# Th3 Solution - 36th International Physics Olympiad...

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36 th International Physics Olympiad. Salamanca (España) 2005 Th 3 Solution Page 1 of 3 R.S.E.F. Th3 QUANTUM EFFECTS OF GRAVITY SOLUTION 1. The only neutrons that will survive absorption at A are those that cannot cross H . Their turning points will be below H . So that, for a neutron entering to the cavity at height z with vertical velocity v z , conservation of energy implies H g M z g M v M z + 2 2 1 ( ) ( ) z H g z v z H g z 2 ) ( 2 2. The cavity should be long enough to ensure the absorption of all neutrons with velocities outside the allowed range. Therefore, neutrons have to reach its maximum height at least once within the cavity. The longest required length corresponds to neutrons that enter at z = H with v z = 0 (see the figure). Calling t f to their time of fall = = 2 2 1 2 f f x c t g H t v L g H v L x c 2 2 = cm 4 . 6 = c L 3. The rate of transmitted neutrons entering at a given height z , per unit height, is proportional to the range of allowed velocities at that height, ρ

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