Checkpoint 4 assesses L11, L12, L13, L15, L14 in the published syllabus sequence.
Assessment is drawn only from this lesson’s repaired effective pool.
Assessment is drawn only from this lesson’s repaired effective pool.
Assessment is drawn only from this lesson’s repaired effective pool.
Assessment is drawn only from this lesson’s repaired effective pool.
Assessment is drawn only from this lesson’s repaired effective pool.
This checkpoint assesses L11, L12, L13, L15, L14 only. Lesson file IDs remain stable; displayed lesson numbers follow the module’s syllabus sequence.
1. An inertial reference frame is one that...
2. Galilean relativity states that the laws of mechanics are the same in all...
3. The Michelson-Morley experiment aimed to detect...
4. Time dilation means that a clock moving relative to an observer...
5. Proper time is defined as the time interval measured by a clock...
6. The time dilation formula is...
7. Length contraction affects the measured length of a moving object in the direction...
8. Proper length is defined as the length measured by an observer...
9. The length contraction formula is...
10. The relativity of simultaneity means that...
11. Two lightning strikes at the ends of a train are simultaneous in the embankment frame. The train moves in the +x direction, and the front strike has the larger x-coordinate. According to the Lorentz time transformation, the train-frame coordinate time assigns:
12. The spacetime interval is significant because it is...
13. Einstein's mass-energy equivalence is expressed by...
14. The rest energy of an object is...
15. The total relativistic energy of a moving object is...
SA1. State Einstein’s two postulates and describe what the Michelson-Morley null result established. (4 marks)
SA2. Define proper time and proper length, then state the time-dilation and length-contraction equations. (4 marks)
SA3. A spacecraft travels at $0.80c$. Calculate $\gamma$. If its proper length is 100 m and a shipboard process lasts 6.0 s, find the Earth-frame length and duration. (4 marks)
SA4. Resolve the twin paradox without treating acceleration as an ageing force. (4 marks)
SA5. Distinguish rest, total and kinetic energy and state the energy-momentum relation using invariant mass. (4 marks)
The laws of physics have the same form in all inertial frames, and every inertial observer measures the same vacuum light speed $c$. Michelson and Morley found no fringe shift consistent with the expected stationary-aether wind within experimental sensitivity. The null result undermined that aether model but did not alone prove the later postulates.
Proper time $\Delta t_0$ is measured by one clock present at both events; $\Delta t=\gamma\Delta t_0$. Proper length $L_0$ is measured in the object’s rest frame; an observer who sees the object moving parallel to its length measures $L=L_0/\gamma$. Endpoint positions must be recorded simultaneously in the measuring frame.
$\gamma=1/\sqrt{1-0.80^2}=1.667$. Earth measures $L=100/1.667=60$ m and $\Delta t=1.667(6.0)=10$ s. The frame and direction conditions must be stated.
The twins reunite after following different spacetime paths, and their clocks record different proper times along those paths. The traveller’s turnaround and frame change make the complete situations asymmetric; acceleration identifies the change of path and simultaneity convention but is not an extra ageing force or the sole mechanism.
$E_0=mc^2$ is rest energy, $E=\gamma mc^2$ is total energy, and $K=E-E_0=(\gamma-1)mc^2$. The relation is $E^2=(pc)^2+(mc^2)^2$. Here $m$ is invariant mass; energy and momentum increase with speed, not the mass.