1.
(2024高三上·重庆市期中) 如图所示,在光滑水平轨道
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右侧固定一个竖直半圆轨道
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, 半圆轨道与水平轨道相切于
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点且平滑连接。半圆轨道的圆心为
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, 半径
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,
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水平。质量
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的小球从
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点以6m/s的水平初速度向
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运动,小球经
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点后沿竖直半圆轨道运动,恰好在圆轨道上的
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点离开轨道,
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与
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的夹角为
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。空气阻力不计,
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,
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,
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。求:
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(1) 小球在
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点的向心加速度大小;
(2) 小球在圆弧轨道上损失的机械能;
(3) 小球在整个过程中能够到达的最高点与
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的竖直高度。
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