SCSA Physics Science as a Human Endeavour
5 sample questions with marking guides and sample answers
A collection of mesons was observed by a detector to move an average distance of 11.0 m when travelling at 95% of the speed of light. However, based on their properties, the mesons were expected to travel an average distance of 3.4 m.
Explain the difference between the observed and expected average distances.
Reveal Answer
The relativistic speed of the mesons indicates they experience time dilation relative to the observed time over the distance travelled. This means the mesons appear to travel for a longer period of time and hence cover a larger distance.
| Descriptor | Marks |
|---|---|
Identifies that an object at relativistic speed experiences time dilation | 1 |
Explains the relationship between time travelled and observed distance | 1 |
The half-life of an unstable subatomic particle is measured by a stationary detector to be longer when its velocity approaches the speed of light. This is because the particle
is moving relative to its frame of reference.
is in the same frame of reference as the detector.
experiences time differently relative to the detector.
cannot be accurately observed at relativistic speeds.
Reveal Answer
is moving relative to its frame of reference.
An object is always at rest within its own frame of reference; it is impossible for a particle to move relative to itself.
is in the same frame of reference as the detector.
Since the particle is moving at a velocity approaching the speed of light relative to the detector, they are in different inertial frames of reference.
experiences time differently relative to the detector.
According to special relativity, time dilation causes time to pass more slowly for an object moving at relativistic speeds relative to a stationary observer, resulting in a longer observed half-life.
cannot be accurately observed at relativistic speeds.
The observed increase in half-life is a real physical phenomenon predicted by special relativity, not a result of measurement inaccuracy or observational limitations.
Muons are unstable particles produced when cosmic rays strike atoms high in the atmosphere. The muons travel downward, perpendicular to Earth's surface, at almost the speed of light.
Classical physics predicts that these muons will decay before they have time to reach Earth's surface.
Explain qualitatively why these muons can reach Earth's surface, regardless of whether their motion is considered from either the muon's frame of reference or the Earth's frame of reference.
Reveal Answer
In the muon's reference frame, the distance travelled is less than that observed by a stationery observer on Earth's surface, due the effects of length contraction. This shortened distance means that they will get further than would be expected by an observer observing the rest length.
From the Earth's frame of reference, the time dilation means that the half-life of the muon is dilated compared to the half-life measured in the rest frame of the muon. This greater time allows more muons to reach the ground than would otherwise be expected.
| Descriptor | Marks |
|---|---|
Explains why muons reach the Earth's surface with reference to relativistic effects in both frames of reference | 3 |
| 2 |
Provides some relevant information | 1 |
None of the above | 0 |
Analyse the consequences of the theory of special relativity in relation to length, time and motion. Support your answer with reference to experimental evidence.
Reveal Answer
The two postulates of special relativity are: the speed of light in a vacuum is an absolute constant, and all inertial frames of reference are equivalent.
The consequences of these postulates are time dilation, length contraction and relativistic momentum dilation. Time dilation means that the measured time between events increases as the speed of an observer increases. Length contraction means that the length of an object decreases as the speed of an observer increases, and relativistic momentum dilation means that objects (with mass) cannot travel at c as it takes increasing amounts of energy to accelerate objects as they approach the speed of light.
Length contraction and time dilation can both be seen in observations of muons at Earth's surface. The short half-life of muons suggests that there should be very few of them that arrive at Earth's surface from their point of origin high in Earth's atmosphere, but the muon flux is greater than suggested by half-life and distance travelled alone. However, when the distance travelled is considered from the muon's frame of reference, it is length-contracted according to , giving an effective shorter distance for them to travel. From the perspective of an observer on Earth's surface, the time taken for them to decay is dilated, giving an effective greater amount of time for them to travel before decaying.
The effects of relativistic momentum can be seen in particle accelerators in terms of the increasing amounts of energy to required to accelerate the particles as they approach the speed of light – it is though the objects are much more massive than they are.
| Descriptor | Marks |
|---|---|
| 8 |
| 7 |
The student response meets all criteria of the 5-mark band, and additionally meets the majority of criteria in the 7-mark band. | 6 |
| 5 |
The student response meets all criteria of the 3-mark band, and additionally meets the majority of criteria in the 5-mark band. | 4 |
Makes some reference to special relativity and/or related experimental evidence | 3 |
The student response meets all criteria of the 1-mark band, and additionally meets the majority of criteria in the 3-mark band. | 2 |
Provides some relevant information | 1 |
None of the above | 0 |
Special relativity accounts for the observation that more muons from cosmic rays are detected near Earth's surface than expected.
Explain this phenomenon by outlining why Newtonian physics cannot explain this scenario while special relativity can. Refer to the frames of reference of both the travelling muons and the observer near the Earth's surface.
Reveal Answer
Since muons are short-lived particles, they shouldn't reach the Earth's surface according to Newtonian physics.
But muons travel at close to the speed of light. As muons enter the atmosphere, an observer external to the particles' frame of reference will witness them existing longer than expected due to time dilation. Muons experience length contraction, so they can travel further than predicted by Newtonian physics.
| Descriptor | Marks |
|---|---|
identifies that muons have a very short half-life | 1 |
explains that muons are unlikely to reach Earth's surface using Newtonian physics | 1 |
identifies that muons travel at relativistic speeds | 1 |
explains that from the observer's frame of reference, the muon's half-life will be longer due to time dilation | 1 |
explains that from the muon's frame of reference, it experiences length contraction | 1 |