Q266 · Practice questionComplex unfamiliar5 marks
QUESTION 266 (5 marks)
A ladder has proper length and a barn has proper length . The ladder moves right at relative to the barn. In the barn frame, both doors close briefly and simultaneously while the whole ladder is inside. They reopen before the ladder reaches either door. No collision occurs.
a)[2 marks]
Calculate the ladder length in the barn frame and the barn length in the ladder frame.
b)[3 marks]
Explain why the two descriptions are consistent. In the ladder frame, identify which door-closing event occurs first.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
(a) and , respectively. (b) The door closings are not simultaneous in the ladder frame. The front/right door closes first and the rear/left door closes later; neither frame requires a collision.
Worked solution
(a) . The barn measures ; the ladder measures the moving barn as .
(b) The barn-frame statement refers to a simultaneous pair of door events in that frame. Simultaneity at separated locations is frame dependent. In the ladder frame the front-door closing occurs before the rear-door closing, so the long ladder need not fit inside the contracted barn between two simultaneously closed doors. The specified reopening prevents contact in either frame.
Equivalent physically justified methods, alternative valid sketches and consistent units accepted.
Accept sensible significant figures and consistent rounding from stated constants.
Part a: Calculate the ladder length in the barn frame.
Part a: Calculate the barn length in the ladder frame.
Part b: Identify relativity of simultaneity as the resolution.
Part b: Give front/right closing before rear/left closing in the ladder frame.
Part b: Explain why no simultaneously enclosed ladder or collision is required in that frame.
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