Question 1

Which one of the following statements concerning the proper length of a meter stick is true?

Accepted Answer

The proper length of a meter stick is always one meter, regardless of the observer's speed, acceleration, or reference frame. This is because the meter is defined as the length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second, and this definition is independent of any observer.

Question 2

At time t = 2.3 s, a 4-kg block that initially moves with a constant speed of 6 m/s undergoes an inelastic collision with another block. Any two inertial observers must agree that

Accepted Answer

E

Question 3

Leah is moving in a spaceship at a constant velocity away from a group of stars. Which one of the following statements indicates a method by which she can determine her absolute velocity through space?

Accepted Answer

There is no known method by which Leah can measure her absolute velocity through space. She can only measure her velocity relative to other objects, such as the stars or planets. This is due to the absence of a universal frame of reference in space.

Question 4

In a science fiction novel, a starship takes three days to travel between two distant space stations according to its own clocks. Instruments on one of the space stations indicate that the trip took four days. How fast did the starship travel, relative to the space station?

Accepted Answer

The correct answer is A because the speed of the starship relative to the space station is given by the formula v = d/t, where d is the distance between the two space stations and t is the time it takes the starship to travel that distance according to the space station's clocks. In this case, d = 3 days * 24 hours/day * 3600 seconds/hour * 3 x 10^8 m/s = 2.592 x 10^12 m, and t = 4 days * 24 hours/day * 3600 seconds/hour = 3.456 x 10^5 seconds. Therefore, v = 2.592 x 10^12 m / 3.456 x 10^5 seconds = 1.98 x 10^8 m/s.

Question 5

Complete the following statement: To measure the proper length of an object moving relative to the surface of the earth, one must note the coordinates of points on the front and back ends

Accepted Answer

Proper length is measured in the rest frame of the object, so the coordinates must be noted at the same time with respect to a clock on the moving object.

Question 6

Which one of the following is a consequence of the postulates of special relativity?

Accepted Answer

According to the postulates of special relativity, there is no preferred or absolute reference frame, and the laws of physics are the same for all inertial observers. As a result, the concept of absolute rest or motion is meaningless, because motion can only be defined relative to another object. Therefore, choice D is the correct consequence of the postulates of special relativity.

Question 7

A spaceship traveling at 0.7370c relative to the Earth monitors a motorcycle drag race on Earth. The space travelers measure the time from the start to the finish of the race to be 15.25 s. What is the proper time interval for the motorcycle race?

Accepted Answer

The proper time interval is the time measured in the rest frame of the event. Using time dilation, the proper time (t₀) is given by t₀ = t / γ, where γ = 1/√(1-v²/c²). For v = 0.7370c, γ ≈ 1.498. Thus, t₀ = 15.25 s / 1.498 ≈ 10.31 s.

Question 8

Which one of the following statements concerning time dilation is true?

Accepted Answer

Time dilation has been observed in experiments involving both atomic clocks and radioactive decay processes. This is one of the most well-established predictions of special relativity, and has been confirmed through numerous experiments over the past century. In these experiments, time is observed to pass more slowly for objects that are moving relative to an observer, or are in a strong gravitational field. This effect has important implications for the behavior of subatomic particles, GPS satellites, and other systems that rely on precise timekeeping.

Question 9

During a baseball game, a batter hits a ball directly back to the pitcher who catches it. An observer flying over the stadium at a speed of 0.75c, measures 0.658 s as the time between the two events (hitting and catching the ball). What is the proper time interval between the two events?

Accepted Answer

The proper time interval is the time measured in the rest frame of the events. Using time dilation, the proper time is calculated as 0.658 s * sqrt(1 - (0.75)^2) = 0.435 s.

Question 10

Which one of the following statements concerning the proper time interval between two events is true?

Accepted Answer

The proper time interval is defined as the time interval measured by an observer who is at rest with respect to the two events. This means that any observer who is moving with respect to the events will measure a longer time interval than the proper time interval. Therefore, option B is correct, as it states that the proper time interval is the shortest time interval that any inertial observer can measure for the event. Options A, C, D, and E are incorrect, as they are not true statements about the proper time interval.

Question 11

Mars rotates about its axis once every 88 642 s. A spacecraft comes into the solar system and heads directly toward Mars at a speed of 0.800c. What is the rotational period of Mars according to the beings on the spaceship?

Accepted Answer

The answer of Mars rotates about its axis once every...

Question 12

A bomb is designed to explode 2.00 s after it is armed. The bomb is launched from earth and accelerated to an unknown final speed. After reaching its final speed, however, the bomb is observed by people on earth to explode 2.90 s after it is armed. What is the final speed of the bomb just before it explodes?

Accepted Answer

The answer of A bomb is designed to explode 2.00...

Question 13

A meter stick is observed to be only 0.850 meters long to an inertial observer. At what speed, relative to the observer, must the meter stick be moving?

Accepted Answer

We can use the Lorentz contraction formula:
L' = L/sqrt(1-v^2/c^2)
where L = 1 m (the rest length of the meter stick), L' = 0.850 m (the observed length), c = 3.00 x 10^8 m/s (the speed of light), and we are solving for v (the velocity of the meter stick).
Plugging in the values, we get:
0.850 m = 1 m / sqrt(1 - v^2/c^2)
Simplifying and rearranging, we get:
v^2/c^2 = 1 - (0.850 m/1 m)^2 = 0.28
v = c * sqrt(0.28) = 1.58 x 10^8 m/s
Therefore, the answer is B.

Question 14

Complete the following statement: The Michelson-Morley experiment

Accepted Answer

The Michelson-Morley experiment was designed to measure the speed of light in different directions relative to Earth's motion through the hypothetical aether. The experiment found that the speed of light was always the same in all directions, regardless of the direction and speed of Earth's motion. This result contradicted the prevailing belief that there was an aether through which light waves traveled and supported Einstein's theory of special relativity, which postulated that the speed of light is the same in all inertial reference frames. Therefore, the correct choice is E, which indicates that the Michelson-Morley experiment indicated that the speed of light is the same in all inertial reference frames.

Question 15

The proper mean lifetime of a muon is 2.2 × 10^-⁶ s. A beam of muons is moving with speed 0.6c relative to an inertial observer. Approximately how far will a muon in the beam travel, on average, before it decays?

Accepted Answer

The answer of The proper mean lifetime of a muon...

Question 16

In the year 2100, an astronaut wears an antique, but accurate, "quartz" wristwatch on a journey at a speed of 2.0 × 10⁸ m/s. According to mission control in Houston, the trip lasts 14 hours. How long was the trip as measured on the watch?

Accepted Answer

According to special relativity, time appears to slow down for an object in motion relative to a stationary observer. This effect is known as time dilation. The faster the object moves, the greater the time dilation.

In this case, the astronaut is moving at a very high speed of 2.0 × 10^18 m/s. As a result of this velocity, time appears to slow down for the astronaut, and the elapsed time during the journey will be less as measured by the watch compared to the time measured by the mission control.

To calculate the time dilation, we can use the equation:

T' = T / √(1 - v^2/c^2)

where T is the time measured by mission control, T' is the time measured by the watch, v is the velocity of the astronaut, and c is the speed of light.

Plugging in the values, we get:

T' = 14 hours / √(1 - (2.0 × 10^18 m/s)^2/(3.0 × 10^8 m/s)^2)
T' = 10.4 hours

Therefore, the trip lasted 10.4 hours as measured on the watch, which is the closest to option C (10.4 hr).

Question 17

Two helium-filled balloons are released simultaneously at points A and B on the x axis in an earth-based reference frame. Which one of the following statements is true for an observer moving in the +x direction?

Accepted Answer

The answer of Two helium-filled balloons are released simultaneously at...

Question 18

An alien spacecraft flies directly over a football stadium at a speed of 0.50c. If the proper length of the field is 100 yards, what field length is measured by the crew of the alien spacecraft?

Accepted Answer

We can use the Lorentz contraction formula to find the length of the football field measured by the crew of the alien spacecraft.

L' = L√(1 - v^2/c^2)

Where L is the proper length of the football field, v is the velocity of the spacecraft (0.50c), c is the speed of light, and L' is the length measured by the crew of the spacecraft.

Plugging in the numbers:

L' = 100 yards * √(1 - (0.50c)^2/c^2)
L' = 100 yards * √(1 - 0.25)
L' = 100 yards * √0.75
L' = 100 yards * 0.866
L' = 86.6 yards

So the field length measured by the crew of the alien spacecraft is approximately 87 yards, which is answer choice C.

Question 19

Which one of the following systems would constitute an inertial reference frame?

Accepted Answer

An inertial reference frame is a frame of reference in which Newton's first law of motion holds true. According to this law, an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. In choice A, the weather balloon is descending at a constant velocity, which means it is moving in a straight line with a constant speed. Since there are no external forces acting on the balloon, it can be considered an inertial reference frame. The other choices involve either non-uniform motion (rocket undergoing uniform acceleration and roller coaster traveling around a corkscrew turn at constant speed) or non-zero net forces acting on the objects (orbiting space station and rotating merry-go-round), making them non-inertial reference frames.

Question 20

Which one of the following statements is a consequence of Special Relativity?

Accepted Answer

The answer of Which one of the following statements is...

Quiz 28: Special Relativity

Which one of the following statements concerning the proper length of a meter stick is true?

At time t = 2.3 s, a 4-kg block that initially moves with a constant speed of 6 m/s undergoes an inelastic collision with another block. Any two inertial observers must agree that

Leah is moving in a spaceship at a constant velocity away from a group of stars. Which one of the following statements indicates a method by which she can determine her absolute velocity through space?

In a science fiction novel, a starship takes three days to travel between two distant space stations according to its own clocks. Instruments on one of the space stations indicate that the trip took four days. How fast did the starship travel, relative to the space station?

Complete the following statement: To measure the proper length of an object moving relative to the surface of the earth, one must note the coordinates of points on the front and back ends

Which one of the following is a consequence of the postulates of special relativity?

A spaceship traveling at 0.7370c relative to the Earth monitors a motorcycle drag race on Earth. The space travelers measure the time from the start to the finish of the race to be 15.25 s. What is the proper time interval for the motorcycle race?

Which one of the following statements concerning time dilation is true?

During a baseball game, a batter hits a ball directly back to the pitcher who catches it. An observer flying over the stadium at a speed of 0.75c, measures 0.658 s as the time between the two events (hitting and catching the ball) . What is the proper time interval between the two events?

Which one of the following statements concerning the proper time interval between two events is true?

Mars rotates about its axis once every 88 642 s. A spacecraft comes into the solar system and heads directly toward Mars at a speed of 0.800c. What is the rotational period of Mars according to the beings on the spaceship?

A meter stick is observed to be only 0.850 meters long to an inertial observer. At what speed, relative to the observer, must the meter stick be moving?

Complete the following statement: The Michelson-Morley experiment

The proper mean lifetime of a muon is 2.2 × 10^-⁶ s. A beam of muons is moving with speed 0.6c relative to an inertial observer. Approximately how far will a muon in the beam travel, on average, before it decays?

In the year 2100, an astronaut wears an antique, but accurate, "quartz" wristwatch on a journey at a speed of 2.0 × 10⁸ m/s. According to mission control in Houston, the trip lasts 14 hours. How long was the trip as measured on the watch?

Two helium-filled balloons are released simultaneously at points A and B on the x axis in an earth-based reference frame. Which one of the following statements is true for an observer moving in the +x direction?

An alien spacecraft flies directly over a football stadium at a speed of 0.50c. If the proper length of the field is 100 yards, what field length is measured by the crew of the alien spacecraft?

Which one of the following systems would constitute an inertial reference frame?

Which one of the following statements is a consequence of Special Relativity?

Quiz 28: Special Relativity

Which one of the following statements concerning the proper length of a meter stick is true?

At time t = 2.3 s, a 4-kg block that initially moves with a constant speed of 6 m/s undergoes an inelastic collision with another block. Any two inertial observers must agree that

Leah is moving in a spaceship at a constant velocity away from a group of stars. Which one of the following statements indicates a method by which she can determine her absolute velocity through space?

In a science fiction novel, a starship takes three days to travel between two distant space stations according to its own clocks. Instruments on one of the space stations indicate that the trip took four days. How fast did the starship travel, relative to the space station?

Complete the following statement: To measure the proper length of an object moving relative to the surface of the earth, one must note the coordinates of points on the front and back ends

Which one of the following is a consequence of the postulates of special relativity?

A spaceship traveling at 0.7370c relative to the Earth monitors a motorcycle drag race on Earth. The space travelers measure the time from the start to the finish of the race to be 15.25 s. What is the proper time interval for the motorcycle race?

Which one of the following statements concerning time dilation is true?

During a baseball game, a batter hits a ball directly back to the pitcher who catches it. An observer flying over the stadium at a speed of 0.75c, measures 0.658 s as the time between the two events (hitting and catching the ball) . What is the proper time interval between the two events?

Which one of the following statements concerning the proper time interval between two events is true?

Mars rotates about its axis once every 88 642 s. A spacecraft comes into the solar system and heads directly toward Mars at a speed of 0.800c. What is the rotational period of Mars according to the beings on the spaceship?

A meter stick is observed to be only 0.850 meters long to an inertial observer. At what speed, relative to the observer, must the meter stick be moving?

Complete the following statement: The Michelson-Morley experiment

The proper mean lifetime of a muon is 2.2 × 10-6 s. A beam of muons is moving with speed 0.6c relative to an inertial observer. Approximately how far will a muon in the beam travel, on average, before it decays?

In the year 2100, an astronaut wears an antique, but accurate, "quartz" wristwatch on a journey at a speed of 2.0 × 108 m/s. According to mission control in Houston, the trip lasts 14 hours. How long was the trip as measured on the watch?

Two helium-filled balloons are released simultaneously at points A and B on the x axis in an earth-based reference frame. Which one of the following statements is true for an observer moving in the +x direction?

An alien spacecraft flies directly over a football stadium at a speed of 0.50c. If the proper length of the field is 100 yards, what field length is measured by the crew of the alien spacecraft?

Which one of the following systems would constitute an inertial reference frame?

Which one of the following statements is a consequence of Special Relativity?

The proper mean lifetime of a muon is 2.2 × 10^-⁶ s. A beam of muons is moving with speed 0.6c relative to an inertial observer. Approximately how far will a muon in the beam travel, on average, before it decays?

In the year 2100, an astronaut wears an antique, but accurate, "quartz" wristwatch on a journey at a speed of 2.0 × 10⁸ m/s. According to mission control in Houston, the trip lasts 14 hours. How long was the trip as measured on the watch?