Question 1

You can see a clock in a spaceship moving past you at 90% of the speed of light.According to you,how much time would pass while the clock in the spaceship ticked through one minute?
A)more than one minute
B)less than one minute
C)A minute is the same on the ship as it is for you.
D)A minute on the ship is exactly two minutes for you.

Accepted Answer

According to the theory of relativity, time appears to move slower for objects moving at a significant fraction of the speed of light relative to an observer. Thus, more than one minute would pass for you while the clock in the spaceship ticked through one minute.

Question 2

In relativity,two people share the same reference frame only if what is true?
A)They are not moving relative to one another.
B)They are both located in the same place.
C)They are both located in the same place and are stationary.
D)They agree on the laws of nature.

Accepted Answer

In relativity, two people share the same reference frame only if they are not moving relative to one another. This is because motion is relative and any measurement of motion must be made in relation to a chosen reference frame. If two people are moving relative to each other, they will have different observations and measurements, and therefore cannot share the same reference frame.

Question 3

Kim is in a spaceship moving past you at half the speed of light.Which of the following correctly describes how you will perceive each other's time?
A)You will say that Kim's time is running slow,and she will say that your time is running fast.
B)You will say that Kim's time is running slow,and she will say that your time is running slow.
C)You will say that Kim's time is running fast,and she will say that your time is running slow.
D)You will both agree that time runs at the same rate for both of you.

Accepted Answer

According to the theory of relativity, when two observers are moving relative to each other, each will perceive the other's clock as running slower. This is known as time dilation. Therefore, you will observe Kim's time as running slow, and Kim will also observe your time as running slow.

Question 4

Explain why relativity allows us to travel,in principle,to the center of the Milky Way,but we would never be able to tell our friends back home about it.

Accepted Answer

The answer of Explain why relativity allows us to travel,in...

Question 5

A clever student decides to spend time cruising around the local solar neighborhood at a speed of 0.95c (95 percent of the speed of light).How much time will pass on her spacecraft during a period in which 70 years pass on Earth?

Accepted Answer

The answer of A clever student decides to spend time...

Question 6

Suppose you stay home on Earth while your twin sister takes a trip to a distant star and back in a spaceship that travels at 99 percent of the speed of light.If both of you are 25 years old when she leaves and you are 45 years old when she returns,how old is your sister when she gets back?
Hint: Recall that the time dilation formula is:
 $ t^{\prime}=\sqrt[t]{1-\left(\frac{v}{c}\right)^{2}} $ 
where t is the time according to the person at home and is the time for the traveler.

Accepted Answer

The answer of Suppose you stay home on Earth while...

Question 7

Process of Science: Devise an experiment you could conduct (using any technology you can dream up-it doesn't have to already exist)to test a prediction of special relativity.

Accepted Answer

The answer of Process of Science: Devise an experiment you...

Question 8

Which of the following statements best describes what is "relative" in the theory of relativity?
A)The theory says that everything is relative.
B)The theory says that the speed of light is relative,and depends on who is measuring it.
C)The theory says that truth can never be established in any absolute sense.
D)The theory says that measurements of motion make sense only when we state what they are measured relative to.

Accepted Answer

In the theory of relativity, the concept of motion can only be understood in terms of the frames of reference used to make measurements. In other words, a measurement of motion only makes sense when we state what it is measured relative to. Therefore, D is the best answer. A is too broad, as the theory of relativity applies specifically to measurements of motion. B is incorrect, as the theory of relativity states that the speed of light is always constant, regardless of who is measuring it. C is also incorrect, as the theory of relativity provides a framework for establishing truth through measurements made in different frames of reference.

Question 9

Julia is traveling away from you at 0.95c when she shoots a probe forward from her spacecraft.According to her,the probe travels at 0.8c.How fast do you see the probe going?

Accepted Answer

The answer of Julia is traveling away from you at...

Question 10

What do we mean by length contraction in relativity?
A)It is the idea that if you measure the size of an object moving relative to you,you will find that it is shorter in every direction than it would be at rest.That is,length,width,and height are all shorter for an object when it is moving by you.
B)It is the idea that moving objects look smaller than nonmoving objects,but their sizes have not really changed.
C)It is the idea that if you measure the size of an object moving relative to you,you will find that in the direction of motion it is shorter than it would be at rest,while its size in other directions is unchanged.
D)It is the idea that if you travel very fast,you'll notice yourself getting shorter.

Accepted Answer

Length contraction refers to the fact that when an object is moving relative to an observer, its size in the direction of motion appears shorter than it would be if the object were at rest. However, its size in other directions remains unchanged. This idea is a consequence of the theory of relativity, which suggests that measurements of distance, time, and other physical quantities are not absolute but depend on the observer's point of view.

Question 11

What do we mean by time dilation in relativity?
A)It is the idea that time seems to run slower in reference frames moving relative to you,but time really is the same for everyone.
B)It is the idea that relativity makes time dilate,or expand,for people who study it.
C)It is a hallucinogenic effect experienced by people who take too much of something.
D)It is the idea that time really runs slower in reference frames moving relative to you.

Accepted Answer

Time dilation in relativity refers to the phenomenon where time appears to move slower in reference frames that are moving relative to an observer. This is not just an illusion, but a real effect that has been observed and measured. So, choice D is the most accurate description of time dilation in relativity.

Question 12

A man is moving by you at a speed close to the speed of light.Which of the following correctly summarizes the effects you would notice on his mass,size,and time?
A)His mass would be increased from its value at rest,his length would be decreased from its rest value but only in the direction in which he is moving,and his time would be running slower than yours.
B)His mass would be increased from its value at rest,his length,width,and height would all be decreased no matter what direction he is moving,and his time would be running slower than yours.
C)His mass would be decreased from its value at rest,his length would be decreased from its rest value but only in the direction in which he is moving,and his time would be running slower than yours.
D)His mass would be increased from its value at rest,his size would be increased,and his time would be running slower than yours.

Accepted Answer

This is a correct statement of the effects of special relativity. As an object moves closer to the speed of light, its mass increases, its length contracts in the direction of motion (known as length contraction), and time dilation occurs, meaning that time appears to run slower for the moving object compared to a stationary observer. These effects have been experimentally verified. Choice B is incorrect because the dimensions in the perpendicular direction to motion do not change. Choice C is also incorrect because mass does not decrease with increasing speed in special relativity. Choice D is incorrect because an increase in speed does not result in an increase in size.

Question 13

You are in an airplane,traveling relative to the ground at 500 km/hr.You throw a baseball toward the front of the plane at a speed of 50 km/hr.How fast would someone on the ground say the baseball is moving?
A)550 km/hr
B)50 km/hr
C)500 km/hr
D)450 km/hr.

Accepted Answer

The speed of the baseball relative to the ground is the sum of the speed of the airplane and the speed at which you throw the baseball. Since the airplane is moving at 500 km/hr and you throw the baseball at 50 km/hr towards the front, someone on the ground would observe the baseball moving at 500 km/hr + 50 km/hr = 550 km/hr.

Question 14

You and Mae are in free-float frames.Mae has just passed you,traveling at a speed of 60 km/hr.You throw a ball toward her at a speed of 60 km/hr.What will Mae see the ball doing?
A)She'll see the ball coming toward her at 60 km/hr.
B)The ball will be stationary,floating freely in her own reference frame.
C)She'll see the ball moving away from her at 60 km/hr.
D)She'll see the ball coming toward her at 120 km/hr.

Accepted Answer

In Mae's reference frame, the ball is thrown at the same speed she is moving relative to you, so it appears stationary to her. This is because velocities are relative, and in her frame, the ball's velocity cancels out her own velocity relative to you.

Question 15

Recall that a π⁺ meson produced at rest has a lifetime of 18 billionths of a second.Thus,in its own reference frame,a π⁺ meson will always "think" it is at rest and therefore decay after 18 billionths of a second
(1.8 × 10⁻⁸ s).Suppose a π⁺ meson is produced in a particle accelerator traveling at 0.998c.
a.According to scientists in the lab,how long will the π⁺ meson last compared to its normal lifetime of 18 billionths of a second (e.g. ,shorter,the same,or longer)?
b.Recall that the time dilation formula is:
$ t^{\prime}=\sqrt[t]{1-\left(\frac{v}{c}\right)^{2}} $0 
where t is the time in the laboratory and is the time for the moving particle.Use the time dilation formula to calculate how long scientists will see the π⁺ meson last before it decays.

Accepted Answer

The answer of Recall that a π⁺ meson produced at...

Question 16

A super train is moving along a track at a speed close to the speed of light.You are watching the train from the ground.You observe lightning to strike in two places along the track,a mile apart,at precisely the same time.What would someone on the train say?
A)The two bolts of lightning struck at different times,and they struck at places that are more than a mile apart.
B)The two bolts of lightning struck at the same time,and they struck at places that are less than a mile apart.
C)The two bolts of lightning struck at different times,and they struck at places that are precisely a mile apart.
D)The two bolts of lightning struck at different times,and they struck at places that are less than a mile apart.

Accepted Answer

According to the theory of relativity, observers moving at different velocities may perceive the timing and spacing of events differently. Someone on the train, moving at a speed close to the speed of light, would observe the lightning strikes as occurring at different times due to the relativistic effects of time dilation and length contraction, making the distance between the strikes appear less than a mile.

Question 17

Suppose a supersonic airplane flies at a speed of 1,650 km/hr from Nairobi,Kenya,to Quito,Ecuador;note that this is the same speed that Earth rotates,but in the opposite direction.Describe how this flight would look to an observer on the Moon.

Accepted Answer

The answer of Suppose a supersonic airplane flies at a...

Question 18

Describe at least three pieces of evidence supporting the special theory of relativity.

Accepted Answer

The answer of Describe at least three pieces of evidence...

Question 19

The measured value of the speed of light is about 300,000 km/s.Suppose a futuristic space train is traveling at 200,000 km/s with its headlights on.If you could measure the speed of the light from the headlights,you would find it to be
A)200,000 km/s.
B)100,000 km/s.
C)300,000 km/s.
D)500,000 km/s.

Accepted Answer

The speed of light is constant and independent of the motion of the source or observer. Therefore, the measured value of the speed of light from the train's headlights will also be 300,000 km/s, the same as the speed of light in a vacuum.

Question 20

The primary difference between the special theory of relativity and the general theory of relativity is that the general theory also describes
A)length contraction.
B)the nature of gravity.
C)time dilation.
D)the constancy of the speed of light.

Accepted Answer

The special theory of relativity only deals with objects moving at a constant velocity in the absence of gravitational fields, while the general theory of relativity includes gravity and its effect on space and time. Therefore, the correct answer is B, as the general theory of relativity offers a more complete and comprehensive explanation of the nature of gravity.

Quiz 26: Space and Time

You can see a clock in a spaceship moving past you at 90% of the speed of light.According to you,how much time would pass while the clock in the spaceship ticked through one minute?

In relativity,two people share the same reference frame only if what is true?

Kim is in a spaceship moving past you at half the speed of light.Which of the following correctly describes how you will perceive each other's time?

Explain why relativity allows us to travel,in principle,to the center of the Milky Way,but we would never be able to tell our friends back home about it.

A clever student decides to spend time cruising around the local solar neighborhood at a speed of 0.95c (95 percent of the speed of light).How much time will pass on her spacecraft during a period in which 70 years pass on Earth?

Process of Science: Devise an experiment you could conduct (using any technology you can dream up-it doesn't have to already exist)to test a prediction of special relativity.

Which of the following statements best describes what is "relative" in the theory of relativity?

Julia is traveling away from you at 0.95c when she shoots a probe forward from her spacecraft.According to her,the probe travels at 0.8c.How fast do you see the probe going?

What do we mean by length contraction in relativity?

What do we mean by time dilation in relativity?

A man is moving by you at a speed close to the speed of light.Which of the following correctly summarizes the effects you would notice on his mass,size,and time?

You are in an airplane,traveling relative to the ground at 500 km/hr.You throw a baseball toward the front of the plane at a speed of 50 km/hr.How fast would someone on the ground say the baseball is moving?

You and Mae are in free-float frames.Mae has just passed you,traveling at a speed of 60 km/hr.You throw a ball toward her at a speed of 60 km/hr.What will Mae see the ball doing?

A super train is moving along a track at a speed close to the speed of light.You are watching the train from the ground.You observe lightning to strike in two places along the track,a mile apart,at precisely the same time.What would someone on the train say?

Suppose a supersonic airplane flies at a speed of 1,650 km/hr from Nairobi,Kenya,to Quito,Ecuador;note that this is the same speed that Earth rotates,but in the opposite direction.Describe how this flight would look to an observer on the Moon.

Describe at least three pieces of evidence supporting the special theory of relativity.

The measured value of the speed of light is about 300,000 km/s.Suppose a futuristic space train is traveling at 200,000 km/s with its headlights on.If you could measure the speed of the light from the headlights,you would find it to be

The primary difference between the special theory of relativity and the general theory of relativity is that the general theory also describes