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Farmer Brown carries a Ladder (rest length 5 m) into a Barn (rest length 4 m) The relative speed of the Ladder and the Barn is 0.8c
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Cow’s frame: A (smart) cow is standing next to the Barn. Cow measures the Barn to be 4 m. Cow measures Ladder (which is length contracted) to be 3 m.
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Farmer Brown’s frame: Farmer Brown is holding the Back of the Ladder. Farmer Brown measures the Ladder to be 5 m. Farmer Brown measures Barn (which is length contracted) to be 2.4 m.
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Puzzler: Does the Ladder fit in the Barn? According to Cow, Ladder is 3 m and Barn is 4 m (can fit) According to Farmer, Ladder is 5 m and Barn is 2.4 m (can’t fit) Question: Who is correct? The Farmer? The Cow? Neither the Farmer nor the Cow? Both the Farmer and the Cow? Consider the following events -- A: Front of Ladder passes Entrance to Barn B: Front of Ladder passes Exit to Barn C: Back of Ladder passes Entrance to Barn D: Back of Ladder passes Exit to Barn
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A: Front of Ladder passes Entrance to Barn B: Front of Ladder passes Exit to Barn C: Back of Ladder passes Entrance to Barn D: Back of Ladder passes Exit to Barn Cow’s Frame A C B D
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x (m) 1 23 (10 lt-ns) 5 6 (20 lt-ns) t (ns) 10 ns 20 ns 4 Entrance to Barn Exit to Barn Front of Ladder Back of Ladder A A: Front of Ladder passes Entrance to Barn B B: Front of Ladder passes Exit to Barn C C: Back of Ladder passes Entrance to Barn D D: Back of Ladder passes Exit to Barn v = 0.8c INVERSE SLOPE of world-line A C B D Cow’s Frame
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A: Front of Ladder passes Entrance to Barn B: Front of Ladder passes Exit to Barn C: Back of Ladder passes Entrance to Barn D: Back of Ladder passes Exit to Barn Farmer’s Frame A B C D
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x (m) 1 23 (10 lt-ns) 5 6 (20 lt-ns) t (ns) 10 ns 20 ns 4 Back of Ladder Front of Lader Entrance to Barn Exit to Barn A A: Front of Ladder passes Entrance to Barn B B: Front of Ladder passes Exit to Barn C C: Back of Ladder passes Entrance to Barn D D: Back of Ladder passes Exit to Barn Farmer’s Frame
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