高中物理曲线运动同步练习 7页

1.图（5）中，是两个共轴圆筒的横截面，外筒半径为，内筒半径比小的多，可以忽略不计，筒的两端是封闭的，两筒之间抽成真空。两筒以相同的角速度绕其中心轴线（图中垂直于纸面）做匀速转动。设从筒内部可以通过窄缝（与筒的轴线平行）不断地向外射出两种不同速率的微粒，从处射出时的初速度的方向都是沿筒的半径方向，微粒到达筒后就附着在筒上。如果都不变，而取某一合适的值则（）A.有可能使微粒落在筒上的位置都在处一条与缝平行的窄条上B.有可能使微粒落在筒上的位置都在某一处如处一条与缝平行的窄条上C.有可能使微粒落在筒上的位置分别在某处如处和处与缝平行的窄条上D.只要时间足够长，筒上将到处都有微粒2.如图（7）所示的锥形圆筒内壁是光滑的，壁上有两个小球，它们的质量相同，各自在不同的水平面内做匀速圆周运动，可以判定，它们的线速度______；角速度_______；向心加速度_______；它们对筒壁的压力_______。（填大于，小于或等于）。3.一根长为的均匀细杆可以绕通过其一端的水平轴在竖直平面内转动，杆最初处于水平位置，杆上距为处放有小物体（可视为质点），杆与其上小物体最初均处于静止状态，如图（11）所示，若此杆突然以角速度绕轴转动，问当取什么值时，小物体与杆可能相碰？\n图（11）4.一光滑的圆锥体固定在水平桌面上，其轴线沿竖直方向，母线与轴线间的夹角为，如图（12）所示，一条长度为的绳（质量不计），一端固定在圆锥体的顶点处，另一端拴着一个质量为的小物体（物体可视为质点），物体以速率绕圆锥体的轴线做水平面内的匀速圆周运动。（1）当时求绳对物体的拉力；（2）当时求绳对物体的拉力。【试题答案】1.ABC由于两筒是同轴匀速转动，它们的角速度相同，而从筒射出的微粒只具有沿半径方向的速度，当微粒运动的距离为时所需时间为在这段时间里，若是两筒转过的角度为（是一段弧长对应的角度），则若（1）式中，其中无论取还是，都落在筒上的位置都在处一条与缝平行的窄条上；若（1）式中，落在筒上的位置都在某一处如处一条与缝平行的窄条上；若（1）式中，对应不同的不同则微粒落在筒上的位置分别为在某两处如处和处与缝平行的窄条上\n2.3.分析思路：物体相遇的条件是在相同的时间内物体的路程或位移相等。本题中是物体自由下落的位移与由于杆的转动而引起的相同时间内的杆的两位置与所在竖直线交点间的距离相等，从图（16）（a）中看出，此最大距离为长，即。物体做自由落体，起始速度较小，速度逐渐变大。而杆在匀速转动，在相同时间内，大于自由落体高度，当两者相等时则相遇，相遇的最大距离为，即为的最大值。若再增大时，当物体落至点时，杆已转过位置。则此时不可能相碰，但当再增大时，即在物体没有到达之前杆可能再次转入区域。这种情况物体与杆也能相碰，这种情况相遇的最长时间是在点相遇，此时的为这种情况的最小值，只要大于该值均能在区域内相碰。如图（16）（b）。图（16）解题方法：应用自由落体求出物体下落到点所用的时间，再由圆周运动求解出杆到所用的时间。相遇具有距离相等，同时还具有等时性。解：小物体作自由落体运动，在时间里下落。此时点转过角度由以上两式得：可见在不同的角度时相遇要有不同的值，小物体追上杆的临界情况是在点相碰，所以有：消去时间有：\n若很大时，即转一圈后追上小物体并与小物体相碰，如图（16）（b）所示。这时杆转过的角度此为第二种情况相遇的最小角速度。故物体与杆相遇的条件是：4.分析思路：物体在水平面内做匀速圆周运动，由重力、拉力、支持力提供向心力，当角速度很小时，物体在圆锥体上运动。当增大，都发生变化，且增大，减小，当大到一定值时，物体将离开锥面做圆锥摆运动。显然当时的线速度值为物体的临界速度。通过比较已知速度与临界速度的关系讨论出物体所处的状态，由物体的受力列出相应的牛顿方程求解。解题方法：由物体的受力分析，令求出物体的临界速度，比较临界速度与的关系，分清物体在不同情况下的受力，然后应用牛顿定律求解。解：如图（17）所示，设物体在圆锥体上做匀速圆周运动，物体受绳对它的拉力，重力为，锥面的支持力。因为物体做匀速圆周运动，所以三个力的合力必沿半径指向圆心，是物体做圆运动的向心力。将三力沿水平方向与竖直方向分解，据牛顿第二定律：图（17）由(1)式知，当增大时，所需的向心力要增大，式中一定，只能使增大，因同时要保证(2)式成立，将减小，当增大到某一值时，减小为0，当继续增大时，物体将离开锥面，都变大，此时物体做圆锥摆运动。先求物体能在圆锥体上做水平匀速圆周运动的最大速度\n此时由(1)(2)两式得：（1）因，物体在圆锥体上做圆运动满足方程联立(3)(4)得：（2）因，此时物体离开了圆锥体，摆线与轴线的夹角受力分析如图（18）所示：图（18）满足下列方程由(5)式得由(6)式得\n年级高中　学科物理版本期数内容标题　　曲线运动---离心现象及其应用3分类索引号　　G.624.6分类索引描述　　考试试题与题解主题词　　曲线运动---离心现象及其应用3栏目名称　试题库供稿老师审稿老师录入一校二校审核读书人是世间幸福人，因为他除了拥有现实的世界之外，还拥有另一个更为浩瀚也更为丰富的世界。9JWKffwvG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRWXmA&UE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmUE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z8vG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRWXmA&UE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^G89AmUE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z8vG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRWXmA&UE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmUE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv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