Option A.2 – Lorentz transformations
Formative Assessment
NAME: _________________________________ TEAM:__
THIS IS A PRACTICE ASSESSMENT. Show formulas, substitutions, answers (in spaces provided) and units!
1. According to the Lorentz-FitzGerald contraction, what would be the length of a rocket ship which
was traveling at 0.866c in the direction of its length, if its rest length were 65.2 m?
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2. What are Einstein’s two postulates of special relativity?
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3. Two trains traveling at a speed of 0.75c approach each other on the same track. At the same instant,
both trains turn on their headlights. How fast do the two beams of light approach one another? Use
Einstein’s postulates, not the Galilean transformations.
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4. During the time dilation derivation, we have to make a choice. The choice is that either time is
absolute, or the speed of light is absolute. What do each of these mean? Which one did we choose?
Why did we choose it? _______________________________________________________________
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5. Define proper time interval. __________________________________________________________
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Suppose S0 has relative speed of v = 0.982c with respect to S.
6. Find the value of .
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7. If Dobson measures the time to cook a 1.5-minute egg in S0, how long does Nosbod measure the
same event in S?
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8. Suppose the Lorentz factor for a spaceship observed from Earth is  = 8.25.
What is the speed of the ship relative to the earth observer, in terms of c?
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9. Dobson is in the spaceship of 8. The spaceship’s length, as measured by Dobson (who is on board
the ship), is 125 m. What is the length of the spaceship in the Earth reference frame of Nosbod?
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A muon - is created during the collision of a cosmic ray with a molecule in the upper atmosphere 2.700
km above a detector in a laboratory. Muons decay in 2.197 s according to the reaction -   + e- + e.
10. Draw a Feynman diagram of this reaction.
11. If this muon is traveling toward the ground at 0.9750c relative to the laboratory, what is its lifetime
in the laboratories frame of reference? How far can the muon thus travel before decay?
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12. In the muon’s frame of reference: how fast is the laboratory approaching it? How far can the muon
travel before decay? What is the distance the lab is from the muon?
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13. John is in the center of a train car that is moving to the north. Barbara is standing on the side of the
tracks watching John’s car roll by. At the precise instant John is opposite Barbara lights are turned
on at the north and south ends of the car. John sees the lights simultaneously. Explain why Barbara
does not. Which light does she see first? ________________________________________________
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Clocks in two IRFs S and S’ are synchronized so that x = x’ = 0.00 m at t = t’ = 0.00 s. Frame S’ has a speed
of v = 0.667c relative to S. Two events occur in frame S. Event 1: x1 = 20.0 m, t1 = 0.150 s. Event 2: x2 =
40.0 m, t2 = 0.350 s.
14. Find the distance between the events in IRF S.
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15. Find the time interval between the events in IRF S.
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16. Find the distance between the events in IRF S’.
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17. Find the time interval between the events in IRF S’.
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18. The relative velocity between S’ and S is 0.866c. A satellite is
launched from S’ with a speed of 0.750c relative to S’. Find the
speed of the satellite relative to S.
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19. The relative velocity between S’ and S is 0.250c. A satellite is
launched from S’ with a speed of 0.500c relative to S. Find the
speed of the satellite relative to S’.
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IRF S’ has a speed of v = 0.667c relative to IRF S. An event occurs in frame S having spacetime coordinates
x = 20.0 m, t = 0.150 s.
20. Find the values of x’ and t’ for this same event.
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21. Show that the spacetime interval is invariant for this scenario.