Special Relativity Flashcards: Reference Frames, Time, and Length

הכרטיסים בחפיסה הזו

1. כרטיס 1

   שאלה

   What two kinds of coordinates identify an event in an inertial frame?

   תשובה

   A position and a time. A camera shutter closing is one event, and the frame gives the coordinates of that closure.

2. כרטיס 2

   שאלה

   An instrument is bolted to a pod that coasts past a lab. Which is the instrument’s rest frame?

   תשובה

   The pod frame. The instrument stays at a fixed position in that frame.

3. כרטיס 3

   שאלה

   A pod recedes from a lamp in vacuum. What speed does the pod measure for light from the lamp?

   תשובה

   $c$, the same speed the lab measures for the light.

4. כרטיס 4

   שאלה

   A beacon flashes and its light reaches a distant camera. Which event does the camera’s detection timestamp give directly?

   תשובה

   The light’s arrival at the camera. The flash is a separate event at the beacon.

5. כרטיס 5

   שאלה

   Two events occur beside the same clock at rest in a frame. What interval does that clock record between them?

   תשובה

   The proper time, $\Delta\tau$, between the two events.

6. כרטיס 6

   שאלה

   In one inertial frame, how can two separated events be timed locally and compared?

   תשובה

   Place a clock at each event location. Keep both clocks at rest and synchronized in the chosen frame, then subtract the event readings.

7. כרטיס 7

   שאלה

   In which frame is the proper length of a rigid calibration bar measured?

   תשובה

   The bar’s rest frame, where both ends stay at fixed positions.

8. כרטיס 8

   שאלה

   A probe coasts in a straight line at constant speed relative to an inertial lab. Is the frame attached to the coasting probe inertial?

   תשובה

   Yes. Constant velocity relative to an inertial frame gives another inertial frame.

9. כרטיס 9

   שאלה

   A detector at rest midway between two stationary lamps receives their vacuum flashes together. When were the flashes emitted in the lamps’ frame?

   תשובה

   At the same time. The paths to the detector have equal length and light travels at the same speed along both.

10. כרטיס 10

    שאלה

    How do you calculate the Lorentz factor $\gamma$ from the relative speed $v$?

    תשובה

    $\gamma=1/\sqrt{1-(v/c)^2}$, where $c$ is the speed of light in vacuum.

11. כרטיס 11

    שאלה

    A rod moves along the lab’s track. Which two lab events give the rod’s length in that frame?

    תשובה

    Record the front and rear endpoint positions at the same lab time. Their separation at that time is the lab length.

12. כרטיס 12

    שאלה

    Two events happen at different lab stations but both happen beside the same clock on a coasting probe. Which clock gives the proper time?

    תשובה

    The probe clock. The events occur at its one fixed probe location.

13. כרטיס 13

    שאלה

    A detector at rest in a lab receives a flash at lab time $6\,\mu\mathrm{s}$. The light traveled for $2\,\mu\mathrm{s}$ in the lab frame. When was the flash emitted in that frame?

    תשובה

    At $4\,\mu\mathrm{s}$. Subtract travel time from arrival time in the same frame.

14. כרטיס 14

    שאלה

    What is the Lorentz factor at relative speed $0.60c$?

    תשובה

    $1.25$. The square root in the denominator is $\sqrt{1-0.60^2}=0.80$.

15. כרטיס 15

    שאלה

    A lab timed two flashes when they were emitted. Which events should a passing pod use to compare the time interval in its own frame?

    תשובה

    The same two emissions. The arrival of either flash at a detector is a separate event.

16. כרטיס 16

    שאלה

    A moving rod’s front position is recorded first and its rear position one lab second later. Does the difference between the recorded positions give the lab length?

    תשובה

    No. Use endpoint positions at one lab time. The rear has moved during that second.

17. כרטיס 17

    שאלה

    A clock coasts past an inertial lab and records proper time $\Delta\tau$ between two ticks. What interval $\Delta t$ does the lab assign to those same ticks?

    תשובה

    $\Delta t=\gamma\Delta\tau$. The lab uses synchronized clocks to time the ticks at different positions.

18. כרטיס 18

    שאלה

    Two flashes at different positions along a test range are simultaneous in the range frame. A pod coasts along the line joining them. Are the emissions simultaneous in the pod frame?

    תשובה

    No, for a nonzero relative speed along that line. The two frames assign different time differences to the same emissions.

19. כרטיס 19

    שאלה

    If the relative velocity reverses direction without changing speed, what happens to the Lorentz factor?

    תשובה

    It stays the same. The factor depends on $(v/c)^2$.

20. כרטיס 20

    שאלה

    A bar coasts past an inertial lab with its length perpendicular to its velocity. How does the length measured in the lab compare with the bar’s rest length?

    תשובה

    They are equal. The lab records both ends at the same lab time, and their separation is entirely transverse to the motion.

21. כרטיס 21

    שאלה

    A pod coasting at $0.80c$ relative to the lab records $9\,\mathrm{s}$ between two ticks of its own clock. How much lab time separates those ticks?

    תשובה

    $15\,\mathrm{s}$. The lab interval is $(5/3)\times9\,\mathrm{s}$.

22. כרטיס 22

    שאלה

    How do you find the measured length $L$ of an object moving along its length at constant speed, given its proper length $L_0$?

    תשובה

    $L=L_0/\gamma$. Measure both ends at one time in the frame where the object moves.

23. כרטיס 23

    שאלה

    Two lamps and a detector are at rest in the same frame. Their flashes travel directly through vacuum to the detector and arrive together. If one lamp is farther away, which lamp emitted first in that frame?

    תשובה

    The farther lamp. Both flashes traveled at the same speed, so the longer path took more time.

24. כרטיס 24

    שאלה

    A boom’s endpoints are measured at the same lab time while it moves lengthwise. Does the boom frame assign the same time to those two measurements?

    תשובה

    No. Simultaneity is frame-dependent for these two events because they occur at different points along the direction of relative motion.

25. כרטיס 25

    שאלה

    Two ticks of a clock coasting at $0.60c$ relative to the lab are $15\,\mathrm{s}$ apart in lab time. How much time elapsed on the moving clock?

    תשובה

    $12\,\mathrm{s}$. Its proper time is $15\,\mathrm{s}/1.25$.

26. כרטיס 26

    שאלה

    A $75\,\mathrm{m}$ bar in its rest frame moves lengthwise at $0.80c$ in the lab. What length does the lab measure?

    תשובה

    $45\,\mathrm{m}$. Divide $75\,\mathrm{m}$ by $5/3$.

27. כרטיס 27

    שאלה

    Two inertial crews coast past one another and each uses clocks synchronized in its own frame. How can each assign a slower rate to the other crew’s clock?

    תשובה

    They compare different pairs of ticks. Each times two ticks of the other crew’s clock with separated clocks synchronized in its own frame.

28. כרטיס 28

    שאלה

    The nose of a coasting probe passes two checkpoints at rest in an inertial lab. Which frame gives the proper time between those crossings?

    תשובה

    The probe frame. Both crossings happen at its nose, where one clock on the probe can time them.

29. כרטיס 29

    שאלה

    Two light pulses reach the same detector at the same instant. Do all inertial frames agree that the pulses arrive together?

    תשובה

    Yes. They arrive at one place and time, so their arrivals coincide in a single event. Each frame still assigns its own coordinates to that event.

30. כרטיס 30

    שאלה

    A bar moves lengthwise at $0.60c$ relative to the lab, which measures its length as $52\,\mathrm{m}$. What is the bar’s proper length?

    תשובה

    $65\,\mathrm{m}$. Multiply the lab length by $1.25$.

30 כרטיסים

Special Relativity Flashcards: Reference Frames, Time, and Length

ללמוד את החפיסה הזו בחינם

Nibomo תיפתח כדי שתוכל להתחיל ללמוד.