(a) What is the speed of the light signal as measured by the observer (i) at rest in the rocket and (ii) at rest on Earth if a rocket 642 m long is traveling parallel to Earth's surface at 0.5c from left to right, at time t = 0 a light flashes for an instant at the center of the rocket, detectors at opposite ends of the rocket record the arrival of the light signal, call event A the light striking the left detector and event B the light striking the right detector. Observers at rest in the rocket and on Earth record the events?

Question

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Answer 1

Question

Chapter 25, Problem 85QAP

To determine

(a)

What is the speed of the light signal as measured by the observer (i) at rest in the rocket and (ii) at rest on Earth if a rocket 642 m long is traveling parallel to Earth's surface at 0.5c from left to right, at time t = 0 a light flashes for an instant at the center of the rocket, detectors at opposite ends of the rocket record the arrival of the light signal, call event A the light striking the left detector and event B the light striking the right detector. Observers at rest in the rocket and on Earth record the events?

Expert Solution

Explanation of Solution

Calculation:

A rocket that is 642 m long is traveling parallel to Earth's surface at a speed V = 0.5c from left to right. At t = 0, a light flash for an instant at the center of the rocket. Detectors at opposite ends of the rocket detect when the light arrives-event A is when the light strikes the left side of the rocket, and event B is when the light strikes the right side of the rocket. The events are recorded by observers at rest in the rocket and observers at rest on Earth. Since the speed of light must be constant in all inertial reference frames, the speed of the light measured by both sets of observers must be the same and equal to c. In the observations made on the rocket, the light travels an equal distance to the detectors on the left and right ends of the ship. Events A and B will take place at a time equal to half of the length of the rocket divided by the speed of light. Both length contraction of the rocket and the relative motion of the rocket and the light need to be considered in the measurements made on Earth. The light for event A must travel half of the contracted length of the rocket minus the distance the rocket travels during that time. The light for event B must travel half of the contracted length of the rocket plus the distance the rocket travels during that time. We can also perform this calculation using time dilation-the proper time is the time measured on the rocket and the observed time interval is the time difference between events A and B as measured in Earth's frame.
The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

Conclusion:

The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

To determine

(b)

At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

Expert Solution

Explanation of Solution

Calculation:

Observer in the rocket
tA=tB=xc=3213×108=1.07×10−6s
Observer in the Earth
Event A:
ctA=xA=x1− v 2 c 2 −VtAtA=x 1− v 2 c 2 c+V=x 1− (0.5c) 2 c 2 c+0.5c=321 1− (0.5c) 2 c 2 c+0.5c=6.178×10−7s

Event B:
ctB=xB=x1− v 2 c 2 +VtBtB=x 1− v 2 c 2 c−V=x 1− (0.5c) 2 c 2 c−0.5c=321 1− (0.5c) 2 c 2 0.5c=1.853×10−6s

To determine

(c)

That the results in part (b) are consistent with time dilation?

Expert Solution

Explanation of Solution

Calculation:

Δt=Δt proper 1− v 2 c 2 1.853×10−6−6.178×10−7=1.07× 10 −6 1− (0.5c) 2 c 2 1.235×10−6s=1.235×10−6s

Conclusion:

This is consistent with time dilation.

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Answer 2

Question

Chapter 25, Problem 85QAP

To determine

(a)

What is the speed of the light signal as measured by the observer (i) at rest in the rocket and (ii) at rest on Earth if a rocket 642 m long is traveling parallel to Earth's surface at 0.5c from left to right, at time t = 0 a light flashes for an instant at the center of the rocket, detectors at opposite ends of the rocket record the arrival of the light signal, call event A the light striking the left detector and event B the light striking the right detector. Observers at rest in the rocket and on Earth record the events?

Expert Solution

Explanation of Solution

Calculation:

A rocket that is 642 m long is traveling parallel to Earth's surface at a speed V = 0.5c from left to right. At t = 0, a light flash for an instant at the center of the rocket. Detectors at opposite ends of the rocket detect when the light arrives-event A is when the light strikes the left side of the rocket, and event B is when the light strikes the right side of the rocket. The events are recorded by observers at rest in the rocket and observers at rest on Earth. Since the speed of light must be constant in all inertial reference frames, the speed of the light measured by both sets of observers must be the same and equal to c. In the observations made on the rocket, the light travels an equal distance to the detectors on the left and right ends of the ship. Events A and B will take place at a time equal to half of the length of the rocket divided by the speed of light. Both length contraction of the rocket and the relative motion of the rocket and the light need to be considered in the measurements made on Earth. The light for event A must travel half of the contracted length of the rocket minus the distance the rocket travels during that time. The light for event B must travel half of the contracted length of the rocket plus the distance the rocket travels during that time. We can also perform this calculation using time dilation-the proper time is the time measured on the rocket and the observed time interval is the time difference between events A and B as measured in Earth's frame.
The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

Conclusion:

The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

To determine

(b)

At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

Expert Solution

Explanation of Solution

Calculation:

Observer in the rocket
tA=tB=xc=3213×108=1.07×10−6s
Observer in the Earth
Event A:
ctA=xA=x1− v 2 c 2 −VtAtA=x 1− v 2 c 2 c+V=x 1− (0.5c) 2 c 2 c+0.5c=321 1− (0.5c) 2 c 2 c+0.5c=6.178×10−7s

Event B:
ctB=xB=x1− v 2 c 2 +VtBtB=x 1− v 2 c 2 c−V=x 1− (0.5c) 2 c 2 c−0.5c=321 1− (0.5c) 2 c 2 0.5c=1.853×10−6s

To determine

(c)

That the results in part (b) are consistent with time dilation?

Expert Solution

Explanation of Solution

Calculation:

Δt=Δt proper 1− v 2 c 2 1.853×10−6−6.178×10−7=1.07× 10 −6 1− (0.5c) 2 c 2 1.235×10−6s=1.235×10−6s

Conclusion:

This is consistent with time dilation.

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Answer 3

Question

Chapter 25, Problem 85QAP

To determine

(a)

What is the speed of the light signal as measured by the observer (i) at rest in the rocket and (ii) at rest on Earth if a rocket 642 m long is traveling parallel to Earth's surface at 0.5c from left to right, at time t = 0 a light flashes for an instant at the center of the rocket, detectors at opposite ends of the rocket record the arrival of the light signal, call event A the light striking the left detector and event B the light striking the right detector. Observers at rest in the rocket and on Earth record the events?

Expert Solution

Explanation of Solution

Calculation:

A rocket that is 642 m long is traveling parallel to Earth's surface at a speed V = 0.5c from left to right. At t = 0, a light flash for an instant at the center of the rocket. Detectors at opposite ends of the rocket detect when the light arrives-event A is when the light strikes the left side of the rocket, and event B is when the light strikes the right side of the rocket. The events are recorded by observers at rest in the rocket and observers at rest on Earth. Since the speed of light must be constant in all inertial reference frames, the speed of the light measured by both sets of observers must be the same and equal to c. In the observations made on the rocket, the light travels an equal distance to the detectors on the left and right ends of the ship. Events A and B will take place at a time equal to half of the length of the rocket divided by the speed of light. Both length contraction of the rocket and the relative motion of the rocket and the light need to be considered in the measurements made on Earth. The light for event A must travel half of the contracted length of the rocket minus the distance the rocket travels during that time. The light for event B must travel half of the contracted length of the rocket plus the distance the rocket travels during that time. We can also perform this calculation using time dilation-the proper time is the time measured on the rocket and the observed time interval is the time difference between events A and B as measured in Earth's frame.
The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

Conclusion:

The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

To determine

(b)

At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

Expert Solution

Explanation of Solution

Calculation:

Observer in the rocket
tA=tB=xc=3213×108=1.07×10−6s
Observer in the Earth
Event A:
ctA=xA=x1− v 2 c 2 −VtAtA=x 1− v 2 c 2 c+V=x 1− (0.5c) 2 c 2 c+0.5c=321 1− (0.5c) 2 c 2 c+0.5c=6.178×10−7s

Event B:
ctB=xB=x1− v 2 c 2 +VtBtB=x 1− v 2 c 2 c−V=x 1− (0.5c) 2 c 2 c−0.5c=321 1− (0.5c) 2 c 2 0.5c=1.853×10−6s

To determine

(c)

That the results in part (b) are consistent with time dilation?

Expert Solution

Explanation of Solution

Calculation:

Δt=Δt proper 1− v 2 c 2 1.853×10−6−6.178×10−7=1.07× 10 −6 1− (0.5c) 2 c 2 1.235×10−6s=1.235×10−6s

Conclusion:

This is consistent with time dilation.

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Answer 4

Question

Chapter 25, Problem 85QAP

To determine

(a)

What is the speed of the light signal as measured by the observer (i) at rest in the rocket and (ii) at rest on Earth if a rocket 642 m long is traveling parallel to Earth's surface at 0.5c from left to right, at time t = 0 a light flashes for an instant at the center of the rocket, detectors at opposite ends of the rocket record the arrival of the light signal, call event A the light striking the left detector and event B the light striking the right detector. Observers at rest in the rocket and on Earth record the events?

Expert Solution

Explanation of Solution

Calculation:

A rocket that is 642 m long is traveling parallel to Earth's surface at a speed V = 0.5c from left to right. At t = 0, a light flash for an instant at the center of the rocket. Detectors at opposite ends of the rocket detect when the light arrives-event A is when the light strikes the left side of the rocket, and event B is when the light strikes the right side of the rocket. The events are recorded by observers at rest in the rocket and observers at rest on Earth. Since the speed of light must be constant in all inertial reference frames, the speed of the light measured by both sets of observers must be the same and equal to c. In the observations made on the rocket, the light travels an equal distance to the detectors on the left and right ends of the ship. Events A and B will take place at a time equal to half of the length of the rocket divided by the speed of light. Both length contraction of the rocket and the relative motion of the rocket and the light need to be considered in the measurements made on Earth. The light for event A must travel half of the contracted length of the rocket minus the distance the rocket travels during that time. The light for event B must travel half of the contracted length of the rocket plus the distance the rocket travels during that time. We can also perform this calculation using time dilation-the proper time is the time measured on the rocket and the observed time interval is the time difference between events A and B as measured in Earth's frame.
The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

Conclusion:

The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

To determine

(b)

At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

Expert Solution

Explanation of Solution

Calculation:

Observer in the rocket
tA=tB=xc=3213×108=1.07×10−6s
Observer in the Earth
Event A:
ctA=xA=x1− v 2 c 2 −VtAtA=x 1− v 2 c 2 c+V=x 1− (0.5c) 2 c 2 c+0.5c=321 1− (0.5c) 2 c 2 c+0.5c=6.178×10−7s

Event B:
ctB=xB=x1− v 2 c 2 +VtBtB=x 1− v 2 c 2 c−V=x 1− (0.5c) 2 c 2 c−0.5c=321 1− (0.5c) 2 c 2 0.5c=1.853×10−6s

To determine

(c)

That the results in part (b) are consistent with time dilation?

Expert Solution

Explanation of Solution

Calculation:

Δt=Δt proper 1− v 2 c 2 1.853×10−6−6.178×10−7=1.07× 10 −6 1− (0.5c) 2 c 2 1.235×10−6s=1.235×10−6s

Conclusion:

This is consistent with time dilation.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 25, Problem 85QAP

To determine

(a)

What is the speed of the light signal as measured by the observer (i) at rest in the rocket and (ii) at rest on Earth if a rocket 642 m long is traveling parallel to Earth's surface at 0.5c from left to right, at time t = 0 a light flashes for an instant at the center of the rocket, detectors at opposite ends of the rocket record the arrival of the light signal, call event A the light striking the left detector and event B the light striking the right detector. Observers at rest in the rocket and on Earth record the events?

Expert Solution

Explanation of Solution

Calculation:

A rocket that is 642 m long is traveling parallel to Earth's surface at a speed V = 0.5c from left to right. At t = 0, a light flash for an instant at the center of the rocket. Detectors at opposite ends of the rocket detect when the light arrives-event A is when the light strikes the left side of the rocket, and event B is when the light strikes the right side of the rocket. The events are recorded by observers at rest in the rocket and observers at rest on Earth. Since the speed of light must be constant in all inertial reference frames, the speed of the light measured by both sets of observers must be the same and equal to c. In the observations made on the rocket, the light travels an equal distance to the detectors on the left and right ends of the ship. Events A and B will take place at a time equal to half of the length of the rocket divided by the speed of light. Both length contraction of the rocket and the relative motion of the rocket and the light need to be considered in the measurements made on Earth. The light for event A must travel half of the contracted length of the rocket minus the distance the rocket travels during that time. The light for event B must travel half of the contracted length of the rocket plus the distance the rocket travels during that time. We can also perform this calculation using time dilation-the proper time is the time measured on the rocket and the observed time interval is the time difference between events A and B as measured in Earth's frame.
The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

Conclusion:

The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

To determine

(b)

At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

Expert Solution

Explanation of Solution

Calculation:

Observer in the rocket
tA=tB=xc=3213×108=1.07×10−6s
Observer in the Earth
Event A:
ctA=xA=x1− v 2 c 2 −VtAtA=x 1− v 2 c 2 c+V=x 1− (0.5c) 2 c 2 c+0.5c=321 1− (0.5c) 2 c 2 c+0.5c=6.178×10−7s

Event B:
ctB=xB=x1− v 2 c 2 +VtBtB=x 1− v 2 c 2 c−V=x 1− (0.5c) 2 c 2 c−0.5c=321 1− (0.5c) 2 c 2 0.5c=1.853×10−6s

To determine

(c)

That the results in part (b) are consistent with time dilation?

Expert Solution

Explanation of Solution

Calculation:

Δt=Δt proper 1− v 2 c 2 1.853×10−6−6.178×10−7=1.07× 10 −6 1− (0.5c) 2 c 2 1.235×10−6s=1.235×10−6s

Conclusion:

This is consistent with time dilation.

Answer 6

Chapter 25, Problem 85QAP

To determine

(a)

What is the speed of the light signal as measured by the observer (i) at rest in the rocket and (ii) at rest on Earth if a rocket 642 m long is traveling parallel to Earth's surface at 0.5c from left to right, at time t = 0 a light flashes for an instant at the center of the rocket, detectors at opposite ends of the rocket record the arrival of the light signal, call event A the light striking the left detector and event B the light striking the right detector. Observers at rest in the rocket and on Earth record the events?

Expert Solution

Explanation of Solution

Calculation:

A rocket that is 642 m long is traveling parallel to Earth's surface at a speed V = 0.5c from left to right. At t = 0, a light flash for an instant at the center of the rocket. Detectors at opposite ends of the rocket detect when the light arrives-event A is when the light strikes the left side of the rocket, and event B is when the light strikes the right side of the rocket. The events are recorded by observers at rest in the rocket and observers at rest on Earth. Since the speed of light must be constant in all inertial reference frames, the speed of the light measured by both sets of observers must be the same and equal to c. In the observations made on the rocket, the light travels an equal distance to the detectors on the left and right ends of the ship. Events A and B will take place at a time equal to half of the length of the rocket divided by the speed of light. Both length contraction of the rocket and the relative motion of the rocket and the light need to be considered in the measurements made on Earth. The light for event A must travel half of the contracted length of the rocket minus the distance the rocket travels during that time. The light for event B must travel half of the contracted length of the rocket plus the distance the rocket travels during that time. We can also perform this calculation using time dilation-the proper time is the time measured on the rocket and the observed time interval is the time difference between events A and B as measured in Earth's frame.
The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

Conclusion:

The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

Answer 7

Chapter 25, Problem 85QAP

To determine

(a)

What is the speed of the light signal as measured by the observer (i) at rest in the rocket and (ii) at rest on Earth if a rocket 642 m long is traveling parallel to Earth's surface at 0.5c from left to right, at time t = 0 a light flashes for an instant at the center of the rocket, detectors at opposite ends of the rocket record the arrival of the light signal, call event A the light striking the left detector and event B the light striking the right detector. Observers at rest in the rocket and on Earth record the events?

Answer 8

Expert Solution

Explanation of Solution

Calculation:

A rocket that is 642 m long is traveling parallel to Earth's surface at a speed V = 0.5c from left to right. At t = 0, a light flash for an instant at the center of the rocket. Detectors at opposite ends of the rocket detect when the light arrives-event A is when the light strikes the left side of the rocket, and event B is when the light strikes the right side of the rocket. The events are recorded by observers at rest in the rocket and observers at rest on Earth. Since the speed of light must be constant in all inertial reference frames, the speed of the light measured by both sets of observers must be the same and equal to c. In the observations made on the rocket, the light travels an equal distance to the detectors on the left and right ends of the ship. Events A and B will take place at a time equal to half of the length of the rocket divided by the speed of light. Both length contraction of the rocket and the relative motion of the rocket and the light need to be considered in the measurements made on Earth. The light for event A must travel half of the contracted length of the rocket minus the distance the rocket travels during that time. The light for event B must travel half of the contracted length of the rocket plus the distance the rocket travels during that time. We can also perform this calculation using time dilation-the proper time is the time measured on the rocket and the observed time interval is the time difference between events A and B as measured in Earth's frame.
The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

Conclusion:

The speed of light is equal to c in all inertial reference frames, so it is the same for both the observer at rest in the rocket and the observer at rest on Earth.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

(b)

At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

Expert Solution

Explanation of Solution

Calculation:

Observer in the rocket
tA=tB=xc=3213×108=1.07×10−6s
Observer in the Earth
Event A:
ctA=xA=x1− v 2 c 2 −VtAtA=x 1− v 2 c 2 c+V=x 1− (0.5c) 2 c 2 c+0.5c=321 1− (0.5c) 2 c 2 c+0.5c=6.178×10−7s

Event B:
ctB=xB=x1− v 2 c 2 +VtBtB=x 1− v 2 c 2 c−V=x 1− (0.5c) 2 c 2 c−0.5c=321 1− (0.5c) 2 c 2 0.5c=1.853×10−6s

Answer 13

To determine

(b)

At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

Answer 14

Expert Solution

Explanation of Solution

Calculation:

Observer in the rocket
tA=tB=xc=3213×108=1.07×10−6s
Observer in the Earth
Event A:
ctA=xA=x1− v 2 c 2 −VtAtA=x 1− v 2 c 2 c+V=x 1− (0.5c) 2 c 2 c+0.5c=321 1− (0.5c) 2 c 2 c+0.5c=6.178×10−7s

Event B:
ctB=xB=x1− v 2 c 2 +VtBtB=x 1− v 2 c 2 c−V=x 1− (0.5c) 2 c 2 c−0.5c=321 1− (0.5c) 2 c 2 0.5c=1.853×10−6s

Answer 15

Expert Solution

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

To determine

(c)

That the results in part (b) are consistent with time dilation?

Expert Solution

Explanation of Solution

Calculation:

Δt=Δt proper 1− v 2 c 2 1.853×10−6−6.178×10−7=1.07× 10 −6 1− (0.5c) 2 c 2 1.235×10−6s=1.235×10−6s

Conclusion:

This is consistent with time dilation.

Answer 19

To determine

(c)

That the results in part (b) are consistent with time dilation?

Answer 20

Expert Solution

Explanation of Solution

Calculation:

Δt=Δt proper 1− v 2 c 2 1.853×10−6−6.178×10−7=1.07× 10 −6 1− (0.5c) 2 c 2 1.235×10−6s=1.235×10−6s

Conclusion:

This is consistent with time dilation.

Answer 21

Expert Solution

Answer 22

Expert Solution

Answer 23

Expert Solution

Answer 24

Ch. 25 - Prob. 1QAP Ch. 25 - Prob. 2QAP Ch. 25 - Prob. 3QAP Ch. 25 - Prob. 4QAP Ch. 25 - Prob. 5QAP Ch. 25 - Prob. 6QAP Ch. 25 - Prob. 7QAP Ch. 25 - Prob. 8QAP Ch. 25 - Prob. 9QAP Ch. 25 - Prob. 10QAP

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Explanation of Solution

(b)

At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

Explanation of Solution

(c)

That the results in part (b) are consistent with time dilation?

Explanation of Solution

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Chapter 25 Solutions

Videos

Explanation of Solution

(b) At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

Explanation of Solution

(c) That the results in part (b) are consistent with time dilation?

Explanation of Solution

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Chapter 25 Solutions

(b)

At what time after the flash do events A and B occur as measured by (r) the observer in the rocket and (it) the observer at rest on Earth? Which event occurs first in each case??

(c)

That the results in part (b) are consistent with time dilation?