Q9 · 2025 · Paper 2Complex unfamiliar5 marks
QUESTION 9 (5 marks)
Describe the ladder in the barn paradox in special relativity. In your response, explain how it is resolved by frames of reference.
WORKED SOLUTION
5 marksQCAA guide · typeset solution
ANSWER
See worked solution below.
Worked solution
The ladder in the barn paradox describes a scenario where a ladder that is too long to fit in a barn at rest approaches that barn at relativistic speeds.
From the ladder’s frame of reference, the barn’s length will contract, meaning it will not fit within the barn with both doors shut.
From the barn’s frame of reference, the ladder’s length will contract, so it will easily fit in the barn.
The paradox is resolved using simultaneity. Since part of the ladder is moving towards and then away from the barn, in the ladder’s frame of reference, the doors do not open and close simultaneously. The barn’s frame of reference is the same as the doors’ frame of reference, so the ladder will fit.
describes the general scenario
identifies from ladder’s frame of reference that length of barn will contract, so ladder will not fit in barn
identifies from barn’s frame of reference that length of ladder will contract, so ladder will easily fit in barn
recognises that the paradox is resolved using simultaneity
explains that what is viewed as simultaneous in one frame of reference is not necessarily viewed as simultaneous in another frame of reference
One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
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