Question 1

The relativistic kinetic energy formula is valid

Accepted Answer

The relativistic kinetic energy formula is valid at all speeds, but its effects become significantly noticeable and different from classical predictions at speeds close to the speed of light.

Question 2

Suppose one twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again, while the other twin remains on Earth. Compared to the twin who remained on Earth, the astronaut twin is

Accepted Answer

This scenario is an example of the twin paradox, a thought experiment in special relativity. According to the theory of relativity, time dilates, or slows down, for an observer in motion relative to a stationary observer. Therefore, the twin who travels at a high speed in a spaceship will age more slowly compared to the twin who remains on Earth.

Question 3

According to the equation $$E = m c ^ { 2 }$$ an object turns into energy when it reaches the speed of light.

Accepted Answer

The equation $E = mc^2$ describes the equivalence of mass and energy, not the transformation of an object into energy by reaching the speed of light.

Question 4

One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that

Accepted Answer

Einstein's postulate of the special theory of relativity states that the laws of physics are the same in all inertial frames of reference, which are frames that either are at rest or move at a constant velocity with respect to each other. This excludes frames that accelerate or oscillate.

Question 5

Which of the following are basic postulates of special relativity? (There could be more than one correct choice.)

Accepted Answer

The basic postulates of special relativity are: (C) The laws of physics are the same in all inertial reference frames, and (D) The speed of light is the same for all observers, regardless of their motion relative to the light source.

Question 6

If you were in a spaceship traveling close to the speed of light with respect to Earth, you would notice that

Accepted Answer

According to the theory of relativity, you would not notice any changes in your mass, pulse rate, or dimensions from your own perspective. These effects are observed by an outside observer, not by someone traveling at that speed.

Question 7

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The length of the train, as measured by a stationary observer on the ground,

Accepted Answer

According to the theory of relativity, objects appear to contract along the direction of motion as they approach the speed of light. This phenomenon is known as length contraction.

Question 8

A spaceship traveling at constant velocity passes by Earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time?

Accepted Answer

The proper time between two events is defined as the time measured by a clock that is present at both events. In this scenario, the spaceship is the only frame of reference that is present at both events (passing Earth and later passing Mars) without changing its velocity, making it the frame where the proper time is measured.

Question 9

Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be TA. Observer B moves along with the rocket and measures the period of the
Pendulum to be TB. What is true about these two time measurements?

Accepted Answer

According to the theory of relativity, time dilates (or slows down) from the perspective of a stationary observer watching a moving clock. Therefore, Observer A, who is stationary relative to the moving rocket, would measure the pendulum's period $T_A$ to be longer than $T_B$, the period measured by Observer B who is moving with the rocket.

Question 10

When an object moves close to the speed of light relative to Earth, what happens to its dimensions compared to what they were before it began moving, as measured by an Earth-based observer?

Accepted Answer

According to the theory of relativity, lengths parallel to the direction of travel are contracted (Lorentz contraction) when an object moves at speeds close to the speed of light relative to an observer. Lengths perpendicular to the direction of travel are not affected.

Question 11

A spaceship is moving in a straight line away from Earth at 0.80c, measured relative to Earth. It launches a missile that moves away from the spaceship in the forward direction at 0.60c, relative to
The ship. Relative to Earth, what is the speed of this missile?

Accepted Answer

To find the speed of the missile relative to Earth, we use the formula for addition of velocities in special relativity: $v = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}}$, where $v_1 = 0.80c$ is the speed of the spaceship relative to Earth, $v_2 = 0.60c$ is the speed of the missile relative to the spaceship, and $c$ is the speed of light. Plugging in these values, we find that the speed of the missile relative to Earth is greater than 0.80c but less than c, making option B correct.

Question 12

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

Accepted Answer

The answer of You are a passenger on a spaceship....

Question 13

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

Accepted Answer

According to the theory of relativity, from your own frame of reference (inside the spaceship), you would not notice any difference in the behavior of your watch. Time dilation affects how an observer in a different inertial frame (e.g., someone stationary relative to the spaceship's motion) would perceive the passage of time on the spaceship, not how you perceive time on the spaceship itself.

Question 14

Observer A sees a ruler moving by in a relativistic rocket and measures its length to be LA. Observer B moves along with the rocket and measures the length of the ruler to be LB. What is true
About these two length measurements?

Accepted Answer

According to the theory of relativity, an object in motion appears shorter to a stationary observer compared to an observer moving with the object. Therefore, $L_A < L_B$, as observer A sees the ruler moving and measures it to be shorter than observer B, who moves along with the ruler.

Question 15

You are riding in a spaceship that has no windows, radios, or other means for you to observe or measure what is outside. You wish to determine if the ship is stopped or moving at constant
Velocity. How can you do this?

Accepted Answer

According to the principle of relativity, if you are in a smoothly moving vehicle without any interaction with the outside world, there is no experiment you can perform to tell whether you are moving or at rest. This is because the laws of physics are the same in all inertial frames (frames moving at constant velocity).

Question 16

A 30-year-old astronaut goes off on a long-term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 20 years as measured on Earth. Biologically speaking, at the end of the mission, the astronaut's age would be

Accepted Answer

Due to the effects of time dilation under the theory of relativity, time passes more slowly for objects moving at speeds close to the speed of light compared to those at rest. Therefore, the astronaut would age less than 20 years during the mission, making their biological age less than 50 years upon return.

Question 17

The special theory of relativity predicts that there is an upper limit to the speed of an object. It therefore follows that there is also an upper limit on which of the following properties of the
Object? (There could be more than one correct choice.)

Accepted Answer

The answer of The special theory of relativity predicts that...

Question 18

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The height of the train, as measured by a stationary observer on the ground,

Accepted Answer

The height of the train does not change due to the motion because length contraction only affects the dimension parallel to the direction of motion, not perpendicular dimensions like height.

Question 19

You are moving at a speed 2/3 c toward Randy when shines a light toward you. At what speed do you see the light approaching you?

Accepted Answer

According to the theory of relativity, the speed of light in a vacuum is always constant and observed to be the same by all observers, regardless of their relative motion. Therefore, you would see the light approaching you at speed c.

Question 20

An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in the figure. From the point of view of an observer who sees the spaceship moving near the speed of light parallel to the floor, the angle the bed makes with the floor

Accepted Answer

The answer of An astronaut is resting on a bed...

Quiz 26: The Special Theory of Relativity

The relativistic kinetic energy formula is valid

Suppose one twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again, while the other twin remains on Earth. Compared to the twin who remained on Earth, the astronaut twin is

According to the equation $E = m c ^ { 2 }$ an object turns into energy when it reaches the speed of light.

One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that

Which of the following are basic postulates of special relativity? (There could be more than one correct choice.)

If you were in a spaceship traveling close to the speed of light with respect to Earth, you would notice that

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The length of the train, as measured by a stationary observer on the ground,

A spaceship traveling at constant velocity passes by Earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time?

Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be TA. Observer B moves along with the rocket and measures the period of the Pendulum to be TB. What is true about these two time measurements?

When an object moves close to the speed of light relative to Earth, what happens to its dimensions compared to what they were before it began moving, as measured by an Earth-based observer?

A spaceship is moving in a straight line away from Earth at 0.80c, measured relative to Earth. It launches a missile that moves away from the spaceship in the forward direction at 0.60c, relative to The ship. Relative to Earth, what is the speed of this missile?

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

Observer A sees a ruler moving by in a relativistic rocket and measures its length to be LA. Observer B moves along with the rocket and measures the length of the ruler to be LB. What is true About these two length measurements?

You are riding in a spaceship that has no windows, radios, or other means for you to observe or measure what is outside. You wish to determine if the ship is stopped or moving at constant Velocity. How can you do this?

A 30-year-old astronaut goes off on a long-term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 20 years as measured on Earth. Biologically speaking, at the end of the mission, the astronaut's age would be

The special theory of relativity predicts that there is an upper limit to the speed of an object. It therefore follows that there is also an upper limit on which of the following properties of the Object? (There could be more than one correct choice.)

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The height of the train, as measured by a stationary observer on the ground,

You are moving at a speed 2/3 c toward Randy when shines a light toward you. At what speed do you see the light approaching you?

An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in the figure. From the point of view of an observer who sees the spaceship moving near the speed of light parallel to the floor, the angle the bed makes with the floor

Quiz 26: The Special Theory of Relativity

The relativistic kinetic energy formula is valid

Suppose one twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again, while the other twin remains on Earth. Compared to the twin who remained on Earth, the astronaut twin is

According to the equation E=mc2E = m c ^ { 2 }E=mc2 an object turns into energy when it reaches the speed of light.

One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that

Which of the following are basic postulates of special relativity? (There could be more than one correct choice.)

If you were in a spaceship traveling close to the speed of light with respect to Earth, you would notice that

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The length of the train, as measured by a stationary observer on the ground,

A spaceship traveling at constant velocity passes by Earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time?

Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be TA. Observer B moves along with the rocket and measures the period of the Pendulum to be TB. What is true about these two time measurements?

When an object moves close to the speed of light relative to Earth, what happens to its dimensions compared to what they were before it began moving, as measured by an Earth-based observer?

A spaceship is moving in a straight line away from Earth at 0.80c, measured relative to Earth. It launches a missile that moves away from the spaceship in the forward direction at 0.60c, relative to The ship. Relative to Earth, what is the speed of this missile?

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

Observer A sees a ruler moving by in a relativistic rocket and measures its length to be LA. Observer B moves along with the rocket and measures the length of the ruler to be LB. What is true About these two length measurements?

You are riding in a spaceship that has no windows, radios, or other means for you to observe or measure what is outside. You wish to determine if the ship is stopped or moving at constant Velocity. How can you do this?

A 30-year-old astronaut goes off on a long-term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 20 years as measured on Earth. Biologically speaking, at the end of the mission, the astronaut's age would be

The special theory of relativity predicts that there is an upper limit to the speed of an object. It therefore follows that there is also an upper limit on which of the following properties of the Object? (There could be more than one correct choice.)

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The height of the train, as measured by a stationary observer on the ground,

You are moving at a speed 2/3 c toward Randy when shines a light toward you. At what speed do you see the light approaching you?

An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in the figure. From the point of view of an observer who sees the spaceship moving near the speed of light parallel to the floor, the angle the bed makes with the floor

According to the equation $E = m c ^ { 2 }$ an object turns into energy when it reaches the speed of light.