2017年泛珠三角与中华名校物理奥林匹克邀请赛试题与答案test1_solution.pdf

Pan Pearl River Delta Physics Olympiad 2017 2017 年泛珠三角及中华名校物理奥林匹克邀请赛 Sponsored by Institute for Advanced Study, HKUST 香港科技大学高等研究院赞助 Simplified Chinese Part-1 (Total 7 Problems, 45 Points) 简体版卷-1 （共7题，45分） (9:00 am – 12:00 pm, 3 February, 2017) 1. No-Shadow Day (5 points) 立竿无影 （5 分） (a) In the figure, ABCD is a rectangle lying on an inclined plane making an angle  with the horizontal plane. ABEF is the projection of the rectangle on the horizontal plane. If the measure of the angle DAC is , derive an expression for the angle . [1] 如图所示，矩形 ABCD 位于斜面上，斜面与水平面夹角为。ABEF 为该矩形于水平 面的投影。设角DAC 为，试推导角的表达式。[1] D C  F E   A B Let h = AC. Then CE = ℎ sin . BC = AD = ℎ cos . CE = BC sin = ℎ cos sin . Equating the expressions of CE, ℎ sin = ℎ cos sin  = arcsin(cos sin ). (b) The ecliptic is the plane on which the Earth revolves around the Sun. The axis of rotation of the Earth is inclined at an angle of 23.4o with the normal to the ecliptic. The day of the Summer Solstice (in the Northern Hemisphere) is 21 June. The latitude of Hong Kong is o 22.25 , and the no-shadow days are those days on which the Sun does not cast a shadow of a vertical pole at noon in Hong Kong. Using the result of (a) or otherwise, derive the angular displacement of the Earth’s revolution between the Summer Solstice and the no-shadow days in Hong Kong. Give your answer to 3 significant figures. [2]