理论力学复习题.doc

Total Review of Theoretical Mechanics一、静力学（STATICS）1、由AC和CD构成的组合梁通过铰链C连接。它的支承和受力如图所示。已知均布载荷强度q=10KN/m，力偶矩M= 40 KNm，不计梁重。求支座A，B，D的约束力和铰链C处所受的力。1. Beams AC and CD are joined by a smooth pin C, Knowing q=10KN/m, M=40KNm, other conditions are shown as figure. Determine the reaction forces at points A, B, D, C. Neglect the weights of the beams.2、水平梁AB由铰链A和杆BC所支持，如图所示。在梁上D处用销子安装半径为r=0.1m的滑轮。有一跨过滑轮的绳子，其一端水平地系于墙上，另一端悬挂有重P=1800N的重物。如AD=0.2m， BD=0.4m， ，且不计梁、杆、滑轮和绳的重量。求铰链A处的约束力和杆BC的内力。2. A bracket consists of members AB, CB and pulley D as shown in figure. A string supporting a weight P=1800N passes through over pulley D, the other end of the string is secured to the wall. r=0.1m, AD=0.2m, BD=0.4m, j=45o . Determine the reaction forces at points A and the internal force of rod BC. The weight of the members and pulley are negligible.3、在图示连续梁中，已知q，a及 。不计梁的自重。求梁在A，B，C三处的约束力。3. Beams AB and BC are joined by a smooth pin B. Knowing q, a, and q . The weights of the beams are negligible. Determine the reaction forces at points A, B and C. 4、图示构架中，物体重1200N，由细绳跨过滑轮E而水平系于墙上，尺寸如图，不计杆和滑轮的重量。求支承A和B处的约束力。4. A posite truss is shown as figure. A block of weight 1200N is connected to a string wrapped around the pulley E，the other end of the string is secured to the wall. Other conditions are shown as figure. The weights of links and pulley are negligible. Determine the reaction forces at points A and B.5、求A、B、C处的约束反力。5. Find the reaction forces at points A, B and C. The weights of the elements are negligible.6、图示构架中，各杆重均略去不计，B、C为光滑铰链，已知载荷P。试求固定端A及支座D的约束反力。6. A posite truss is shown as figure. The weights of links are negligible. The pins B and C are smooth pins. Knowing the load P. Other conditions are shown as figure. Determine the reaction forces at points A and B. 7、无重水平梁的支承和载荷如图所示。已知集中力F、力偶矩M和均布载荷q。求支座A和B处的约束力。7. A horizontal beam is shown as figure. The weight of the beam is negligible. Knowing F, M and q. Other conditions are shown as figure. Determine the reaction forces at points A and B.8、由AC和CD构成的组合梁通过铰链C连接。不计梁重。求A，B，D处的约束力和铰链C处所受的力。8. Beams AC and CD are joined by a smooth pin C. The weights of the beams are negligible. Other conditions are shown as figure. Determine the reaction forces at points A, B, D and C.二、运动学（KINEMATICS）填空题（1）题1图所示平面机构中，AB杆的A端靠在光滑墙上，B端铰接在滑块上，若选AB上的A为动点，滑块为动系，则A的相对运动为 以B为圆心，AB为半径的圆周运动。 。（2）圆盘以 t rads绕水平轴AB转动，盘上M点沿半径按OM4t2 cm的规律运动，如题2图所示。当t1s时，科氏加速度 24 cm/s 。（题1图）（题2图）（3）在题3图所示的公路上行驶的两车的速度均为20ms，图示瞬时，在A车中的观察者看来，B车的速度大小应为 386ms 。（题4图）（题3图）（4）平面机构如题4图所示，画出M点的速度方向 。1、四连杆机构由杆O1A、O2B及半圆形平扳ADB组成，动点M沿圆弧运动，如图所示。已知O1AO2B18cm，R18cm，sBMt2cm。求：t 3s时，M点的绝对速度和绝对加速度。1.Consider a mechanism of four connecting rods shown in the figure. The semi-circular plate ADB of radius R is supported by two parallel links, and O1AO2B18cm, R18cm.The angle of rotation of link is . At the same time, a moving particle M moves along the circular path in the plate, and sBMt2cm. Determine the absolute velocity and absolute acceleration of particle M at t =3s.2、如图所示，半径为R4cm的圆盘，以匀角速度o1.5rads绕O轴转动，并带动连有螺旋弹簧且紧压在圆盘上的杆CD，使该杆绕Ol轴转动。试求300时，杆CD的角速度与角加速度。2. As shown in the figure, the disk A of radius R4cm rotates about axis O with a constant angular velocity o1.5rads. Rod CD, which is free to rotate about the axis O1, is leaning against the disk. Find the angular velocity and acceleration of rod CD when 3003、如图所示，曲柄OA长为40cm，以等角速度0.5rads绕O轴转动，曲柄的A端推动水平板B使得杆BC上升，求300时，滑杆BC的速度和加速度。3.In the mechanism shown in the figure, crank OA of length l=40cm rotates about axis O with a constant angular velocity = 0.5 rad/s and pushes up a slide rod BC moving in a vertical runner. Determine the velocity and acceleration of slide rod BC when300 . 4、图示机构中，已知：OA0.1m，BD0.1m，DE0.1m，EF0.1m；曲柄OA的角速度4rads。在图示位置时，曲柄OA与水平线OB垂直；且B，D和F在同一铅直线上，又DE垂直于EF。求杆EF的角速度和点F的速度。4.Consider a mechanism shown in the figure, OA0.1m, BD0.1m, DE0.1m, EF0.1m, the crank OA rotates with uniform 4rads. At the instant shown in the figure, OAOB, point B, D and F in the same vertical line, and DEEF. Determine the angular velocity of rod EF and the velocity of point F for this position. 5、在图示机构中，曲柄OA长为r ，绕O轴以等角速度o转动，AB6r，BC3r。求图示位置时，滑块C的速度和加速度。5.In the mechanism, OA= r , rod OA rotates with uniform o. At the moment, ABBC, AB6r，BC3r . Find the velocity and acceleration of block C at this moment.6、已知如图所示平面机构中，ABCDl，OAO1Br ，滚子半径为R，沿水平直线作纯滚动。某瞬时，AB在水平位置，OA与OlB分别在铅垂位置，这时BCD，曲柄OA的角速度和角加速度分别为及，求该瞬时连杆AB中点C的速度、加速度以及滚子的角速度、角加速度。6.In the planar mechanism shown in the figure, C is the center of rod AB, ABCDl, OAO1Br , the wheel of radius R is rolling without slipping on a horizontal plane. At the moment, rod AB is horizontal, OA and OlB are vertical lines, BCD. In addition, the angular velocity and angular acceleration of rod OA are known when BCD. Find the velocity and acceleration at point C, the angular velocity and acceleration of the wheel.三、动力学( DYNAMICS)1、（概念题）匀质轮重为P，半径为 r ，在水平面上作纯滚动。某瞬时角速度 ，角加速度为 ，求轮对质心C 的转动惯量，轮的动量、动能，对质心轴的动量矩，向质心简化的惯性力系主矢与主矩，并在图上画出惯性力系主矢与主矩。1.The weight of a homogeneous wheel is P, its radius is r. It is purely rolling on the horizontal plane. At a given time, the angle velocity is , the angle acceleration is . Determine the moment of inertia of the wheel with respect to the center of mass C, the momentum and the kinetic energy of the wheel, the angular momentum with respect to C, the principle vector and the principle moment of the inertial force system with respect to the center of mass. Show your answer on the diagram.2、两根质量各为8 kg的均质细杆固连成T 字型，可绕通过O点的水平轴转动，当OA处于水平位置时, T 形杆具有角速度 =4rad/s 。求该瞬时轴承O处的约束反力。2. A rod formed by two thin homogeneous rods fixed together takes the shape of the letter “T”. It rotates around a horizontal axis through the center O. The angular velocity of the rod is w=4rad/s when OA is in the horizontal position. Determine the reaction of the bearing O at that moment.3、重物A质量为m1，系在绳子上，绳子跨过不计质量的固定滑轮C，并绕在鼓轮B上，如图所示。由于重物下降，带动了鼓轮B，使它沿水平轨道只滚不滑。设鼓轮大小半径为分别为R和r ，总质量为m2，对于其水平轴O的回转半径为 。求重物A下降的加速度。3. In the system shown in the diagram, the mass of load A is m1, it hangs from the rope which passes over the pulley C (the weight of pulley C can be neglected), the other end of the rope is wounded on a tub wheel B. Under the action of gravity the system starts to move, and the wheel B rolls without slipping. The mass of wheel B is m2 ,its radius of gyration with respect to the axis O is . Knowing R and r, determine the acceleration of load A when it falls. (At the initial instant the whole system is at rest) 4、行星齿轮传动机构处于垂直平面内。 动齿轮半径r ,重P, 视为均质圆盘；曲柄重Q, 长L, 其上作用一力偶, 矩为M(常量), 曲柄由静止开始转动；求曲柄转过 角后的角速度和角加速度。4. A planetary gearing is placed in a vertical plane, the movable gear of radius r and weight P may be regarded as a homogeneous disc. The crank of weight Q and length L is subjected to a couple with moment M=constant, giving rise to a rotation starting from rest. Determine the angular velocity and the angular acceleration of the crank when the crank has rotated through5、在图示机构中，沿斜面向上作纯滚动的圆柱体A 和鼓轮O 均为均质物体，各重为P和Q，半径均为R，绳子不可伸长，其质量不计，斜面倾角 ，如在鼓轮上作用一常力偶矩M， 试求：(1)鼓轮的角加速度？ (2)绳子的拉力？ (3)轴承 处的约束反力？ (4)圆柱体与斜面间的摩擦力（不计滚动摩擦）？ 5. In the mechanism shown below the cylinder and the tub wheel O are all homogenous, the weight of the two cylinders are P and Q, the radii of both are R. They are performing pure rolling. The rope (without weight) can not be stretched, the angle of inclination is . A constant torque M is acting on the tub wheel. Determine (1)the angle acceleration of the tub wheel, (2) the tensile force of the rope, (3) the reaction forces at point O on the bearing, (4)the friction force between the cylinder and the inclined plane (neglecting the rolling friction).6、重150N半径为8cm的均质圆盘与重60N、长24cm的均质杆AB在B处用铰链连接。 系统由图示位置无初速地释放。求系统经过最低位置B点时AB杆B处的速度以及支座A的约束反力。6. A circular homogeneous disc of weight 150N and radius 8cm, a homogeneous rod of weight 60 N and length 24cm are joined at the point B. The system is released without initial velocity from the position shown in the diagram. Determine the velocity of the point B and the reaction force of the constraint at A when the system passes through its lowest position.（备注：以下两题要求用动静法求解）(Remark: Solve the following problems by DAlemberts principle)7、图示长方形均质平板，质量为27kg，由两个销钉A和B悬挂。如果突然撤去销B，求在撤去销B的瞬时平板的角加速度和销A处的约束力。7. A homogeneous 27-kg rectangular plate is pined at A and B. Determine the angular acceleration of the plate and the reaction force at A at a moment at which the joint B suddenly takes away.8、如图所示，质量为m1的物体A下落时，带动质量为m2的均质圆盘B转动，不计支架和绳子的重量及轴上的摩擦，BC=a，盘B的半径为R，求固定端C的约束力。8. In the mechanism shown in the diagram, a load of mass m1 is connected to a string wrapped around a homogenous disk B, the disk is of radius R and mass m2, BC=a. Neglect the friction force at axis B, and the weights of string and bracket are negligible. Determine the reaction forces at the fixed end C.