Question 1

I am stationary in a reference system but if my reference system is not an inertial reference system, then, relative to me, a system that is an inertial reference system must:
A) be accelerating.
B) move with constant velocity.
C) remain at rest.
D) be none of these choices.

Accepted Answer

If you are stationary in a non-inertial reference system, it means your reference system is accelerating. Therefore, an inertial reference system must appear to be accelerating relative to you.

Question 2

At what speed would a clock have to be moving in order to run at a rate that is one-third the rate of a clock at rest?
A) 0.97c
B) 0.75c
C) 0.87c
D) 0.94c

Accepted Answer

D

Question 3

From a stationary position, I observe a moving boxcar, which has a mirror along the front wall, but it is open at the back of the boxcar. I send a flash of light from my flashlight and time the flash of light as it goes to the front of the boxcar and returns to the back of the boxcar. A passenger in the boxcar also times the round trip of the flash of light. Previously I had measured the time required for the round trip of a flash of light when the boxcar was stationary, and I call this the stationary time. Which two times are the same?
A) the time recorded on the passenger's watch and the previous stationary time
B) the time recorded on my watch and the time recorded on the passenger's watch
C) the time recorded on my watch and the previous stationary time
D) None of the times are the same.

Accepted Answer

The time recorded on the passenger's watch and the previous stationary time are the same due to the principle of relativity, which states that the laws of physics are the same in all inertial frames. The passenger in the moving boxcar is in an inertial frame where the boxcar is stationary, so they measure the same time as when the boxcar was previously stationary.

Question 4

A ground observer measures the period of a pendulum moving as a part of an inertial frame of reference to be 2.30 s as the inertial frame moves by at a velocity of 0.800c. What would the observed period be of the same pendulum if its inertial frame were at rest with respect to the observer?
A) 3.03 s
B) 1.38 s
C) 1.84 s
D) 4.25 s

Accepted Answer

According to time dilation, the time interval between two events in a moving frame of reference is longer than that in a rest frame of reference. The observed period in the ground observer's frame will be longer than the actual period in the pendulum's rest frame. Using the time dilation equation:

Δt' = Δt/γ

where Δt is the time interval in the rest frame, Δt' is the time interval in the moving frame, and γ is the Lorentz factor:

γ = 1/√(1 - v^2/c^2)

where v is the velocity of the moving frame and c is the speed of light.

In this problem, Δt' = 2.30 s and v = 0.800c. Solving for γ:

γ = 1/√(1 - (0.800c)^2/c^2) = 1.67

Substituting into the time dilation equation:

Δt = Δt'/γ = 2.30 s/1.67 = 1.38 s

Therefore, the observed period of the pendulum in the rest frame of reference is 1.38 s, which corresponds to choice B.

Question 5

According to the special theory of relativity, if a 35 year old astronaut sent on a space mission is accelerated to speeds close to that of light, and then returns to Earth after 20 years as measured on earth, what would be his biological age upon returning?
A) less than 55 years
B) more than 55 years
C) exactly 110 years
D) 55 years

Accepted Answer

According to the special theory of relativity, time dilation occurs at speeds close to the speed of light, meaning the astronaut would age more slowly compared to those on Earth. Therefore, his biological age would be less than 55 years upon returning.

Question 6

A boxcar without a front or a back is moving toward the right. Two electrons move through the boxcar, one moving from back to front toward the right, the other moving from front to back toward the left. According to me, each electron is moving with a speed of 0.8c, and the boxcar is moving with a speed of 0.6c. A passenger in the boxcar records how long it takes each electron to pass from one end of the boxcar to the other end. According to the passenger, which took less time?
A) the electron going from front to back
B) the electron going from back to front
C) Since nothing can go faster than light, an electron cannot move toward the left with a speed of 0.8c through a boxcar moving toward the right with a speed of 0.6c.
D) They both took the same time.

Accepted Answer

The answer of A boxcar without a front or a...

Question 7

The astronaut whose heart rate on Earth is 60 beats/min increases his velocity to v = 0.60c. Now what is his heart rate as measured by an Earth observer?
A) 100 beats/min
B) 75 beats/min
C) 36 beats/min
D) 48 beats/min

Accepted Answer

The answer of The astronaut whose heart rate on Earth...

Question 8

A boxcar without a front or a back is moving toward the right. Two flashes of light move through the boxcar, one moving from back to front toward the right, the other moving from front to back toward the left. A passenger in the boxcar records how long it takes each flash of light to pass from one end of the boxcar to the other end. According to the passenger, which took longer?
A) the flash going from back to front
B) the flash going from front to back
C) They both took the same time.
D) It depends on whether the passenger is sitting at the front or the back of the boxcar.

Accepted Answer

Both flashes of light took the same time to pass from one end of the boxcar to the other end. This is because the speed of light is constant and does not depend on the motion of the boxcar. Additionally, the fact that the boxcar has no front or back does not affect the time it takes for light to travel through it.

Question 9

A tuning fork has a frequency of 400 Hz and hence a period of 2.50 *10 ^- ³s. If the tuning fork is in an inertial frame of reference moving by the observer at speed of 0.680c, what is the frequency of the fork as measured by the observer? (Assume that measurements are strictly by optical means and that the speed of sound waves in air is not pertinent here.) A) 454 Hz B) 293 Hz C) 605 Hz D) 265 Hz

Accepted Answer

The answer of A tuning fork has a frequency of...

Question 10

An astronaut at rest has a heart rate of 65 beats/min. What will her heart rate be as measured by an earth observer when the astronaut's spaceship goes by the earth at a speed of 0.80c?
A) 108 beats/min
B) 39 beats/min
C) 81 beats/min
D) 52 beats/min

Accepted Answer

According to time dilation, time moves slower for an object in motion relative to a stationary observer. Therefore, the observer on Earth would measure the astronaut's heart rate to be slower than 65 beats/min. Using the time dilation formula, we can calculate the new heart rate:

f' = f / sqrt(1 - v^2/c^2)

where f is the original heart rate, v is the velocity of the spaceship, and c is the speed of light. Plugging in the values, we get:

f' = 65 / sqrt(1 - 0.8^2) = 39 beats/min.

Therefore, the answer is B.

Question 11

According to a postulate of Einstein, which of the following describes the nature of the laws of physics as one observes processes taking place in various inertial frames of reference?
A) Laws are the same only in inertial frames moving at near speed of light.
B) Laws are the same in all inertial frames.
C) Laws are the same only in inertial frames with zero velocity.
D) Laws are the same only in inertial frames moving at low velocities.

Accepted Answer

According to Einstein's principle of relativity, the laws of physics are the same in all inertial frames of reference, regardless of their relative motion.

Question 12

The relativistic effect of time dilation has been verified by which of the following?
A) twin experiments
B) red shift in distant galaxies
C) muon experiments
D) the discovery of black holes

Accepted Answer

Muon experiments have verified time dilation by showing that muons, which have a short lifespan, can reach the Earth's surface due to time dilation effects at high speeds.

Question 13

The speed of light is equal to: A) one light-year per year. B) 5.28 * 10⁷ miles per hour. C) one meter per nanosecond. D) none of the above.

Accepted Answer

The speed of light is defined as one light-year per year because a light-year is the distance light travels in one year.

Question 14

A muon formed high in the Earth's atmosphere travels at a speed 0.990c for a distance of 6.40 km before it decays. What is the muon's lifetime as measured in its reference frame? A) 4.65 *10 ^- ⁶ s B) 1.55*10 ^- ⁵ s C) 2.18 *10 ^- ⁶ s D) 3.04 *10 ^- ⁶ s

Accepted Answer

The answer of A muon formed high in the Earth's...

Question 15

According to the special theory of relativity, which of the following happens to the size of the time interval between two events occurring in an inertial frame of reference as the frame's velocity with respect to the observer increases?
A) interval decreases
B) interval vanishes to zero when velocity equals half speed of light
C) interval increases
D) interval remains constant

Accepted Answer

According to the special theory of relativity, time dilation occurs, meaning the time interval between two events increases as the relative velocity of the inertial frame with respect to the observer increases.

Question 16

The period of an oscillating weight on a spring in an inertial frame of reference is 0.80 s. What would be its speed if it were to move by an observer who measures its period as 1.2 s? (c = 3.00 * 10⁸ m/s) A) 2.5 * l0⁸ m/s B) 1.1* l0⁸m/s C) 2.9 * 10⁸ m/s D) 2.2 *10⁸ m/s

Accepted Answer

The time dilation formula is used here: T' = T / sqrt(1 - v^2/c^2). Solving for v when T' = 1.2 s and T = 0.8 s gives v ≈ 2.2 x 10^8 m/s.

Question 17

Einstein's theory of relativity is based in part on which one of the following postulates?
A) Speed of light in a vacuum is same for all observers regardless of source velocity.
B) Energy is conserved only in elastic collisions.
C) Space and time are absolutes.
D) Mass and energy are equivalent.

Accepted Answer

Einstein's theory of relativity includes the postulate that the speed of light in a vacuum is constant and the same for all observers, regardless of the motion of the light source or observer.

Question 18

A mass is bouncing on the end of a spring with a period T when measured by a ground observer. What would the period of oscillation be (as measured by the same observer) if the mass and spring were moving past the ground observer at a speed of 0.600c?
A) 0.440 T
B) 1.25 T
C) 0.600 T
D) 1.67 T

Accepted Answer

The period of oscillation as measured by the ground observer when the mass and spring are moving at a speed of 0.600c would be affected by time dilation, a consequence of Einstein's theory of relativity. The formula for time dilation is $T' = T / \sqrt{1 - v^2/c^2}$, where $T'$ is the dilated time period, $T$ is the original time period, $v$ is the velocity of the moving object, and $c$ is the speed of light. Plugging in $v = 0.600c$, we get $T' = T / \sqrt{1 - (0.600)^2} = T / \sqrt{1 - 0.36} = T / \sqrt{0.64} = T / 0.8 = 1.25T$. This shows that the period of oscillation increases due to the relativistic effect of time dilation.

Question 19

From a stationary position, I observe a moving boxcar, which has a mirror along the front wall, but it is open at the back of the boxcar. I send a flash of light from my flashlight and time the flash of light as it goes to the front of the boxcar and returns to the back of the boxcar. A passenger in the boxcar also times the round trip of the flash of light. Compare the times recorded on our watches.
A) The time recorded on the two watches is the same.
B) The time recorded on his watch is shorter.
C) The time recorded on his watch is longer.
D) The answer depends on the reference system you are in.

Accepted Answer

The time recorded on the passenger's watch is shorter due to time dilation, as the boxcar is moving relative to the stationary observer.

Question 20

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 0.80c with respect to the inertial frame of reference?
A) 1.6 s
B) 1.2 s
C) 2.5 s
D) 3.3 s

Accepted Answer

The answer of The period of a pendulum is 2.0...

Quiz 27: Relativity

I am stationary in a reference system but if my reference system is not an inertial reference system, then, relative to me, a system that is an inertial reference system must:

At what speed would a clock have to be moving in order to run at a rate that is one-third the rate of a clock at rest?

A ground observer measures the period of a pendulum moving as a part of an inertial frame of reference to be 2.30 s as the inertial frame moves by at a velocity of 0.800c. What would the observed period be of the same pendulum if its inertial frame were at rest with respect to the observer?

According to the special theory of relativity, if a 35 year old astronaut sent on a space mission is accelerated to speeds close to that of light, and then returns to Earth after 20 years as measured on earth, what would be his biological age upon returning?

The astronaut whose heart rate on Earth is 60 beats/min increases his velocity to v = 0.60c. Now what is his heart rate as measured by an Earth observer?

An astronaut at rest has a heart rate of 65 beats/min. What will her heart rate be as measured by an earth observer when the astronaut's spaceship goes by the earth at a speed of 0.80c?

According to a postulate of Einstein, which of the following describes the nature of the laws of physics as one observes processes taking place in various inertial frames of reference?

The relativistic effect of time dilation has been verified by which of the following?

The speed of light is equal to:

A muon formed high in the Earth's atmosphere travels at a speed 0.990c for a distance of 6.40 km before it decays. What is the muon's lifetime as measured in its reference frame?

According to the special theory of relativity, which of the following happens to the size of the time interval between two events occurring in an inertial frame of reference as the frame's velocity with respect to the observer increases?

The period of an oscillating weight on a spring in an inertial frame of reference is 0.80 s. What would be its speed if it were to move by an observer who measures its period as 1.2 s? (c = 3.00 * 108 m/s)

Einstein's theory of relativity is based in part on which one of the following postulates?

A mass is bouncing on the end of a spring with a period T when measured by a ground observer. What would the period of oscillation be (as measured by the same observer) if the mass and spring were moving past the ground observer at a speed of 0.600c?

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 0.80c with respect to the inertial frame of reference?

The period of an oscillating weight on a spring in an inertial frame of reference is 0.80 s. What would be its speed if it were to move by an observer who measures its period as 1.2 s? (c = 3.00 * 10⁸ m/s)