Physics: Higher Level
Special relativity — HL Theme A
- 1.
State the two postulates of Einstein's special theory of relativity.
[2 marks] · no calculator - 2.
Marking analysis: A learner attempts the following task: “State the two postulates of Einstein's special theory of relativity.” Their response addresses only this point: “States that the laws of physics are the same in all inertial (non-accelerating) reference frames.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator - 3.
Define proper time, and state which observer measures the proper time interval between two events.
[2 marks] · no calculator - 4.
Marking analysis: A learner attempts the following task: “Define proper time, and state which observer measures the proper time interval between two events.” Their response addresses only this point: “Defines proper time as the time interval between two events measured by an observer for whom both events occur at the same location.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator - 5.
A spacecraft clock measures a proper time interval of 10.0 s. The spacecraft moves at 0.80c relative to an observer on Earth. Calculate the time interval measured by the Earth observer, using the Lorentz factor γ = 1/√(1 − v²/c²).
[4 marks] - 6.
Marking analysis: A learner attempts the following task: “A spacecraft clock measures a proper time interval of 10.0 s. The spacecraft moves at 0.80c relative to an observer on Earth. Calculate the time interval measured by the Earth observer, using the Lorentz factor γ = 1/√(1 − v²/c²).” Their response addresses only this point: “Calculates the Lorentz factor: γ = 1/√(1 − 0.80²) = 1/√(0.36) = 1/0.6.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] - 7.
Define proper length, and state what happens to the measured length of a moving object, as observed from a frame in which the object is moving.
[2 marks] · no calculator - 8.
Marking analysis: A learner attempts the following task: “Define proper length, and state what happens to the measured length of a moving object, as observed from a frame in which the object is moving.” Their response addresses only this point: “Defines proper length as the length of an object measured in the reference frame in which the object is at rest.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator - 9.
A spacecraft has a proper length of 120 m and travels at 0.60c relative to an observer on Earth. Calculate the length of the spacecraft as measured by the Earth observer.
[4 marks] - 10.
Marking analysis: A learner attempts the following task: “A spacecraft has a proper length of 120 m and travels at 0.60c relative to an observer on Earth. Calculate the length of the spacecraft as measured by the Earth observer.” Their response addresses only this point: “Calculates the Lorentz factor: γ = 1/√(1 − 0.60²) = 1/√(0.64) = 1/0.8 = 1.25.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] - 11.
Explain why no object with mass can be accelerated to reach or exceed the speed of light, using the relativistic mass-energy relationship.
[3 marks] · no calculator - 12.
Marking analysis: A learner attempts the following task: “Explain why no object with mass can be accelerated to reach or exceed the speed of light, using the relativistic mass-energy relationship.” Their response addresses only this point: “States that as an object's speed approaches c, the energy required to accelerate it further increases without bound.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator - 13.
State Einstein's mass-energy equivalence relation, and calculate the energy equivalent of 1.0 g of mass. Use c = 3.00 × 10⁸ m s⁻¹.
[3 marks] - 14.
Marking analysis: A learner attempts the following task: “State Einstein's mass-energy equivalence relation, and calculate the energy equivalent of 1.0 g of mass. Use c = 3.00 × 10⁸ m s⁻¹.” Their response addresses only this point: “States E = mc².” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] - 15.
Two events occur simultaneously in the reference frame of observer A, but at different locations. Explain, using relativity of simultaneity, why observer B, moving relative to A, may not measure the two events as simultaneous.
[3 marks] · no calculator - 16.
Marking analysis: A learner attempts the following task: “Two events occur simultaneously in the reference frame of observer A, but at different locations. Explain, using relativity of simultaneity, why observer B, moving relative to A, may not measure the two events as simultaneous.” Their response addresses only this point: “States that simultaneity (whether two events occur at the same time) is not absolute in special relativity — it depends on the observer's reference frame.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator - 17.
A muon is created in the upper atmosphere and has a proper lifetime of 2.2 μs. Explain, using time dilation, how muons travelling close to the speed of light can be detected at the Earth's surface despite this short lifetime.
[2 marks] · no calculator - 18.
Marking analysis: A learner attempts the following task: “A muon is created in the upper atmosphere and has a proper lifetime of 2.2 μs. Explain, using time dilation, how muons travelling close to the speed of light can be detected at the Earth's surface despite this short lifetime.” Their response addresses only this point: “States that from the Earth observer's frame, the muon's lifetime is time-dilated (appears longer) because the muon is moving at a speed close to c.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator - 19.
Outline why, at everyday (non-relativistic) speeds, the effects of time dilation and length contraction are completely unnoticeable.
[2 marks] · no calculator - 20.
Marking analysis: A learner attempts the following task: “Outline why, at everyday (non-relativistic) speeds, the effects of time dilation and length contraction are completely unnoticeable.” Their response addresses only this point: “States that for everyday speeds, v is extremely small compared to c, so v²/c² is extremely close to zero.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator - 21.
A particle of mass 2.0 × 10⁻²⁷ kg moves at a speed of 0.90c. Calculate its relativistic momentum, given that the Lorentz factor at this speed is γ = 2.29. Use c = 3.00 × 10⁸ m s⁻¹.
[4 marks] - 22.
Marking analysis: A learner attempts the following task: “A particle of mass 2.0 × 10⁻²⁷ kg moves at a speed of 0.90c. Calculate its relativistic momentum, given that the Lorentz factor at this speed is γ = 2.29. Use c = 3.00 × 10⁸ m s⁻¹.” Their response addresses only this point: “Uses relativistic momentum p = γmv.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] - 23.
A spacecraft moving at 0.50c relative to Earth fires a probe forward at a speed of 0.60c relative to the spacecraft. Using the relativistic velocity addition formula u = (v + u′)/(1 + vu′/c²), calculate the probe's speed relative to Earth, and explain why this is less than the value 1.10c predicted by simple (Galilean) addition.
[4 marks] - 24.
Marking analysis: A learner attempts the following task: “A spacecraft moving at 0.50c relative to Earth fires a probe forward at a speed of 0.60c relative to the spacecraft. Using the relativistic velocity addition formula u = (v + u′)/(1 + vu′/c²), calculate the probe's speed relative to Earth, and explain why this is less than the value 1.10c predicted by simple (Galilean) addition.” Their response addresses only this point: “Substitutes v = 0.50c and u′ = 0.60c into u = (v + u′)/(1 + vu′/c²), giving u = (0.50c + 0.60c)/(1 + 0.50 × 0.60).” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] - 25.
In the 'twin paradox', one twin travels on a high-speed round trip to a distant star while the other twin remains on Earth. Explain why, upon reunion, the travelling twin is found to have aged less than the twin who stayed on Earth, and state why this is not a true paradox despite each twin seeing the other's clock as running slow during the trip.
[4 marks] · no calculator - 26.
Marking analysis: A learner attempts the following task: “In the 'twin paradox', one twin travels on a high-speed round trip to a distant star while the other twin remains on Earth. Explain why, upon reunion, the travelling twin is found to have aged less than the twin who stayed on Earth, and state why this is not a true paradox despite each twin seeing the other's clock as running slow during the trip.” Their response addresses only this point: “States that, from Earth's frame, the travelling twin's clock runs slow (is time-dilated) throughout the journey due to their high speed.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] · no calculator - 27.
A particle has rest mass 1.67 × 10⁻²⁷ kg and moves with a Lorentz factor γ = 1.50. Calculate its total relativistic energy and its relativistic kinetic energy. Use c = 3.00 × 10⁸ m s⁻¹.
[5 marks] - 28.
Marking analysis: A learner attempts the following task: “A particle has rest mass 1.67 × 10⁻²⁷ kg and moves with a Lorentz factor γ = 1.50. Calculate its total relativistic energy and its relativistic kinetic energy. Use c = 3.00 × 10⁸ m s⁻¹.” Their response addresses only this point: “Calculates the rest energy: E₀ = mc² = 1.67 × 10⁻²⁷ × (3.00 × 10⁸)² ≈ 1.50 × 10⁻¹⁰ J.” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[5 marks] - 29.
A distant galaxy is moving away from Earth at a significant fraction of the speed of light. State and explain, using the relativistic Doppler effect, what happens to the observed wavelength of light received from this galaxy.
[3 marks] · no calculator - 30.
Marking analysis: A learner attempts the following task: “A distant galaxy is moving away from Earth at a significant fraction of the speed of light. State and explain, using the relativistic Doppler effect, what happens to the observed wavelength of light received from this galaxy.” Their response addresses only this point: “States that the observed wavelength is increased (redshifted) compared to the wavelength emitted by the source.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator