有一底面圆半径为R、高为H的正圆柱体(密度为ρ)，在其中心轴上高出上底为α处有一质量为m的质点，求此柱体对该质点的引力.

<br>建立如图所示的坐标系,质量为<img src="/s/tiw/p3/UpLoadImage/2013-05-07/11257e58-35bc-418a-bf8a-c18475843647.png" width="18" height="15">的质点在原点<img src="/s/tiw/p3/UpLoadImage/2013-05-07/62a83c5e-930a-4bdc-b707-eff8d663ed85.png" width="16" height="18">处,圆柱体得中心轴在<img src="/s/tiw/p3/UpLoadImage/2013-05-07/8e0b1174-302e-40e3-90ea-2b63b83a0ecb.png" width="13" height="13">轴上,由圆柱体的对称性可知,圆柱体对质点的引力<img src="/s/tiw/p3/UpLoadImage/2013-05-07/49d04ae0-a325-4e28-b439-ab11e58f6f57.png" width="18" height="18">在<img src="/s/tiw/p3/UpLoadImage/2013-05-07/a919bc47-4d42-4a5b-b3b0-1a55d777675f.png" width="13" height="15">轴和<img src="/s/tiw/p3/UpLoadImage/2013-05-07/0031d468-1ace-42ab-a474-22d261564c66.png" width="15" height="18">轴方向的分力为0,即<img src="/s/tiw/p3/UpLoadImage/2013-05-07/81735321-e995-4aa7-9aeb-15171b4e6015.png" width="91" height="25">.在<img src="/s/tiw/p3/UpLoadImage/2013-05-07/8e0b1174-302e-40e3-90ea-2b63b83a0ecb.png" width="13" height="13">轴方向的分力为<br><img src="/s/tiw/p3/UpLoadImage/2013-05-07/1048d42c-a590-463a-929f-f776a027e309.jpg" width="491" height="282"><br>故此柱体对该质点的引力为<img src="/s/tiw/p3/UpLoadImage/2013-05-07/b109ff37-3c7b-40fd-a1e0-cfe040f68c45.jpg" width="471" height="41"><br><span style="text-align:center;display:block"><img src="/s/tiw/p3/UpLoadImage/2013-05-07/008843cc-4a1d-4a0c-8f30-36b558f4a3d7.jpg" width="314" height="267"></span>