on whether they are moving toward her or away from her.

Question 7

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship which travels away from Earth at a speed of 0.60c for five years (as measured by Courtney), then immediately turns around and comes back at 0.60c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?

Accepted Answer

A)  10 y 
B)  12 y 
C)  15 y 
D)  18 y 
E)  20 y 
A)  10 y 
B)  12 y 
C)  15 y 
D)  18 y 
E)  20 y

Question 8

A particle in a 453 m-long linear particle accelerator is moving at 0.875c. How long does the particle accelerator appear to the particle?

Accepted Answer

A)  219 m 
B)  589 m 
C)  104 m 
D)  936 m 
A)  219 m 
B)  589 m 
C)  104 m 
D)  936 m

Question 9

Astronaut Spud Nick is space-traveling from planet X to planet Y at a speed of 0.60c relative to the planets, which are at rest relative to each other. When he is precisely halfway between the planets, a distance of 1.0 light-hour from each one as measured in the planet frame, nuclear devices are detonated on each planet. The explosions are simultaneous in the frame of the planets. What is the difference in the time of arrival of the flashes from the explosions as observed by Spud?

Accepted Answer

A)  300 min 
B)  150 min 
C)  75 min 
D)  0 min 
E)  113 min 
A)  300 min 
B)  150 min 
C)  75 min 
D)  0 min 
E)  113 min

Question 10

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 0.70c. At what speed would an observer in Alpha see the galaxy Beta moving?

Accepted Answer

A)  0.82c 
B)  0.70c 
C)  0.94c 
D)  0.35c 
E)  0.57c 
A)  0.82c 
B)  0.70c 
C)  0.94c 
D)  0.35c 
E)  0.57c

Question 11

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. 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. What is the new velocity of the spaceship relative to the beacon?

Accepted Answer

A)  0.20c 
B)  0.22c 
C)  0.24c 
D)  0.26c 
E)  0.28c 
A)  0.20c 
B)  0.22c 
C)  0.24c 
D)  0.26c 
E)  0.28c

Question 12

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y, while an astronaut on the space ship says that the trip took 6.27 y. Find the speed of the spaceship in terms of the speed of light.

Accepted Answer

A)  0.779c 
B)  0.687c 
C)  0.975c 
D)  0.384c 
A)  0.779c 
B)  0.687c 
C)  0.975c 
D)  0.384c

Question 13

How much work must be done to accelerate a particle of mass 2.1 × 10-14 kg from a speed of 1.5 × 108 m/s to a speed of 2.5 × 108 m/s? (c = 3.00 × 108 m/s)

Accepted Answer

Question 14

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

Accepted Answer

A)  2.51 × 10-19 kg ∙ m/s 
B)  2.89 × 10-19 kg ∙ m/s 
C)  4.34 × 10-19 kg ∙ m/s 
D)  5.01 × 10-19 kg ∙ m/s 
E)  8.68 × 10-19 kg ∙ m/s 
A)  2.51 × 10-19 kg ∙ m/s 
B)  2.89 × 10-19 kg ∙ m/s 
C)  4.34 × 10-19 kg ∙ m/s 
D)  5.01 × 10-19 kg ∙ m/s 
E)  8.68 × 10-19 kg ∙ m/s

Question 15

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 108 m/s)

Accepted Answer

A)  1.8 × 1017 J 
B)  9.0 × 1016 J 
C)  2.7 × 1012 J 
D)  4.5 × 109 J 
E)  3.0 × 103 J 
A)  1.8 × 1017 J 
B)  9.0 × 1016 J 
C)  2.7 × 1012 J 
D)  4.5 × 109 J 
E)  3.0 × 103 J

Question 16

In an "atom smasher," two particles collide head on at relativistic speeds. If the velocity of the first particle is 0.741c to the left, and the velocity of the second particle is 0.35c to the right (both of these speeds are measured in Earth's rest frame), how fast are the particles moving with respect to each other?

Accepted Answer

A)  0.866c 
B)  1.091c 
C)  0.883c 
D)  0.788c 
A)  0.866c 
B)  1.091c 
C)  0.883c 
D)  0.788c

Question 17

A spacecraft is measured by an observer on the ground to have a length of 53 m as it flies toward the earth with a speed 1.7 × 108 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 on the launchpad. What result does he now get for the length? (c = 3.00 × 108 m/s)

Accepted Answer

Question 18

A rocket is moving at 1/4 the speed of light relative to Earth. At the center of this rocket, a light suddenly flashes. To an observer at rest in the rocket

Accepted Answer

A)  the light will reach the front of the rocket at the same instant that it reaches the back of the rocket. 
B)  the light will reach the front of the rocket before it reaches the back of the rocket. 
C)  the light will reach the front of the rocket after it reaches the back of the rocket. 
A)  the light will reach the front of the rocket at the same instant that it reaches the back of the rocket. 
B)  the light will reach the front of the rocket before it reaches the back of the rocket. 
C)  the light will reach the front of the rocket after it reaches the back of the rocket.

Question 19

At what speed relative to the lab will a 0.272-kg object have the same momentum as a 1.30-kg object that is moving at 0.515c relative to the lab?

Accepted Answer

A)  0.944c 
B)  0.922c 
C)  0.981c 
D)  0.592c 
A)  0.944c 
B)  0.922c 
C)  0.981c 
D)  0.592c

Question 20

System Sʹ has a velocity u = +0.45c relative to system S, as shown in the figure. The clocks of S and Sʹ are synchronized at t = tʹ = 0 when the origins O and Oʹ 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. What is the xʹ-coordinate of the event, measured by an observer in Sʹ ?

Accepted Answer

A)  380 m 
B)  340 m 
C)  360 m 
D)  350 m 
E)  310 m 
A)  380 m 
B)  340 m 
C)  360 m 
D)  350 m 
E)  310 m

Exam 36: Relativity

Relative to the frame of the observer making the measurement, at what speed parallel to its length is the length of a meterstick 60 cm?

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. What is the frequency of the beacon radio signal that is detected on the ship?

The special theory of relativity predicts that there is an upper limit to the speed of a particle. It therefore follows that there is also an upper limit on the following properties of a particle.

In the lab, a relativistic proton has a momentum of 1.00 × 10-19 kg ∙ m/s and a rest energy of 0.150 nJ. What is the speed of the proton in the lab? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

As measured in Earth's rest frame, a spaceship traveling at 0.964c takes 11.2 y to travel between planets. How long does the trip take as measured by someone on the spaceship?

An astronaut in an inertial reference frame measures a time interval Δt between her heartbeats. What will observers in all other inertial reference frames measure for the time interval between her heartbeats?

A particle in a 453 m-long linear particle accelerator is moving at 0.875c. How long does the particle accelerator appear to the particle?

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 0.70c. At what speed would an observer in Alpha see the galaxy Beta moving?

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y, while an astronaut on the space ship says that the trip took 6.27 y. Find the speed of the spaceship in terms of the speed of light.

How much work must be done to accelerate a particle of mass 2.1 × 10-14 kg from a speed of 1.5 × 108 m/s to a speed of 2.5 × 108 m/s? (c = 3.00 × 108 m/s)

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 108 m/s)

A rocket is moving at 1/4 the speed of light relative to Earth. At the center of this rocket, a light suddenly flashes. To an observer at rest in the rocket

At what speed relative to the lab will a 0.272-kg object have the same momentum as a 1.30-kg object that is moving at 0.515c relative to the lab?

Units, Physical Quantities, and Vectors

Motion Along a Straight Line

Motion in Two or Three Dimensions

Newtons Laws of Motion

Applying Newtons Laws

Work and Kinetic Energy

Potential Energy and Energy Conservation

Momentum, Impulse, and Collisions

Rotation of Rigid Bodies

Equilibrium and Elasticity

Fluid Mechanics

Gravitation

Periodic Motion

Mechanical Waves

Sound and Hearing

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

The Second Law of Thermodynamics

Electric Charge and Electric Field

Gausss Law

Electric Potential

Capacitance and Dielectrics

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic Field

Electromagnetic Induction

Inductance

Alternating Current

Electromagnetic Waves

The Nature and Propagation of Light

Geometric Optics

Interference

Diffraction

Photons: Light Waves Behaving As Particles

Particles Behaving As Waves

Quantum Mechanics

Atomic Structure

Molecules and Condensed Matter

Nuclear Physics

Particle Physics and Cosmology

Filters

In the lab, a relativistic proton has a momentum of 1.00 × 10^-19 kg ∙ m/s and a rest energy of 0.150 nJ. What is the speed of the proton in the lab? (c = 3.00 × 10⁸ m/s, mproton = 1.67 × 10^-27kg)

How much work must be done to accelerate a particle of mass 2.1 × 10^-14 kg from a speed of 1.5 × 10⁸ m/s to a speed of 2.5 × 10⁸ m/s? (c = 3.00 × 10⁸ m/s)

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10⁸ m/s, mproton = 1.67 × 10^-27kg)

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 10⁸ m/s)