求下列曲线所围成的均匀薄板的质心坐标 :[tex=11.0x1.5]/IvfOGB9YQ1VoCtTiQ7GboUAI7pdrCHcjwCHHXZdO4A=[/tex]
[b]解[/b]:设均匀薄板的密度为常数 [tex=0.571x1.0]GYJ0hpBI/gsBk7Z5+ceVug==[/tex].由已知可得[tex=25.857x10.571]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[/tex]于是,质心坐标为[p=align:center][tex=9.071x2.786]CUSX85vyvN4N/ph+GAjVtzsGBWTeItjiTUDpgAR5KfvzwRmsk18AhXi0cRXFhKUJ6NseoN6OS+faPTvOunMGxQ==[/tex]
举一反三
- 求下列曲线所围成的均匀薄板的质心坐标 :[tex=10.357x1.357]hzlHzEjAGwE5NT8LxECxjh8wOHxEb2qbqok9Nhj+3GPkVQGwAsNlthh/skiybxXU[/tex]
- 求以下列曲线为界的均匀薄板的质心坐标:[tex=14.357x1.714]1BBD6hHqOM5KMBcPcZuCAblXpTLqR0zirLCcxcegRP5kqSg+hy8Os9FXThyVoFPB+RlFQNtYREOTH4rnCvoSmw==[/tex]
- 求以下列曲线为界的均匀薄板的质心坐标:[tex=10.0x1.5]YrYonaDGUnAtNuaGUsfGJ9kCEC5eKb7Tln4hdH8iwTc=[/tex]
- 求以下列曲线为界的均匀薄板的质心坐标:[tex=10.357x1.5]DvX+IzsPWOqsCQGm3dPZkKi0Ape8GUB5lowYvQA3JLkcxEkhgt0qbhqr5R5a1rQu[/tex]
- 求以下列曲线为界的均匀薄板的质心坐标:[tex=8.571x1.357]TYZO38wVeR16nX/f46E4nFuxVX9f8BSsKgmK7r8M9lQ=[/tex]
内容
- 0
求下面曲线所界薄板的质心坐标:[tex=2.786x1.429]/1M/qWk56WIOhhKuRNPImQ==[/tex],[tex=6.786x1.357]2RUj78oQttwvG17Pdu0FPg==[/tex];
- 1
求下面曲面所围成的立体的质心坐标(假设体密度为 1).[tex=5.929x1.286]tN1kgP+8DeZ0qNq4KOOW8W9COUYHgNeiveZcv68wSxM=[/tex] 及 [tex=2.286x1.286]NGblVJ4MOxCzYWTiKwrJpw==[/tex].
- 2
求由坐标轴与直线[tex=4.571x1.286]Nfi0+kab4C/i5sRq/UUI3g==[/tex]所围成的三角形均匀薄片的质心 .
- 3
求由坐标轴与直线[tex=4.571x1.286]Nfi0+kab4C/i5sRq/UUI3g==[/tex]所围成的三角形均匀薄片的质心.
- 4
求曲线[tex=8.786x1.571]VvsnOSv2k2ZQijv59FsbL1yYPe+6eB3rlLltYVMW1Wc=[/tex]所围图形的质心在参数X变化时所描绘的曲线。