[size=150][b]一、什么是自由落体运动[br][br][/b][/size]当物体在只受重力作用时由静止开始下落的运动被称为自由落体运动。[br][br]自由落体要满足两个特征，[color=#980000]只受重力作用[/color]和[color=#980000]无初速释放[/color]。[br][br]我们周边总有空气，物体下落总会受到空气阻力，理想的自由落体运动只有在真空环境中才存在。[br][br]在现实生活中，静止下落时受空气阻力远小于重力的物体可以近似看成自由落体。[br][br]比如一棵苹果树上掉下的苹果和树叶，苹果可以看成自由落体，树叶则不行，因为相较于所受的重力，树叶本身受到的空气阻力和浮力更大，完全不可忽略。[br][br]跳伞运动员还没打开伞时可以近似看成自由落体，已经打开伞后则不行。[br]

[size=150][b]二、伽利略对自由落体运动的研究[br][br][/b][size=100]自由落体运动在物理学中占据的特殊地位很大程度源于[url=https://enjoyphysics.cn/Article3231]伽利略对它的研究[/url]。[br][br][/size][size=100]古希腊哲学家亚里士多德基于观察提出了这样一个观点：[color=#980000]物体从高空中下落的速度与重量成正比[/color]。比如苹果和树叶从同样的高度下落，苹果很快落地，树叶则慢慢悠悠地在空中飘荡。[/size][br][/size][br]伽利略用了一个思想实验来反驳亚里士多德的观点：[br]假设有一个大球，质量为[math]M[/math]，有一个小球，质量为[math]m[/math]。根据亚里士多德的观点，大球和小球从同一高度掉下，大球会先落地；[br][br]假设大球落地时速度为[math]v_M[/math]，小球落地时速度为[math]v_m[/math]。[br][br]现在将两个球绑在一起，自由释放。大球下落快，会被下落慢的小球拖着而减慢；小球下落慢，则会被下落快的大球拖着而加快。最后两者的速度应该介于两个球单独释放时的速度的中间，即[math]v_M[/math]>[math]v_{m+M}[/math]>[math]v_m[/math][br][br]但是我们根据亚里士多德的观点，两个球绑在一起更重了，应该会比大球单独下落时更快，速度[math]v_{m+M}[/math]>[math]v_M[/math]>[math]v_m[/math]。[br][br]这就出现了悖论，[color=#980000]说明不同重量的物体下落的速度应该一样快[/color]。[br][br][url=https://www.bilibili.com/video/BV1YW411t76q/?spm_id_from=333.337.search-card.all.click&vd_source=f9ac96b2701ce94e9b6ad668bd8d26f0]点击观看真空下落的视频[br][br][/url][img]data:image/png;base64,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[/img]

紧接着，伽利略猜想，物体下落的运动是一个速度随着时间均匀变大的运动，即匀变速直线运动，并设计实验进行了验证。[br][br]伽利略时代没有精确计时工具，更没有频闪照片，物体自由下落的时间太快了，来不及反应。于是伽利略将不同的铜球放在一个倾角很小的斜面上让球自由滚下，测量小球等时间间隔的位移。[br][img]https://s2.loli.net/2024/10/27/c27JHPLuVpriBDo.png[/img][br]我们现在已经知道了，如果物体做初速度为零的匀变速直线运动，它的位移和运动时间将成正比，即[math]x\propto t^2[/math]，其时间位移比会满足1：4：9：16……这样的平方比。[br][br]伽利略测得不同质量的小球沿同一斜面滚下的等时间位移是一样的，说明小球在斜面上的运动[color=#980000]与物体重量无关[/color]。[br][br]伽利略又增大斜面角度，再测了几组小球的运动，发现虽然单位时间内的位移不一样，但是等时间间隔位移比都满足一样的比例，说明小球从斜面静止滚下的运动无论倾角多少都是匀变速直线运动。[br][br]伽利略将这个结论合理外推，假设斜面倾斜角为90°，小球再从斜面滚下就是自由落体了，自由落体运动也应该是匀变速直线运动。[br][img]https://s2.loli.net/2024/10/27/32NSHLzMbqJ4u7W.png[/img][br]经过精彩的推理、实验、测量和分析后，伽利略得出了结论：[color=#980000][b]自由落体的物体做的是匀变速直线运动，且这个运动的加速度与物体本身的质量无关。[br][/b][/color][br]伽利略对自由落体的研究是物理学结合推理、实验和数学对自然现象进行研究的典范，为后世物理学的发展奠定了坚实的思想基础。

借助现代的测量手段，我们测出伽利略所说的物体做自由落体运动时与物体无关的那个加速度的值是[math]9.8m/s^2[/math][br][br]这个加速度和物体的质量无关，会受到物体所处的纬度、海拔的轻微影响。但只要在地球上，这个值就是几乎不变的，我们把这个值记为[math]g[/math]，称为[color=#980000]重力加速度[/color]。[br][br]不过在不同星球上重力加速度一般会不一样，比如月球上的重力加速度只有大约[math]1.62m/s^2[/math]，比地球上小得多。[br][br][color=#980000]（注：后续为了计算方便我们取[/color][math]g=10m/s^2[/math][color=#980000]）[/color]

[size=150][b]三、自由落体运动的基本规律[br][br][/b][/size]自由落体运动实际上是一种初速度为零，且加速度固定不变的特殊匀变速直线运动，它的运动规律仍满足一般的匀变速直线运动规律，但是更简单。[br][br]因为自由落体运动是竖直方向上的运动，我们用[math]h[/math]来代表位移，再将加速度[math]a[/math]换成[math]g[/math]，并让[math]v_0=0m/s[/math]。[br]

和普通的匀变速直线运动相比，自由落体运动因为已经知道了初速度[math]v_0[/math]和加速度[math]g[/math]，只有末速度[math]v[/math]、时间[math]t[/math]、位移[math]h[/math]三个变量，所以它具有知一求二的特点，即知道任意一个变量就能求出另外两个变量。[br][br]再具体点说，[math]v-h[/math]、[math]v-t[/math]、[math]h-t[/math]这三个关系都是一一对应的，我们可以做到知道一个就马上算出另外一个。

[color=#0000ff][b]例1[/b]：（多选）物体做自由落体运动，取[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/8517774547e328a278ad47c2da716aaa.svg[/img]，该物体（　　）[table][tr][td]A．在前2s内下落的距离为20m[/td][td]B．在前2s内平均速度为10m/s[/td][/tr][tr][td]C．第2s末的速度为30m/s[/td][td]D．第2s末的速度为40m/s[/td][/tr][/table][/color][br][color=#ff0000]解析：[br]前2s内的位移：[/color][math]h=\frac{1}{2}gt^2=\frac{1}{2}\times10\times2^2m=20m[/math][color=#ff0000][br]第2s末的速度：[/color][math]v=gt=10\times2m/s=20m/s[/math][color=#ff0000][br]前2s平均速度：[/color][math]\overline{v}=\frac{v}{2}=10m/s[/math][color=#ff0000][br]故选A、B。[br][br][br][/color][color=#0000ff][b]例2：[/b]（多选）一个做自由落体运动的物体，其落地速度为20m/s，重力加速度[i]g[/i]取10m/s[sup]2[/sup]，则下列描述正确的是（　　）[/color][color=#ff0000][br][/color][color=#0000ff]A．下落的时间为2s                  B．下落时距地面的高度为25m[br]C．下落过程中的平均速度为5m/s      D．在下落中点位置的速度为15m/s[/color][color=#ff0000][br][br]解析：[br][/color][color=#ff0000]下落时间[math]t=\frac{v}{g}=2s[/math][br][/color][color=#ff0000]下落高度[math]h=\frac{v^2}{2g}=20m[/math][br][/color][color=#ff0000]下落平均速度[math]\overline{v}=\frac{v}{2}=10m/s[/math][br]中间位置的速度[math]v_{\frac{x}{2}}=\frac{\sqrt{2}}{2}v=10\sqrt{2}m/s[/math][br][/color][color=#ff0000]故选A[br][br][br][/color][color=#0000ff][b]例3[/b]：（多选）甲、乙两物体分别从10m和20m高处同时自由落下，不计空气阻力，下面描述正确的是（　　）[/color][color=#ff0000][br][/color][color=#0000ff]A．落地时甲的速度是乙的[math]\frac{1}{2}[/math][br]B．落地的时间乙是甲的[math]\sqrt{2}[/math]倍[br]C．下落1s时甲的速度与乙的相同[br]D．乙的加速度是甲的2倍[br][br][/color][color=#ff0000]解析：[br][math]v_甲=\sqrt{2gh_甲}=10\sqrt{2}m/s[/math][br][/color][color=#ff0000][math]t_甲=\sqrt{\frac{2h_甲}{g}}=\sqrt{2}s[/math][br][math]v_乙=\sqrt{2gh_乙}=20m/s[/math][br][math]t_乙=\sqrt{\frac{2h_乙}{g}}=2s[/math][br]A错、B对。[br]对自由落体运动来说，无论物体轻重，加速度都是[math]g[/math]，D错误。[br]由[math]v=gt[/math]，两个物体下落时间相同，速度一定相同，C对[/color][br]

[color=#0000ff][b]例4[/b]：从离地面高[i][math]H[/math][/i]的空中自由落下一个小球，落地前瞬间小球的速度为[math]50m/s[/math]，取[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/799edf593e3ba2b2372a83d9782be3a2.svg[/img]，求小球落地前最后[math]1s[/math]内的位移的大小[/color][math]\Delta h[/math][color=#0000ff]。[br][br][/color][color=#ff0000]解析：[br]小球落地时间[math]t_2=\frac{v}{g}=5s[/math][br]小球下落的位移[math]H=\frac{1}{2}gt_2^2=125m[/math][br]小球在[math]t_1=4s[/math]内下落的位移[math]h=\frac{1}{2}gt_1^2=80m[/math][br]小球在最后[math]1s[/math]内的位移[math]Δh=H-h=45m[/math][/color]

[color=#0000ff][b]例5[/b]：（多选）如图所示，一栋三层楼房，每层楼高均为3m，且每层楼墙壁正中间有一个高为1m的窗户。现将一石块从楼顶边缘自由释放，不计空气阻力，以下说法正确的是（　　）[br][br][img width=58px,height=109px]https://img.xkw.com/dksih/QBM/editorImg/2024/10/30/0859f302-c4d1-4983-9ed2-13aba646a561.png[/img][br][br]A．石块依次到达三个窗户上边缘的速度大小之比为[/color][math]1∶2∶\sqrt{7}[/math][color=#0000ff][br]B．石块依次通过三个窗户的平均速度之比为[/color][math]（\sqrt{2}＋1）∶（\sqrt{5}＋2）∶（2+\sqrt{7}）[/math][color=#0000ff][br]C．石块依次到达三个窗户下边缘的时间之比为[/color][math]2∶5∶8[/math][color=#0000ff][br]D．石块依次通过三个窗户的时间之比为[/color][math]（\sqrt{2}－1）∶（\sqrt{5}－2）∶（2\sqrt{2}-\sqrt{7}）[/math][br][br][color=#ff0000]解析：[br]由题意可知，石块经过第一、第二、第三个窗户上边缘时的位移分别为1m、4m、7m，根据[/color][math]v=\sqrt{2gh}[/math][color=#ff0000]可得石块依次到达三个窗户上边缘的速度大小之比[/color][math]1:2:\sqrt{7}[/math][color=#ff0000]，A正确；[br]根据[/color][math]t=\sqrt{\frac{2h}{g}}[/math][color=#ff0000]可得,石块依次经过三个窗户上边缘的时间之比为[/color][math]t_1:t_2:t_3=\sqrt{1}:\sqrt{4}:\sqrt{7}[/math][color=#ff0000][br][br]石块到达三个窗户下边缘的位移分别为2m、5m、8m，根据[/color][math]t=\sqrt{\frac{2h}{g}}[/math][color=#ff0000]可得,石块依次到达三个窗户下边缘的时间之比为[/color][math]t_1':t_2':t_3'=\sqrt{2}:\sqrt{5}:\sqrt{8}[/math][color=#ff0000],C错误[br][br]石块依次通过三个窗户的时间之比为[/color][math]Δt_1:Δt_2:Δt_3=\sqrt{2}-\sqrt{1}:\sqrt{5}-\sqrt{4}:\sqrt{8}-\sqrt{7}[/math][color=#ff0000]，D正确；[br][br]根据[/color][math]\overline{v}=\frac{h}{t}[/math][color=#ff0000]可得石块依次通过三个窗户的平均速度之比为[math]\overline{v_1}:\overline{v_2}:\overline{v_3}=\frac{1}{t_1}:\frac{1}{t_2}:\frac{1}{t_3}=\frac{1}{\sqrt{2}-\sqrt{1}}:\frac{1}{\sqrt{5}-\sqrt{4}}:\frac{1}{\sqrt{8}-\sqrt{7}}[/math]，B正确。[br][br]故选ABD。[br][/color]

自由落体运动的初速度为零，所以可以直接运用之前所讲的那几个初速度为零的匀变速直线运动的比例推论。

[color=#0000ff][b]例6[/b]：科技馆中的一个展品如图所示，在较暗处有一个不断均匀滴水的水龙头，在一种特殊的间歇闪光灯的照射下，若调节间歇闪光间隔时间正好与水滴从[i]A[/i]下落到[i]B[/i]的时间相同，可以看到一种奇特的现象，水滴似乎不再下落，而是像固定在图中的[i]A[/i][i]、[/i][i]B[/i][i]、[/i][i]C[/i][i]、[/i][i]D[/i]四个位置不动，对出现的这种现象，下列描述正确的是（[i]g[/i]取10 m/s[sup]2[/sup]）（　　）[br][img width=173px,height=186px]https://img.xkw.com/dksih/QBM/editorImg/2022/9/5/f3bba8f2-3277-4445-aa14-e76699710637.png[/img][br][table][tr][td]A．水滴在下落过程中通过相邻两点之间的时间满足[i]t[/i][sub]AB[/sub]＜[i]t[/i][sub]BC[/sub]＜[i]t[/i][sub]CD[/sub][/td][/tr][tr][td]B．闪光的间隔时间是[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/bd92f594c348f7a956607f7b381cc22a.svg[/img]s[/td][/tr][tr][td]C．水滴在相邻两点间的平均速度满足[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/77539d5d6f098b515321cf8e5dc72329.svg[/img][sub]AB[/sub]∶[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/77539d5d6f098b515321cf8e5dc72329.svg[/img][sub]BC[/sub]∶[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/77539d5d6f098b515321cf8e5dc72329.svg[/img][sub]CD[/sub]=1∶4∶9[/td][/tr][tr][td]D．水滴在各点的速度之比满足[i]v[/i][sub]B[/sub]∶[i]v[/i][sub]C[/sub]∶[i]v[/i][sub]D[/sub]=1∶3∶5[/td][/tr][/table][/color][br][color=#ff0000]解析：[br]由图知，[math]h_{AB}:h_{BC}:h_{CD}=1:3:5[/math]，符合初速度为零的等时间位移推论，说明[math]t_{AB}:t_{BC}:t_{CD}=1:1:1[/math]，A错。[br]我们取AB段位移进行计算，[math]T=\sqrt{\frac{2h_{AB}}{g}}=\frac{\sqrt{2}}{10}m/s[/math]，B对。[br][math]\overline{v}=\frac{h}{t}[/math]，故[math]\overline{v_{AB}}:\overline{v_{AB}}:\overline{v_{AB}}=h_{AB}:h_{BC}:h_{CD}=1:3:5[/math]，C错[br]由初速度为0的等时间推论，[math]v_B:v_C:v_D=1:2:3[/math]，D错[/color]

[color=#0000ff][b]例7[/b]：屋檐上每隔相同的时间间隔滴下一滴水，当第7滴正欲滴下时，第1滴已刚好到达地面，而第5滴与第4滴分别位于高为1m的窗户的上、下沿，如图所示，问：[br]（1）滴水的时间间隔是多少；（[i]g[/i]取10m/s[sup]2[/sup]）[br]（2）此屋檐离地面多高。[/color][br][img]https://www.helloimg.com/i/2024/10/31/6722fdda32a3b.png[/img][br][br][color=#ff0000]解析：[br]（1）根据初速度为零的匀加速直线运动的规律可知[math]h_{67}:h_{56}:h_{45}:h_{34}:h_{23}:h_{12}=1:3:5:7:9:11[/math]，[br] 由[math]h_{45}=1m[/math]可知[math]h_{67}=0.2m[/math],[br] 根据[math]h_{67}=\frac{1}{2}gT^2[/math]可得[math]T=0.2s[/math][br][br]（2）屋檐离地面高度[math]H=h_{67}+h_{56}+h_{45}+h_{34}+h_{23}+h_{12}=0.2x(1+3+5+7+9+11)=7.2m[/math][/color]

自由落体运动的规律和推论只能运用于自由落体运动，初速度一定为0。如果我们选取的是自由落体运动中间的某一段运动，则不属于自由落体运动，是不能硬套自由落体的运动公式的，这时候要当作一般的匀变速直线运动去处理。

[color=#0000ff][b]例8[/b]:（多选）如图是一张在真空实验室里拍摄的羽毛与苹果同时下落的局部频闪照片。已知频闪照相机的频闪周期为[i]T[/i]。下列说法正确的是（     ）[br][img width=107px,height=131px]https://img.xkw.com/dksih/QBM/editorImg/2024/10/24/46ee8902-69c7-428c-8b7f-3a278e0ead90.png[/img][br][/color][table][tr][td][color=#0000ff]A．[i]x[/i][sub]1[/sub]、[i]x[/i][sub]2[/sub]、[i]x[/i][sub]3[/sub]一定满足[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/0a937fd27fc35d224df4d61b30442d3f.svg[/img][/color][/td][/tr][tr][td][color=#0000ff]B．羽毛下落到[i]B[/i]点的速度大小为[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce93dc17884097059a9f65a85971659.svg[/img][/color][/td][/tr][tr][td][color=#0000ff]C．苹果在点[i]C[/i]的速度大小为2[i]gT[/i][/color][/td][/tr][tr][td][color=#0000ff]D．羽毛下落的加速度大小为[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/e204fd855202cd94bf9de76b3beae7f8.svg[/img][/color][/td][/tr][/table][br][br][color=#ff0000]解析:[br]不知道A点是否为初始释放点，不能直接用初速度为0的等时间推论，A错[br]同理，C点的速度不能直接用[/color][math]v_C=gt_c=g2T=2gT[/math][color=#ff0000]，C错[/color][color=#ff0000][br]根据中间时刻速度推论：[math]v_B=\frac{x_{AC}}{t_{AC}}=\frac{x_1+x_2}{2T}[/math]，B对[br]根据位移差推论，[math]g=\frac{x_3-x_1}{(3-1)T^2}[/math]，D对[/color]

[size=150][b]四、自由落体运动的几类典型问题[/b][/size]

[b]1、先自由落体再减速[br][br][/b][color=#0000ff][b]例1[/b]．跳伞员从[math]H=116m[/math]的高空自由下落一段距离后才打开降落伞，假设伞打开后以大小为[math]a=2m/s^2[/math]的加速度匀减速下降，到达地面时速度为[math]v=4m/s[/math]（[i]g[/i]取[math]10m/s^2[/math]），求：[br]（1）跳伞员打开伞时距地面的高度[math]h_2[/math]是多少？下落的最大速度[/color][math]v_m[/math][color=#0000ff]为多大？[/color][br][color=#0000ff]（2）跳伞员下落的总时间[i][math]T[/math][/i]是多少？[br][br][/color][color=#ff0000]解析：[br]（1）以向下为正方向，[math]a=-2m/s^2[/math][br] 设自由落体的时间为[math]t_1[/math]，下落位移[math]h_1=\frac{1}{2}gt_1^2[/math]，最大速度[math]v_m=gt_1[/math][br] 打开降落伞后的位移[math]h_2=\frac{v^2-v_m^2}{2a}[/math][br] 由题知，[math]H=h_1+h_2[/math][br] 联立上式并代入数据解得：[math]t_1=2s，h_1=20m，h_2=96m，v_m=20m/s[/math][br][br]（2）跳伞员打开降落伞后的减速时间[math]t_2=\frac{v-v_m}{a}=8s[/math][br] 下落总时间[math]T=t_1+t_2=10s[/math][/color]

[size=150][b][size=100]2、高空坠物避免相撞[br][br][/size][/b][size=100][color=#0000ff][b]例1：[/b]如图所示，某居民楼[/color][/size][color=#0000ff][size=100]距地面高[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe52e57e640f47b6c1fc50eb09b564e.svg[/img]阳台上的花盆如受扰动而掉落，掉落过程可看作自由落体运动，花盆可视为质点。一骑手正以[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/59ba0a6a01bc1024bca29d96413518e7.svg[/img]的速度骑着自行车匀速驶向阳台正下方的通道，自行车长度[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/f56fbee9c429f09dd8b80b297f7dd342.svg[/img]。花盆刚开始掉落时，自行车车头距花盆的水平距离[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/6c96ad3ac666896d42508974b2cf1070.svg[/img]，由于道路狭窄，自行车只能直行通过阳台正下方的通道，且骑手的头部离地面高度[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/813aa43d9054fa0ba5442ce59a1a2b30.svg[/img]，为简化计算，设人和车整体高度也为[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/813aa43d9054fa0ba5442ce59a1a2b30.svg[/img]，如果花盆下落到这个高度，我们就认为它砸到了车子。求：[br][img width=284px,height=140px]https://img.xkw.com/dksih/QBM/editorImg/2024/10/17/005c1b10-84dc-4319-8e4b-790da59a09e0.png[/img][br](1)若骑手没有发现花盆掉落，保持匀速直行，通过计算说明自行车是否会被花盆砸到？[br](2)若骑手发现花盆开始掉落，且反应时间[img]https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd30e017883b283a93a1c39ee69f06c.svg[/img]，则骑手至少以多大的加速度进行加速，才能确保实现避险。（自行车加速过程可视为匀变速运动）[/size][br][/color][/size][color=#ff0000][size=100]解析：[br]（1）花盆掉落至与人头顶等高处的时间为[math]t=\sqrt{\frac{2(H-h_0)}{g}}=2s[/math][br]这段时间内人的位移[math]x=v_0t=8m[/math][br]因为[math]L_2[/math]<[math]x[/math]<[math]L_1+L_2[/math],所以会被砸到。[br][br]（2）设骑手加速通过的加速度为[math]a[/math]，骑手要不被砸，加速通行的位移[math]x_2[/math]要满足：[br][math]x_2=v_0(t-Δt)+\frac{1}{2}a(t-Δt)^2[/math][br][math]x_2=L_1+L_2-x_1[/math][br]联立解得,[/size][math]a=3m/s^2[/math][/color]

[b]3、质点穿过一段距离[br][br][/b][color=#0000ff][b]例1[/b]：如图所示，一长为[i]L[/i]的金属管放在地面，管口正上方高[i]h[/i]处有一小球自由下落，已知重力加速度为[i]g[/i]，不计空气阻力。求小球穿过管所用时间。[br][/color][b][color=#0000ff][img width=81px,height=189px]https://img.xkw.com/dksih/QBM/editorImg/2024/10/29/0d92c03a-e942-4a74-a229-4f7d8a021f32.png[/img][br][/color][br][/b][color=#ff0000]解析：[br][/color][color=#ff0000]小球到达管上端的时间为[math]t_1=\sqrt{\frac{2h}{g}}[/math][br]到达管下端的时间为[math]t_2=\sqrt{\frac{2(h+L)}{g}}[/math][br]小球穿过管所用时间[math]Δt=t_2-t_1=\sqrt{\frac{2(h+L)}{g}}-\sqrt{\frac{2h}{g}}[/math][br][br][br][/color][color=#0000ff][b]例2[/b][/color][color=#0000ff]：下雨时，屋檐上每隔一段时间会掉下一滴雨水，其运动可看作自由落体运动，重力加速度取10m/s[/color][sup]2[/sup][color=#0000ff]。屋檐下边有一窗户，它的上下边缘高度差为1.2m，雨滴完全通过窗户（从上边檐到下边檐）的时间为0.2s。试求：[br](1)雨滴落到窗子上边缘时的速度大小；[br](2)屋檐距离窗户上边檐的距离；[br](3)雨滴从屋檐下落到窗户中点的时间。[br][/color][img width=99px,height=182px]https://img.xkw.com/dksih/QBM/editorImg/2024/9/19/ced61884-b308-4d31-9e7b-b3579f55563d.png[/img][br][color=#ff0000]解析:[br](1)雨滴在穿过窗户的这段运动的中间时刻速度[math]v_{\frac{t}{2}}=\frac{h}{Δt}=6m/s[/math][br]雨滴落到上边缘时的速度[math]v_1=v_{\frac{t}{2}}-g\frac{Δt}{2}=5m/s[/math][br][br](2)屋檐距离窗户的上边缘距离[math]h_1=\frac{v_1^2}{2g}=1.25m[/math][br][br](3)雨滴到达下边缘时的速度[math]v_2=v_{\frac{t}{2}}+g\frac{Δt}{2}=7m/s[/math][br]雨滴在窗户中点的速度[math]v_{\frac{h}{2}}=\sqrt{\frac{v_1^2+v_2^2}{2}}=\sqrt{37}m/s[/math][br]下落到中点的时间[math]t_{\frac{h}{2}}=\frac{v_{\frac{h}{2}}}{g}=\sqrt{0.37}m/s\approx0.61s[/math][/color]

[b]4、非质点的自由落体[br][/b][br][color=#0000ff][b]例1[/b]:如图所示，用绳拴住木棒[i]AB[/i]的[i]A[/i]端，使木棒在竖直方向上静止不动，在悬点[i]A[/i]端正下方有一点[i]C[/i]距[i]A[/i]端0.8m．若把绳轻轻剪断，测得[i]A[/i]、[i]B[/i]两端通过[i]C[/i]点的时间差是0.2s，重力加速度[i]g[/i]=10m/s[sup]2[/sup]，不计空气阻力．[br]（1）求木棒[i]AB[/i]的长度[br]（2）[i]D[/i]为[i]AB[/i]棒上的一点，若[i]AD[/i]、[i]DB[/i]两段通过[i]C[/i]点的时间相同，求[i]AD长[/i][br][br][/color][img]data:image/png;base64,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[/img][br][br][color=#ff0000]解析:[br]（1）设木棒的长度为[math]l[/math]，绳子剪断后木棒自由下落，可将[i]A[/i]、[i]B[/i]两端分别看做自由下落的质点，它们下落到[i]C[/i]点所用时间分别为[math]t_1[/math]、[math]t_2[/math]。[br]依题意有,[br][math]h_{AC}=\frac{1}{2}gt_1^2=0.8m[/math][br][math]h_{BC}=h_{AC}-l=\frac{1}{2}gt_2^2[/math][br][math]Δt=t_1-t_2=0.2s[/math][br]联立三式解得：[br][math]l=0.6m，t_1=0.2s，t_2=0.4s[/math][br][br]（2）由于[i]AD[/i]、[i]DB[/i]两段通过[i]C[/i]点的时间相同，为等时间间隔。[br]根据[math]Δx=aΔT^2[/math],可得：[math]h_{AD}-h_{DB}=g(\frac{Δt}{2})^2=0.1m[/math].[br]而且：[math]h_{AD}+h_{DB}=l=0.6m[/math][br]联立解得：[math]h_{AD}=0.35m[/math][/color]

[color=#0000ff][b]例2[/b]：如图所示，直棒[i]AB[/i]长11.25m，上端为[i]A[/i]、下端为[i]B[/i]，在[i]B[/i]的正下方5m处有一长度为15m，内径比直棒大得多的固定空心竖直管，手持直棒由静止释放，让棒做自由落体运动，不计空气阻力，重力加速度[i]g=[/i]10m/s[sup]2[/sup]，求：[br]（1）直棒下端[i]B[/i]刚好开始进入空心管时的瞬时速度v[sub]B[/sub]；[br]（2）直棒下端[i]B[/i]通过空心管所用的时间；[br]（3）直棒在空心管中运动的时间。[br][/color][img]data:image/png;base64,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[/img][br][br][color=#ff0000]解析：[/color][color=#ff0000][br](1)直棒下端[i]B[/i]刚好开始进入空心管时下落的高度为[math]h=5m[/math]，[math]v_B=\sqrt{2gh}=10m/s[/math][br](2)设直棒下端[i]B[/i]通过空心管所用的时间为[math]t_1[/math]，空心管长度为[math]L=15m[/math]，[br]则有[math]L=v_Bt_1+\frac{1}{2}gt_1^2[/math][br]解得[math]t_1=1s[/math][br](3)设直棒在空心管中运动的时间为[math]t_2[/math]，直棒长度为[math]l=11.25m[/math]，[br]则有[math]l+L=v_Bt_2+\frac{1}{2}gt_2^2[/math][br]解得[/color][math]t_2=1.5s[/math][br][br]

[b]5、两个物体自由下落[br][br][/b][color=#0000ff][b]例1[/b]：如图所示，两个小球[i]a[/i]、[i]b[/i]的质量分别为[i]m[/i][sub]a[/sub]、[i]m[/i][sub]b[/sub]，且[i]m[/i][sub]a[/sub]>[i]m[/i][sub]b[/sub]，两球竖直方向相距[i]l[/i]，小球[i]a[/i]距离地面的高度为[i]h[/i]。现让小球[i]a[/i]、[i]b[/i]由静止同时释放，两个小球相继落地的时间间隔为∆[i]t[/i]，不计空气阻力，下列说法中正确的是（　　）[br][img width=93px,height=161px]https://img.xkw.com/dksih/QBM/editorImg/2024/10/22/aac87ef4-e7c6-4192-a54f-4697681e1020.png[/img][br][table][tr][td]A．[i]a[/i]有可能先落地[/td][td]B．[i]a[/i]下落的加速度比[i]b[/i]大[/td][/tr][tr][td]C．[i]l[/i]越大，∆[i]t[/i]越小[/td][td]D．[i]h[/i]越大，∆[i]t[/i]越小[/td][/tr][/table][/color][br][color=#ff0000]解析：[br]对于不同高度同时释放的小球，因为[/color][math]v=gt[/math][color=#ff0000]，[/color][math]h=\frac{1}{2}gt^2[/math][color=#ff0000]，两物体的运动时间都是一样的，所以速度和位移都一样。[br]两者会保持相对距离l一直不变落地。[br]对a来说，落地时间[/color][math]t_a=\sqrt{\frac{2h}{g}}[/math][color=#ff0000][br]对b来说，落地时间[/color][math]t_b=\sqrt{\frac{2(h-l)}{g}}[/math][math]Δt=t_a-t_b=\sqrt{\frac{2h}{g}}-\sqrt{\frac{2(h-l)}{g}}=\sqrt{\frac{2}{g}}\cdot(\sqrt{h}-\sqrt{h-l})=\sqrt{\frac{2}{g}}\cdot\frac{l}{\sqrt{h}+\sqrt{h-l}}[/math][color=#ff0000][br]可知，l越大，Δt越大，h越大，Δt越小。[br]故选D。[br][br][/color]如果两个物体先后释放，我们可以利用v-t图像来解决问题。[color=#ff0000][br][br][/color][color=#0000ff][b]例2[/b]：下雨时雨水从屋檐滴落是生活中常见的现象，假设屋檐某一位置每隔相同的时间无初速滴落一滴雨滴，不计空气作用力，则已滴出且未落地的相邻雨滴之间的（　　）[br]A．距离保持不变                                                   B．距离越来越大[br]C．速度之差越来越小                                          D．速度之差越来越大[br][/color][color=#ff0000][br]解析：[br][img]data:image/png;base64,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[/img][br]从v-t图像可以看出，两物体的速度之差一直不变，但是相对距离（两图像中间围成的面积）越来越大。[br]故选D。[br][/color]