一、单选题:本大题共<strong><span>7</span></strong>小题,共<strong><span>28</span></strong>分。
-
1.
生活中曲线运动随处可见。关于曲线运动,下列说法正确的是( )
A . 匀速圆周运动是一种匀速运动
B . 平抛运动是匀变速曲线运动,斜抛运动是变加速曲线运动
C . 速度方向有时与曲线上的某点相切,有时与曲线上某点的切线垂直
D . 物体所受合外力恒定时,可能做曲线运动
-
-
3.
如图所示,轻质弹簧固定在光滑斜面底端,弹簧轴线与斜面平行,将一物块从斜面顶端无初速度释放,物块从开始运动,到弹簧被压缩到最短的整个过程中,下列说法正确的是( )
![](//tikupic.21cnjy.com/2024/04/28/42/78/427899f61c01b550e18be73e5a2bdcbf.jpeg)
A . 物块的速度先变大后变小
B . 物块的加速度先变大后交小
C . 该物块速度达到最大时,弹簧处于原长
D . 从刚接触弹簧到压缩弹簧至最短的过程中,该物块机械能守恒
-
4.
2024年央视春晚舞蹈节目《锦鲤》华丽登场,舞者巧借威亚展现别样东方美,寓意鱼跃龙门好运连连。如图所示,图甲为吊威亚表演者的照片,图乙为其简化示意图,工作人员 A以速度v沿直线水平向左匀速拉轻绳,表演者 B在空中升起,则在此过程中( )
![](//tikupic.21cnjy.com/2024/04/28/2f/78/2f787f08b8abe796cf3987ed728d64ae.jpeg)
A . 表演者B匀速上升
B . 表演者B上升速度越来越小
C . 表演者B处于超重状态
D . 经过图示位置
时, A与B的速度大小之比为
-
-
6.
北斗卫星导航系统是我国自行研制的全球卫星导航系统,由55颗卫是组成。如图所示,人造地球卫星A、B均做匀速圆周运动,卫星B为地球静止卫星,C为地球赤道表面随地球一起自转的物体。若某时刻A、B、C与地心O在同一平面内,且
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3EO%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3EA%3C%2Fmi%3E%3Cmo%3E%E2%8A%A5%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3EA%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
, 下列说法正确的是( )
![](//tikupic.21cnjy.com/2024/04/28/17/c7/17c79989d3c6a714b212d1ffee868d94.png)
A . 卫星B的线速度小于物体c的线速度
B . 卫星A、B的线速度之比为
C . 卫星A、B周期之比
D . 物体C的向心加速度大于卫星A的向心加速度
-
二、多选题:本大题共<strong><span>3</span></strong>小题,共<strong><span>12</span></strong>分。
-
8.
关于功和能量的说法,下列说法正确的是( )
A . 做变速运动的物体机械能可能守恒
B . 动能不变的物体,一定处于平衡状态
C . 在有阻力的情况下,物体重力做功不等于重力势能的减少量
D . 合外力做功为零,物体的机械能不一定守恒
-
-
10.
竖直平面内有一个固定的四分之一圆弧AB,OA为水平半径,现从圆心O处以不同的初速度水平抛出许多个相同质量的小球。小球可以看作质点,不计空气阻力,当小球落到圆弧上时( )
![](//tikupic.21cnjy.com/2024/04/28/25/4e/254ee0040c5830eab90128734ba71169.jpeg)
A . 小球速度的反向延长线不可能过OA的中点
B . 小球落在圆弧AB中点处时的动能最大
C . 小球动能最小的位置在圆弧AB中点的上方
D . 小球落到圆弧上时的动能从圆弧A点到B点先增大后减小
三、实验题:本大题共<strong><span>2</span></strong>小题,共<strong><span>16</span></strong>分。
-
11.
某同学用如图甲所示装置测量当地的重力加速度,器材如下:一端有挡板、长为 L的光滑木板,一把刻度尺,一个质量为 m的重物,一劲度系数为 k的轻弹簧。实验步骤如下:
甲
![](//tikupic.21cnjy.com/2024/04/28/f3/40/f34001ee3d2c2be0d638e950937eb495.jpeg)
-
-
-
(3)
将木板的右端缓慢抬高不同的高度,测出弹簧的长度 x
1、x
2...和此时木板右端到水平面的高度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Eh%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
、
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Eh%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%E2%8B%AF%3C%2Fmo%3E%3C%2Fmath%3E)
, 以x为纵轴,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%28%3C%2Fmo%3E%3C%2Fmath%3E)
选填“h”或“
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Eh%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
”
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E)
为横轴,作出的图像如图乙所示,其图像斜率大小为P,则当地的重力加速度为
,图像纵轴截距的物理意义是
。
-
12.
洗手后我们往往都有“甩水”的动作,某实验小组对此进行了“关于甩手动作物理原理”的研究。如图所示是由每秒25帧的频闪照片合成的图片,记录了手臂各部位在不同时刻的位置信息。以下面的简化模型分析甩手运动:将人的上肢简化由上臂、前臂和手掌组成,认为在甩手过程中,上臂可以绕肩关节转动,前臂可以绕肘关节 M转动,手掌可以绕腕关节 N转动。图中的A、B、C是甩手动作最后3帧照片指尖的位置,M、N是最后1帧照片的时关节和腕关节的位置。已知图中任意两点间的实际距离都可以通过照片上的距离根据比例尺折算测得。
-
(1)
甩手时很容易将手上的水滴甩掉,这是因为水滴做
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%28%3C%2Fmo%3E%3C%2Fmath%3E)
选填“近心”或“离心”或“匀速圆周”
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E)
运动。
-
(2)
照片中实验者手臂自然下垂时肩膀到指尖的距离为13cm,而相应的实际距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E65%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Ec%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%3A%3C%2Fmo%3E%3C%2Fmath%3E)
照片中A、B两点间距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E5.2%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Ec%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
, 则A、B两点的实际距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Ec%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%3A%3C%2Fmo%3E%3C%2Fmath%3E)
由此可以计算指尖实际在A、B间运动的平均速度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%3E%3C%2Fmath%3E)
, 并粗略认为这就是指尖过B点的线速度。同理,得到BN的实际距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E17%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Ec%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%3A%3C%2Fmo%3E%3C%2Fmath%3E)
计算指尖在B处绕N点转动的向心加速度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3En%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3C%2Fmath%3E)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%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%3Cmo%3E%28%3C%2Fmo%3E%3C%2Fmath%3E)
结果均保留两位有效数字
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E)
![](//tikupic.21cnjy.com/2024/04/28/ba/62/ba6256e07d97791a33574c39f89e3591.jpeg)
-
(3)
下列各项分析中最不合理的一项是( )
A . 近似认为指尖在A、B 间运动时绕M点转动,在B、C间运动时绕N点转动
B . 将指尖在A、B间运动的平均速度大小近似认为是指尖经过B点时的瞬时速度大小
C . 指尖在B、C间运动的加速度是指尖经过B点时的向心加速度
D . 指尖在A、B之间运动的速度比在B、C之间的大
四、计算题:本大题共<strong><span>3</span></strong>小题,共<strong><span>44</span></strong>分。
-
13.
一根长
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3EL%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1.44%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
的滑杆固定在竖直平面内,且与竖直方向夹角
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3E%CE%B8%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E37%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%98%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
如图所示。一个质量
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1.0%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Ek%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Eg%3C%2Fmi%3E%3C%2Fmath%3E)
的小球套在滑杆上,小球与滑杆的动摩擦因数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3E%CE%BC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.75%3C%2Fmn%3E%3C%2Fmath%3E)
。最大静摩擦力等于滑动摩擦力,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Eg%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E10%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%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%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Ei%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3En%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E37%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%98%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.6%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Ec%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Eo%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E37%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%98%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.8%3C%2Fmn%3E%3C%2Fmath%3E)
。试求:
![](//tikupic.21cnjy.com/2024/04/28/bd/33/bd338570c6fdbf87170f8b816c44cbf4.jpeg)
-
(1)
小球在水平向右的
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
作用下恰好不下滑,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
值为多大?
-
(2)
若改成水平向左的力
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E7.5%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3EN%3C%2Fmi%3E%3C%2Fmath%3E)
作用,使小球从A点运动到B点.小球到达B点时拉力
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的瞬时功率为多大?
-
14.
我国在航天和星际探测上取得了令世界瞩目的成就,并计划于2033年实现首次载人探测火星。据资料显示火星质量是地球的
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E20%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 直径约为地球的
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 地球半径为 R,地球表面重力加速度为 g,忽略火星自转的影响。试求:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%28%3C%2Fmo%3E%3C%2Fmath%3E)
用已知量g, R来表示
-
-
-
(3)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2022%3C%2Fmn%3E%3C%2Fmath%3E)
年12月1日,火星距离地球最近,约为81452214km,此时是发射火星探测器的最佳时期。
已知火星的公转周期约是地球公转周期的
倍,认为地球和火星在同一平面上、沿同一方向绕太阳做匀速圆周运动,求下一次火星与地球相距最近要再过多少年
结果保留两位有效数字![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E)
![](//tikupic.21cnjy.com/2024/04/28/11/e5/11e50202fa405e5c5d8423052f67a332.jpeg)
-
15.
如图所示,一光滑圆弧轨道ABCD固定在竖直平面内,半径
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3ER%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E16%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
, 圆弧轨道的圆心O在圆弧最低点B的正上方,其中
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3E%E2%88%A0%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3EA%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3EO%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E53%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%98%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
。圆弧轨道左侧有一顺时针方向匀速转动的水平传送带,传送带上表面与圆弧轨道的圆心O在同一高度。现将可视为质点的物块P从传送带左端M由静止释放,离开传送带右端N时恰好与传送带共速,随后物块P从N点水平抛出,恰好从A点沿切线方向进入圆弧轨道,已知物块P与传送带之间的动摩擦因数为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E0.5%3C%2Fmn%3E%3C%2Fmath%3E)
, 物块P的质量
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Ek%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Eg%3C%2Fmi%3E%3C%2Fmath%3E)
, 重力加速度 g取
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E10%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%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%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Ei%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3En%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E53%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%98%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.8%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Ec%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Eo%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E53%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%98%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.6%3C%2Fmn%3E%3C%2Fmath%3E)
求:
![](//tikupic.21cnjy.com/2024/04/28/3f/64/3f6453490ff0f729f1e07a4c51768504.jpeg)
-
-
(2)
与不放物块P时相比,电动机要多消耗多少能量?
-
(3)
物块P第一次脱离圆弧时的位置和圆心的连线与水平方向的夹角为多大
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%3F%3C%2Fmo%3E%3Cmo%3E%28%3C%2Fmo%3E%3C%2Fmath%3E)
可用三角函数表示