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Theoretical Mechanics Examination

Central South University

2011—2012学年第 1 学期，72学时，4.5学分 考试形式：闭卷，时间：100分钟

1 calculation （20 scores）

Structure shown in Fig.1. Loading weight W with a string around the pulley E with radius R =10cm connected to the rod CD, a moment of couple M=60W ( Ncm ) acting on rod BC, the other dimensions are in Fig.1 Neglecting the weight of rod, pulley and string. Please determine the internal force of rod AC and the reaction force at D jiont.

40cm B 30cm M C B l O1 （Fig.1） （Fig.2）

G R A 60cm D 30cm W E A 600 C D ??l O 2 calculation （15 scores）

A mechanism shown in Fig.2.The crank OA rotates with angular velocity ??. Knowing OA=O1B=l，AB=2l. At the instant shown in the figure, the angle of rocker AB with horizontal line is 600 , C is located in the midpoint of AB, rod OA is vertical, rod O1B is horizontal. Please determine the velocity of rod CD at this instant.

3 calculation （18 scores）

The mechanism shown in Fig.3 , wheel A (radius r )rolls on the plane surface without slipping with the uniform angular velocity ?, the length of rod AB is 4r , Sleeve D is connected by pin with rod AB at the midpoint of AB, at the instant shown in the figure, rod OC is vertical, OD=2r. Please determine the angular velocity and angular acceleration of rod OC respectively.

B C （Fig.3） （Fig.4） D

30 0B M A r ??C300 A O 4 calculation （18 scores）

The system shown in the Fig.4. The homogeneous disks B and C each are of mass 2m and radius R, the mass of loading A is m, a constant moment of couple M acting on disk B, disk C rolls on the rough inclined surface without slipping. Neglecting the mass of string, no sliping between string and disk B.At the initial instant the whole system is at rest, please determine the acceleration of loading A and the friction force of disk C and the tensile force of the string BC when the loading falls through a distance S.

5 calculation （15 scores）

Please use the D'Alembert's principle to solve follow question:

Homogeneous rod AB is of mass m and length l, whose two ends are respectively with two rope suspension and B end is on the smooth 450 inclined surface all the time, please determine the angular acceleration of rod AB, the tensile force of the string at A end and reaction force of smooth inclined surface to AB at the instant of string cutting at B end.

A B l 450

D A B F l C （Fig.5） （Fig.6）

??W O

6 calculation （14 scores）

Please use the theorem of virtual displacement to solve follow question:

The mechanism shown in Fig.6. Homogeneous rod OA is of weight W and length l , neglecting the weight of rod AD, which passes through sleeve B, the stiffness of the spring between BD is K, when ??=00, the spring is at its original length, OA=OB=l , please determine the value of force F when the system is in equilibrium at a certain angle ??