一、单选题(本大题共8小题,共32.0分)
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2.
(2023高二下·龙岗期中)
在如图所示的电路中,电源电动势为E、内电阻为r,C为电容器,R
0为定值电阻,R为滑动变阻器;开关闭合后,灯泡L能正常发光;当滑动变阻器的滑片向右移动后,下列说法中正确的是( )
![](//tikupic.21cnjy.com/2023/06/01/ed/90/ed9012128234ff010db09fbc9fc09354_234x183.png)
A . 灯泡L变亮
B . 电容器C的带电量将增大
C .
两端的电压减小
D . 电源的总功率变大
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3.
一光滑水平地面上静止放着质量为M、半径为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3ER%3C%2Fmtext%3E%3C%2Fmath%3E)
的光滑圆弧轨道,质量也为M小球从轨道最左端的
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EA%3C%2Fmtext%3E%3C%2Fmath%3E)
点由静止滑下
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmtext%3EA%3C%2Fmtext%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmath%3E)
为水平直径
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
,重力加速度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Eg%3C%2Fmtext%3E%3C%2Fmath%3E)
,下列正确的是( )
![](//tikupic.21cnjy.com/2023/12/15/28/ea/28ead9ee4d9f843aa94a520defe5dc21_m_242x115.png)
A . 小球不可能滑到圆弧轨道右端最高端
B . 小球向右运动中轨道先向左加速运动,后向右加速运动
C . 轨道做往复运动,离原先静止位置最大距离为
D . B.小球通过最低点时速度
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4.
飞力士棒是一种健身、康复器材,它由一根
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EP%3C%2Fmtext%3E%3Cmtext%3EV%3C%2Fmtext%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmath%3E)
软杆、两端的负重头和中间的握柄组成,使用时,用手驱动使其振动,如图所示。若某棒的固有振动频率为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmtext%3EH%3C%2Fmtext%3E%3Cmtext%3EZ%3C%2Fmtext%3E%3C%2Fmath%3E)
,下列说法正确的是( )
![](//tikupic.21cnjy.com/2023/10/12/83/7d/837d79868826be46aefd5c214944dd62_248x117.png)
A . 用力越大,该棒振动的越快
B . 增大手驱动的频率,该棒的振幅一定变大
C . 增大手驱动的频率,该棒的振动频率可能减小
D . 用同样大小的力驱动该棒,每分钟完成
次全振动时负重头的振幅最大
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5.
(2023高二下·龙岗期中)
如图所示,圆形区域内有垂直纸面的匀强磁场,三个质量和电荷量都相同的带电粒子a、b、c,以不同的速率对准圆心O沿着AO方向射入磁场,其运动轨迹如图.若带电粒子只受磁场力的作用,则下列说法正确的( )
![](//tikupic.21cnjy.com/2023/06/01/be/f4/bef4dd3cc1fab8b8b78ea297bdc30d41_284x170.png)
A . a粒子速率最大,在磁场中运动时间最长
B . c粒子速率最大,在磁场中运动时间最短
C . a粒子速率最小,在磁场中运动时间最短
D . c粒子速率最大,在磁场中运动时间最长
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A . 该交变电流的周期为2s
B . 该交变电流电压的有效值为200V
C . 将该交变电流加在交流电压表两端时,电压表读数为
D . 将该交变电流加在启辉电压(达到或超过启辉电压后氖管会发光)为200V的氖管上,氖管未被击穿,氖管1秒钟内发光次数为100次
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8.
(2023高二下·龙岗期中)
如图所示,2021年12月9日下午,神舟十三号乘组航天员在中国空间站成功进行了“天宫课堂”第一课。航天员太空授课的画面通过电磁波传输到地面接收站,下列关于电磁波的说法正确的是( )
![](//tikupic.21cnjy.com/2023/06/01/92/83/928327e570d3efd0e8dcfaa05d35e2b9_258x174.png)
A . 麦克斯韦证实了电磁波的存在
B . 电磁波可以在真空中传播
C . 电磁波在各种介质中传播的速度都是
D . 电场周围一定产生磁场,磁场周围一定产生电场
二、多选题(本大题共3小题,每题6分,选对但不全得3分,共18.0分)
三、实验题(本大题共2小题,共16.0分)
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12.
(2022·江门模拟)
某同学利用一根压缩的弹簧来弹开带有遮光片的滑块测量滑块与木板间的动摩擦因数。实验装置如图(a)所示,将木板水平固定在桌面上,弹簧的左端固定在挡板上,右端与滑块刚好接触(但不连接),然后将光电门固定在木板上靠近滑块处。实验步骤如下:
![](//tikupic.21cnjy.com/2022/03/22/da/af/daaf8b73f4e1e8db2b21b6aa548e91a2_552x144.png)
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(1)
用游标卡尺测量遮光片的宽度d,其示数如图(b)所示,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%0A+%3Cmi%3E%0A++d%0A+%3C%2Fmi%3E%3Cmo%3E%0A++%3D%0A+%3C%2Fmo%3E%0A%3C%2Fmath%3E)
cm;
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(2)
将光电门连接计时器,让滑块压缩弹簧至P点(图(a)中未画出),释放后滑块被弹开并沿木板向右滑动,计时器记录遮光片通过光电门的时间
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%0A+%3Cmtext%3E%0A++%CE%94%0A+%3C%2Fmtext%3E%3Cmi%3E%0A++t%0A+%3C%2Fmi%3E%0A%3C%2Fmath%3E)
, 再测量滑块停止时的位置与光电门的距离x,则可用
表示滑块经过光电门时速度的大小;
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(3)
改变P点的位置,多次重复步骤(2);
若用
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%0A+%3Cmfrac%3E%0A++%3Cmrow%3E%0A+++%3Cmn%3E%0A++++1%0A+++%3C%2Fmn%3E%0A++%3C%2Fmrow%3E%0A++%3Cmrow%3E%0A+++%3Cmtext%3E%0A++++%CE%94%0A+++%3C%2Fmtext%3E%0A+++%3Cmsup%3E%0A++++%3Cmrow%3E%0A+++++%3Cmi%3E%0A++++++t%0A+++++%3C%2Fmi%3E%0A++++%3C%2Fmrow%3E%0A++++%3Cmrow%3E%0A+++++%3Cmn%3E%0A++++++2%0A+++++%3C%2Fmn%3E%0A++++%3C%2Fmrow%3E%0A+++%3C%2Fmsup%3E%0A++%3C%2Fmrow%3E%0A+%3C%2Fmfrac%3E%3Cmo%3E%0A++%E2%88%92%0A+%3C%2Fmo%3E%3Cmi%3E%0A++x%0A+%3C%2Fmi%3E%0A%3C%2Fmath%3E)
图像处理数据,所得图像如图(c)所示,设重力加速度为g,则由图线可得滑块与木板间的动摩擦因数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%0A+%3Cmtext%3E%0A++%CE%BC%0A+%3C%2Fmtext%3E%3Cmo%3E%0A++%3D%0A+%3C%2Fmo%3E%0A%3C%2Fmath%3E)
(用物理量的符号表示)。
![](//tikupic.21cnjy.com/2022/03/22/28/01/2801f781725e8e4af26dd554daa35a19_255x252.png)
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13.
(2023高二下·龙岗期中)
测定金属丝的电阻率,提供实验器材如下:
A.待测金属丝R(电阻约8Ω)
B.电流表A(0.6A,内阻约0.6Ω)
C.电压表V(3V,内阻约3kΩ)
D.滑动变阻器R1(0-5Ω,2A)
E.电源E(6V)
F.开关,导线若干
![](//tikupic.21cnjy.com/2023/06/01/8b/05/8b05b932c52b38414e37ae9beba2839c_420x124.png)
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(1)
某同学用螺旋测微器和游标卡尺分别测量金属丝的直径和长度,读出图中的示数,图甲为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
, 图乙为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
。
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(2)
某同学采用如图所示电路进行实验,请用笔画线代替导线,在图中将实物电路图连接完整
。
![](//tikupic.21cnjy.com/2023/06/01/68/b4/68b4401ff796d3b04ad5e9e18c883f1d_299x143.png)
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(3)
测得金属丝的直径为d,改变金属夹P的位置,测得多组金属丝接入电路的长度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EL%3C%2Fmi%3E%3C%2Fmath%3E)
及相应电压表示数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EU%3C%2Fmi%3E%3C%2Fmath%3E)
、电流表示数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EI%3C%2Fmi%3E%3C%2Fmath%3E)
, 作出
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3EU%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3EI%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3EL%3C%2Fmi%3E%3C%2Fmath%3E)
如图所示。测得图线斜率为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmath%3E)
, 则该金属丝的电阻率
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%CF%81%3C%2Fmtext%3E%3C%2Fmath%3E)
为
。
![](//tikupic.21cnjy.com/2023/06/01/39/7b/397bda401105c89e30f5197a39c864ea_201x185.png)
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四、计算题(本大题共3小题,共34.0分,需要写出重要解题步骤和必要的文字说明,只有结果,没有过程不得分)
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14.
如图所示,气缸呈圆柱形,上部有挡板,内部高度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Ed%3C%2Fmtext%3E%3C%2Fmath%3E)
。筒内一个很薄的质量不计的活塞封闭一定量的理想气体,开始时活塞处于离底部
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmtext%3Ed%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
的高度,外界大气压强为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmtext%3EP%3C%2Fmtext%3E%3Cmtext%3Ea%3C%2Fmtext%3E%3C%2Fmath%3E)
,温度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmtext%3E%E2%84%83%3C%2Fmtext%3E%3C%2Fmath%3E)
,现对气体加热。求:
![](//tikupic.21cnjy.com/2023/12/15/87/a8/87a8886f83a02e1010cb61be5e3c123b_m_131x115.png)
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(2)
气体温度达到
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmtext%3E%E2%84%83%3C%2Fmtext%3E%3C%2Fmath%3E)
时气体的压强。
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15.
如图所示,两足够长平行光滑的金属导轨
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EM%3C%2Fmtext%3E%3Cmtext%3EN%3C%2Fmtext%3E%3C%2Fmath%3E)
、
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EP%3C%2Fmtext%3E%3Cmtext%3EQ%3C%2Fmtext%3E%3C%2Fmath%3E)
相距为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EL%3C%2Fmtext%3E%3C%2Fmath%3E)
,导轨平面与水平面夹角a,导轨上端跨接一定值电阻
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3ER%3C%2Fmtext%3E%3C%2Fmath%3E)
,导轨电阻不计.整个装置处于垂直斜面向上的匀强磁场中,长为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EL%3C%2Fmtext%3E%3C%2Fmath%3E)
的金属棒
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Ec%3C%2Fmtext%3E%3Cmtext%3Ed%3C%2Fmtext%3E%3C%2Fmath%3E)
垂直于
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EM%3C%2Fmtext%3E%3Cmtext%3EN%3C%2Fmtext%3E%3C%2Fmath%3E)
、
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EP%3C%2Fmtext%3E%3Cmtext%3EQ%3C%2Fmtext%3E%3C%2Fmath%3E)
放置在导轨上,且与导轨保持电接触良好,金属棒的质量为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
、电阻为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Er%3C%2Fmtext%3E%3C%2Fmath%3E)
,重力加速度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Eg%3C%2Fmtext%3E%3C%2Fmath%3E)
,现将金属棒由静止释放,当金属棒沿导轨下滑距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmath%3E)
时,速度达到最大值
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmtext%3Ev%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmn%3E.%3C%2Fmn%3E%3C%2Fmath%3E)
求:
![](//tikupic.21cnjy.com/2023/12/15/44/51/44511e5418d06a2e751cb268769e8153_m_251x142.png)
-
-
-
(3)
金属棒沿导轨下滑距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmath%3E)
的过程中,电阻
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3ER%3C%2Fmtext%3E%3C%2Fmath%3E)
上产生的电热.
-
16.
如图所示,半径
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3ER%3C%2Fmtext%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
的光滑圆弧轨道
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EB%3C%2Fmtext%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmath%3E)
固定在竖直平面内,轨道的上端点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EB%3C%2Fmtext%3E%3C%2Fmath%3E)
和圆心
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EO%3C%2Fmtext%3E%3C%2Fmath%3E)
的连线与水平方向的夹角
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%CE%B8%3C%2Fmtext%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmath%3E)
,下端点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmath%3E)
为轨道的最低点且与光滑水平面相切。质量
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmtext%3Ek%3C%2Fmtext%3E%3Cmtext%3Eg%3C%2Fmtext%3E%3C%2Fmath%3E)
的小物块
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Ea%3C%2Fmtext%3E%3Cmn%3E%28%3C%2Fmn%3E%3C%2Fmath%3E)
可视为质点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
从空中
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EA%3C%2Fmtext%3E%3C%2Fmath%3E)
点以
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmtext%3Ev%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmath%3E)
的速度水平抛出,恰好从
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EB%3C%2Fmtext%3E%3C%2Fmath%3E)
点沿轨道切线方向进入轨道,经过
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmath%3E)
点后沿水平面并与静止在水平面上的另一小物块
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Eb%3C%2Fmtext%3E%3C%2Fmath%3E)
发生弹性碰撞,碰撞后物块
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Ea%3C%2Fmtext%3E%3C%2Fmath%3E)
恰好可以返回到圆弧轨道与圆心
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EO%3C%2Fmtext%3E%3C%2Fmath%3E)
等高处。
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmtext%3Eg%3C%2Fmtext%3E%3C%2Fmath%3E)
取
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Es%3C%2Fmtext%3E%3Cmtext%3Ei%3C%2Fmtext%3E%3Cmtext%3En%3C%2Fmtext%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
求:
![](//tikupic.21cnjy.com/2023/10/12/bd/78/bd781c23e52472184db05fe810e8ef24_168x210.png)
-
(1)
物块
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Ea%3C%2Fmtext%3E%3C%2Fmath%3E)
由
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EA%3C%2Fmtext%3E%3C%2Fmath%3E)
到
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EB%3C%2Fmtext%3E%3C%2Fmath%3E)
的运动时间,以及
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EA%3C%2Fmtext%3E%3C%2Fmath%3E)
、
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EB%3C%2Fmtext%3E%3C%2Fmath%3E)
两点的高度差;
-
(2)
小物块经过圆弧轨道上
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmath%3E)
点时对轨道的压力大小;
-
(3)
物块
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Eb%3C%2Fmtext%3E%3C%2Fmath%3E)
. 的质量;
(结果可用根式表示,不用化成最简形式。)