H3 Time Dilation, Length Contraction

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Questions on time dilation and length contraction. After a few definitions, then an ongoing question in many parts.

• 1.

• 2.

• 3.

A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth.  It travels at 90% of the speed of light.  What is the value to 2dp of the Lorentz factor (gamma)

• A.

1.2

• B.

2.3

• C.

3.4

• D.

4.5

B. 2.3
Explanation
The Lorentz factor (gamma) is a term used in special relativity to describe the time dilation and length contraction experienced by objects moving at relativistic speeds. It is given by the equation gamma = 1/sqrt(1 - (v^2/c^2)), where v is the velocity of the object and c is the speed of light. In this question, the spaceship is traveling at 90% of the speed of light. Plugging this value into the equation, we find that gamma is approximately 2.3 when rounded to 2 decimal places.

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• 4.

A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth.  It travels at 90% of the speed of light.  How long will this journey take according to the observer on the earth?

• A.

1111s

• B.

2222s

• C.

3333s

• D.

4444s

B. 2222s
Explanation
The journey from Earth to planet X is a distance of 6E11m. The space ship is traveling at 90% of the speed of light. According to the theory of relativity, time dilation occurs when an object is moving at high speeds. This means that time appears to pass more slowly for the moving object compared to a stationary observer. Therefore, the journey will take longer according to the observer on Earth. To calculate the time it takes for the journey, we can use the formula t = d/v, where t is the time, d is the distance, and v is the velocity. Plugging in the values, we get t = (6E11m) / (0.9c), where c is the speed of light. Solving this equation gives us a time of approximately 2222 seconds.

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• 5.

A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth.  It travels at 90% of the speed of light.  Who measures proper time for the journey?

• A.

Observer on the earth

• B.

Pilot of space ship

• C.

Another independent observer

• D.

The cosmic time keeper

B. Pilot of space ship
Explanation
must be the pilot of the space ship since the start and the finish of the journey to him occur at the same place (where he is)

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• 6.

A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth.  It travels at 90% of the speed of light. Calculate the time taken for the voyage according to the pilot of the space ship.

• A.

1111s

• B.

966s

• C.

822s

• D.

733s

• E.

544s

B. 966s
Explanation
since space ship measures proper time,
time = gamma x proper time
proper time = time/gamma
=2222.22/2.3

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• 7.

A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth.  It travels at 90% of the speed of light. Who measures the proper length of the journey from Earth to Planet X?

• A.

Pilot on space ship

• B.

Observer on the Earth

• C.

Independent observer

• D.

Great Galactic time measurer

B. Observer on the Earth
Explanation
The observer on Earth measures the proper length of the journey from Earth to Planet X. Since the observer on Earth is stationary and not moving at relativistic speeds, they can accurately measure the distance between Earth and Planet X. On the other hand, the pilot on the spaceship is moving at a high velocity and time dilation effects come into play, causing the length of the journey to appear shorter for the pilot. An independent observer or a Great Galactic time measurer may not have the necessary frame of reference to accurately measure the distance.

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• 8.

A space 100m long space ship travels to planet X which is a distanace of 6E11m from Earth.  It travels at 90% of the speed of light. Calculate the distnace from Earth to Planet X according to the travelling spaceship?

• A.

6E11m

• B.

3.31E11m

• C.

2.61E11m

• D.

1.42E11m

• E.

1.21E11m

C. 2.61E11m
Explanation
Since proper length is measured by observer on Earth,
Length = properlength/gamma
Length = 6E11/2.3

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• 9.

Are there any parts of this where you had difficulties, and you need to go over in class?

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• Mar 21, 2023
Quiz Edited by
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• Mar 02, 2013
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