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1、名师精编优秀教案第五章曲线运动5.7 生活中的圆周运动（1）主备人：张松审核人：胡怀平 2011-3-12【学习目标】1了解火车转弯、汽车过拱桥向心力的来源，会受力分析2学会用牛顿运动定律求解圆周运动力学问题【问题导学】1火车转弯 火车车轮的结构特点设内外轨间的距离为L，内外轨的高度差为h，火车转弯的半径为R，火车转弯的规定速度为 v0，由图 1 所示力的合成得向心力为F合=mgtanmgsin=mgLh由牛顿第二定律得：F合=mRv20所以 mgLh=mRv20v0=LRgh。即 火 车 转 弯 的 规 定 速 度（2）对火车转弯时速度与向心力的讨论a当火车以规定速度v0转弯时，合力F 等于
2、向心力，这时轮缘与内外轨均无侧压力。b当火车转弯速度vv0时，该合力F 小于向心力，外轨向内挤压轮缘，提供侧压力，与 F 共同充当向心力。c当火车转弯速度vv0时，该合力F 大于向心力，内轨向外侧挤压轮缘，产生的侧压力与该合力F 共同充当向心力。2汽车过桥 汽车过拱桥时，车对桥的压力小于其重力汽车在桥上运动经过最高点时，汽车所受重力G 及桥对其支持力FN提供向心力。如图2 所示。GFN=mRv2所以 FN=GRmv2汽车对桥的压力与桥对汽车的支持力是一对作用力与反作图 1（图 2）名师精编优秀教案用力，故汽车对桥的压力小于其重力。思考汽车的速度不断增大时，会发生什么现象？由上面表达式FN=GR
3、mv2可以看出，v 越大，FN越小。当FN=0 时，由 G=mRv2可得v=gR。若速度大于gR时，汽车所需的向心力会大于重力，这时汽车将“飞”离桥面。我们看摩托车越野赛时，常有摩托车飞起来的现象，就是这个原因。汽车过凹桥时，车对桥的压力大于其重力如图 3，汽车经过凹桥最低点时，受竖直向下的重力和竖直向上的支持力，其合力充当向 心 力.则 有：FN G=mRv2，所 以FN=G+mRv2=G+mRv2，大 于 车 的 重由牛顿第三定律知，车对桥的压力FN力，而且还可以看出，v 越大，车对桥的压力越大。思考汽车不在拱形桥的最高点或最低点时，如图4 所示，它的运动能用上面的方法求解吗？分析可以用上
4、面的方法求解，但要注意向心力的来源发生了变化。如图4，重力沿半径方向的分力和垂直桥面的支持力共同提供向心力。设此时汽车与圆心的连线和竖直方向的夹角为，则有mgcos FN=mRv2所以 FN=mgcosmRv2桥面支持力与夹角、车速 v 都有关。3航天器中的失重现象飞船环绕地球做匀速圆周运动，当飞船距地面高度为一二百千米时，它的轨道半径近似等于地球半径R，航天员受到的地球引力近似等于他在地面测得的体重mg。除了地球引力外，航天员还可能受到飞船座舱对他的支持力FN，引力与支持力的合力为他提供了绕地球做匀速圆周运动所需的向心力F=Rmv2，即mgFN=Rmv2也就是FN=m（gRv2）由此可以解出
5、，当v=gR时，座舱对航天员的支持力FN=0，航天员处于失重状态。思考地球可以看作一个巨大的拱形桥，桥面的半径就是地球半径R（约为 6400 km）。地面上有一辆汽车，重量是G=mg，地面对它的支持力是FN。汽车沿南北方向行驶，不断（图 3）（图 4）（图 5）文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S
6、4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10
7、S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R1
8、0S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R
9、10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10
10、R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G1
11、0R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G
12、10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8文档编码:CG1G2I6R1C4 HZ9O2Z10C8R7 ZY2G10R10S4L8名师精编优秀教案加速。如图 5 所示。会不会出现这样的情况：速度大到一定程度时，地面对车的支持力是零？这时驾驶员与座椅之间的压力是多少？驾驶员躯体各部分之间的压力是多少？他这时可能有什么感觉？其实，这和飞船的情况相似，当汽车速度达到v=gR时（代数计算可得v=7.9103 m/s），地面对车的支持力是零，这时汽车已经飞起来了，此时驾驶员与座椅间无压力。驾驶员、车都处于完全失重状态.驾驶员躯体各部分之间没有压
13、力，他会感到全身都飘起来了。【典型例题】1一辆卡车在丘陵地匀速行驶,地形如图所示，由于轮胎太旧，途中爆胎，爆胎可能性最大的地段应是（）Aa 处Bb 处Cc 处D d 处2一汽车通过拱形桥顶点时速度为10 m/s，车对桥顶的压力为车重的43，如果要使汽车在桥顶对桥面没有压力，车速至少为（）A15 m/s B20 m/s C25 m/s D 30 m/s 3.如图所示，半径为r 的圆筒，绕竖直中心轴OO旋转，小物块 a 靠在圆筒的内壁上，它与圆筒内壁间的动摩擦因数为，现要使 a 不下落，则圆筒转动的角速度 至少为（）A grBgCgrO O文档编码:CX3P1J10R9M8 HO7D10D4V5R
14、4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T
15、4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H
16、5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:
17、CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J
18、10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8
19、 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D1
20、0D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5名师精编优秀教案Dgr【课后巩固】1汽车以一定速率通过拱桥时，下列说法中正确的是（）A在最高点汽车对桥的压力大于汽车的重力B在最高点汽车对桥的压力等于汽车的重力C在最高点汽车对桥的压力小于汽车的重力D汽车以恒定的速率过桥时，汽
21、车所受的合力为零2.关于铁道转弯处内外铁轨间有高度差，下列说法中正确的是（）A.可以使火车顺利转弯，减少车轮与铁轨间的摩擦B.火车转弯时，火车的速度越小，车轮对内侧的铁轨测侧向压力越小C.火车转弯时，火车的速度越大，车轮对外侧的铁轨测侧向压力越大D.外铁轨略高于内铁轨，使得火车转弯时，由重力和支持力的合力提供了部分向心力3有一种大型游戏器械，它是一个圆筒形大容器，筒壁竖直，游客进入容器后靠筒壁站立，当圆筒开始转动，转速加快到一定程度时，突然地板塌落，游客发现自己没有落下去，这是因为（）A游客受到的筒壁的作用力垂直于筒壁B游客处于失重状态C游客受到的摩擦力等于重力D游客随着转速的增大有沿壁向上滑
22、动的趋势4汽车在倾斜的弯道上拐弯，如图所示，弯道的倾角为，半径为r，则汽车完全不靠摩擦力转弯的速率是(提示：转弯半径是水平的)()AsingrBcosgrCtangrDcotgr5如图所示，小物体位于半径为 R 的半球顶端，若给小物体以水平初速度v0时，小物体对球顶恰无压力，则()A物体立即离开球面做平抛运动B物体落地时水平位移为2RC物体的初速度0vgR文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O
23、3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文
24、档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX
25、3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10
26、R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 H
27、O7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D
28、4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4
29、ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5名师精编优秀教案D物体着地时速度方向与地面成45 角6如图所示，内表面光滑的半径为R 的半球形碗内，有一质量为m 的小球以角速度在水平面内做匀速圆周运动求该小球的运动平面离碗底的高度文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4
30、 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4
31、O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5
32、文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:C
33、X3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J1
34、0R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8
35、HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5文档编码:CX3P1J10R9M8 HO7D10D4V5R4 ZN5T4O3H7H5