设有一长度为L，线密度为ρ的均匀细直棒，在与棒的一端垂直距离为a单位处有一质量为m的质点N，试求细棒对质点N的引力.

<br>建立如图所示的坐标系,细棒在<img src="/s/tiw/p3/UpLoadImage/2013-05-07/0031d468-1ace-42ab-a474-22d261564c66.png" width="15" height="18">轴上,原点为细棒的一段,<img src="/s/tiw/p3/UpLoadImage/2013-05-07/4140bbdb-41ae-41c0-93ca-d1d9966fbd40.png" width="38" height="22">点是细棒的另一端,质点<img src="/s/tiw/p3/UpLoadImage/2013-05-07/e1600af4-c948-4b54-9e58-252f8949c89f.png" width="18" height="18">位于<img src="/s/tiw/p3/UpLoadImage/2013-05-07/a919bc47-4d42-4a5b-b3b0-1a55d777675f.png" width="13" height="15">轴上的点<img src="/s/tiw/p3/UpLoadImage/2013-05-07/26583012-6d0b-4f20-9619-1a518be15eec.png" width="36" height="22">处.取区间<img src="/s/tiw/p3/UpLoadImage/2013-05-07/868c2dd9-59b2-4e37-abd6-9d300419d7d7.png" width="69" height="22">对应的一小段细棒为研究对象,可将其近似看做是一个质点,此小段细棒的质量为<img src="/s/tiw/p3/UpLoadImage/2013-05-07/46aea43d-57dc-4958-a8f5-6ce5f78ed8a8.png" width="29" height="22">.<br>由两点之间的引力公式得,小段细棒与质点间的引力为<img src="/s/tiw/p3/UpLoadImage/2013-05-07/67de3710-3a91-44f8-8232-f910afa5190b.jpg" width="155" height="53"><br>小段细棒对质点<img src="/s/tiw/p3/UpLoadImage/2013-05-07/e1600af4-c948-4b54-9e58-252f8949c89f.png" width="18" height="18">的引力在水平方向(<img src="/s/tiw/p3/UpLoadImage/2013-05-07/d2aba48a-45fa-4891-ad4f-9ec4ec5b3b35.png" width="18" height="24">)和垂直方向(<img src="/s/tiw/p3/UpLoadImage/2013-05-07/b4408a2e-1438-4f0c-9241-f69b8a29687d.png" width="20" height="25">)的分力分别为<br><img src="/s/tiw/p3/UpLoadImage/2013-05-07/09f13ae1-a08a-4918-a58d-0cd43f1daa2f.jpg" width="526" height="50"><br>则整个细棒对质点的引力水平方向(<img src="/s/tiw/p3/UpLoadImage/2013-05-07/d2aba48a-45fa-4891-ad4f-9ec4ec5b3b35.png" width="18" height="24">)和垂直方向(<img src="/s/tiw/p3/UpLoadImage/2013-05-07/b4408a2e-1438-4f0c-9241-f69b8a29687d.png" width="20" height="25">)的分力分别为<br><img src="/s/tiw/p3/UpLoadImage/2013-05-07/2d6a8d04-fb97-4752-9a87-650e791505fd.jpg" width="553" height="213"><br><span style="text-align:center;display:block"><img src="/s/tiw/p3/UpLoadImage/2013-05-07/833c2903-e803-41f3-af01-45ebcc9f4aa5.jpg" width="330" height="245"></span>