2021年2020版物理新增分大一轮江苏专用版讲义：第四章曲线运动万有引力与航天本章学科素养提升含解析.pdf

例 1如图 1 所示，在半径为R 的铅球中挖出一个球形空穴，空穴直径为R 且与铅球相切，并通过铅球的球心 在未挖出空穴前铅球质量为M.求挖出空穴后的铅球与距铅球球心距离为d、质量为m 的小球(可视为质点)间的万有引力大小(引力常量为G)图 1 思路分析由于题目中没有告知距离d 与球的半径R 之间的关系，因此不能把挖出球形空穴后的铅球看成质点，故不能直接利用万有引力定律公式来计算引力的大小但是，可以用填补法求解，即先把挖去的部分“补”上，使其成为半径为R 的完整球体，再根据万有引力定律公式，分别计算出半径为R 的球体和补上的球体对小球的万有引力，最后两引力相减即可得到答案解析设挖出空穴前铅球与小球间的万有引力为F1，挖出的球形实体(由球体的体积公式易知质量为M8，这里不再具体计算)与小球间的万有引力为F2，铅球剩余部分与小球间的万有引力为F，则有 F1 FF2根据万有引力定律可得F1GMmd2，F2GMm8 dR22故挖出空穴后的铅球与小球间的万有引力为FF1F2GMmd2GMm8 dR22GMm 7d28dR2R22d22dR2.答案GMm 7d28dR2R22d22dR2点评运用“填补法”解题的关键是紧扣万有引力定律的适用条件，先填补，后运算运用“填补法”解题的过程主要体现了等效的思想类平抛运动的处理|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页，共 4 页(1)受力特点物体所受合力为恒力，且与初速度的方向垂直(2)运动特点在初速度v0方向做匀速直线运动，在合外力方向做初速度为零的匀加速直线运动，加速度aF合m.(3)求解方法常规分解法：将类平抛运动分解为沿初速度方向的匀速直线运动和垂直于初速度方向(即沿合力方向)的匀加速直线运动，两分运动彼此独立，互不影响，且与合运动具有等时性特殊分解法：对于有些问题，可以过抛出点建立适当的直角坐标系，将加速度分解为ax、ay，初速度 v0分解为 vx、vy，然后分别在x、y 方向列方程求解(4)考查特点类平抛运动是对平抛运动研究方法的迁移，是高考命题的热点问题高考考查该类问题常综合机械能守恒、动能定理等知识，以电场或复合场为背景考查学生运用所学知识处理综合问题的能力例 2如图 2 所示的光滑斜面长为l，宽为 b，倾角为，一物块(可看成质点)沿斜面左上方顶点P水平射入，恰好从底端Q 点离开斜面，试求：(重力加速度为g)图 2(1)物块由 P 运动到 Q 所用的时间t；(2)物块由 P 点水平射入时的初速度v0的大小；(3)物块离开Q 点时速度的大小v.解析(1)沿斜面向下由牛顿第二定律有mgsin ma，由平抛运动规律知l12at2联立解得t2lgsin.(2)沿水平方向有bv0t，v0btbgsin 2l(3)物块离开Q 点时的速度大小vv02 at2b24l2gsin 2l.答案(1)2lgsin(2)bgsin 2l(3)b24l2gsin 2l|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页，共 4 页文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 ZH7I6U1M10Y2文档编码:CX6T8H6P9J7 HJ6A5H8R5K3 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