A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Inertial Frames and Special Relativity Postulates — mark scheme explained
The short answer
The concept of an inertial frame of reference is fundamental to understanding Einstein's theory of special relativity. An inertial frame of reference is a coordinate system in which Newton's first law (the law of inertia) holds true.
The question
A spaceship is traveling at a speed of 0.8c relative to an observer on Earth. According to the observer on Earth, how much slower does a clock on the spaceship run compared to a clock on Earth? [Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Identify the relevant formula for time dilation: t' = t / √(1 - v 2 /c 2 )
- S2
Substitute the given values into the formula: t' = t / √(1 - (0.8c) 2 /c 2 )
- S3
Simplify the expression inside the square root: t' = t / √(1 - 0.64) = t / √0.36 = t / 0.6
- S4
Calculate the time dilation factor: t' = t / 0.6 ≈ 1.67t
- S5
The clock on the spaceship runs slower by a factor of 1.67 compared to the clock on Earth.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Identify the relevant formula for time dilation: t' = t / √(1 - v 2 /c 2 )
- S2
Substitute the given values into the formula: t' = t / √(1 - (0.8c) 2 /c 2 )
- S3
Simplify the expression inside the square root: t' = t / √(1 - 0.64) = t / √0.36 = t / 0.6
- S4
Calculate the time dilation factor: t' = t / 0.6 ≈ 1.67t
- S5
The clock on the spaceship runs slower by a factor of 1.67 compared to the clock on Earth.
Final answer: The clock on the spaceship runs slower by a factor of 1.67.
Common mistakes
- Confusing inertial frames with non-inertial frames — Emphasize that an inertial frame is one where objects at rest stay at rest and objects in motion move with constant velocity unless acted upon by a force. Non-inertial frames, such as a rotating or accelerating frame, do not satisfy this condition.
- Misinterpreting the first postulate of special relativity — Clarify that the first postulate means the equations and principles of physics look the same in all inertial frames, not that the outcomes of experiments will necessarily be identical.
- Forgetting the invariance of the speed of light — Reinforce that the speed of light is always c (approximately 3 × 10 8 m/s) in all inertial frames, regardless of the relative motion of the source or observer.
- Confusing time dilation with length contraction — Explain that time dilation causes moving clocks to run slower, and length contraction causes objects in motion to appear shorter in the direction of motion. Use specific examples to illustrate each effect.
- Incorrectly applying the Lorentz factor — Practice using the Lorentz factor in various contexts, such as time dilation and length contraction. Ensure students understand that γ is always greater than or equal to 1 and increases with velocity.
- Failing to account for relativity of simultaneity — Explain the concept of relativity of simultaneity and provide examples where events that are simultaneous in one frame are not simultaneous in another. Use spacetime diagrams to visualize this effect.
Where the marks go
- Full worked solution (all marking points)4 marks