第10届泛珠三角及中华名校物理奥林匹克邀请赛答案详解.pdf

2014 年泛珠三角及中华名校物理奥林匹克邀请赛 Pan Pearl River Delta Physics Olumpiad 2014 Part-1 (Total 6 Problems) 卷-1 （共6 题） 1. Sunset Twice a Day (6 points) 一天两观日落 （6 分） Presently the tallest tower in the world is Burj Khalifa in Dubai. Its height is 828 m. An Internet news article reported that one can watch sunset twice in one day with this tower. 杜拜的哈利法塔是现时世界上最高的建筑，高度为 828 米。互联网上有新闻文章报导，可以利用 这塔在一天内两次观看到日落。 (a) What is the time range of sunset between the bottom and the top of the tower? Give your answer in minutes. Parameters: Earth’s radius = 6400 km. Distance between Sun and Earth = 1.5  1011 m. (3 points) 试求塔底和塔顶之间日落时间的范围。答案请以分钟为单位。参数：地球半径 = 6400 公里。 太阳和地球之间的距离 = 1.5  1011 米。 （3 分） Sun R + h R Neglecting the tilt of Earth’s axis and the latitude of Dubai, the angular displacement of Earth between the two sunsets at the bottom and top of the tower 假设地球转轴的倾角和杜拜的纬度可略，则在塔底和塔顶两次日落之间地球的角位移为 2 2 R ( h )R   sin [1] R h  2 2Rh h 2 (2h )(828)  1    3 0. 0161radian [1] R R R 6400 10  Time between the two sunsets 两次日落之间的时间 0. 0161   ) min(24)( 3.760min [1]    2  (b) Burj Khalifa also has the world’s third fastest elevator (lift) with a speed of v = 10 m/s. Immediately be