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Unformatted text preview: Lecture #5 Part #1 ABSOLUTE DEPENDENT MOTION ANALYSIS OF TWO PARTICLES Today ` s Objectives : Students will be able to: 1. Relate the positions, velocities, and accelerations of particles undergoing dependent motion. InClass Activities : Reading Quiz Applications Define Dependent Motion Develop Position, Velocity, and Acceleration Relationships Concept Quiz Group Problem Solving Attention Quiz READING QUIZ 1. When particles are interconnected by a cable, the motions of the particles are ______ A) always independent. B) always dependent. C) not always dependent. D) None of the above. 2. If the motion of one particle is dependent on that of another particle, each coordinate axis system for the particles _______ A) should be directed along the path of motion. B) can be directed anywhere. C) should have the same origin. D) None of the above. APPLICATIONS The cable and pulley system shown can be used to modify the speed of the mine car, A, relative to the speed of the motor, M. It is important to establish the relationships between the various motions in order to determine the power requirements for the motor and the tension in the cable. For instance, if the speed of the cable (P) is known because we know the motor characteristics, how can we determine the speed of the mine car? Will the slope of the track have any impact on the answer? APPLICATIONS (continued) Rope and pulley arrangements are often used to assist in lifting heavy objects. The total lifting force required from the truck depends on both the weight and the acceleration of the cabinet. How can we determine the acceleration and velocity of the cabinet if the acceleration of the truck is known? DEPENDENT MOTION (Section 12.9) In many kinematics problems, the motion of one object will depend on the motion of another object. The motion of each block can be related mathematically by defining position coordinates , s A and s B . Each coordinate axis is defined from a fixed point or datum line , measured positive along each plane in the direction of motion of each block. The blocks in this figure are connected by an inextensible cord wrapped around a pulley. If block A moves downward along the inclined plane, block B will move up the other incline. DEPENDENT MOTION (continued) In this example, position coordinates s A and s B can be defined from fixed datum lines extending from the center of the pulley along each incline to blocks A and B. If the cord has a fixed length , the position coordinates s A and s B are related mathematically by the equation s A + l CD + s B = l T Here l T is the total cord length and l CD is the length of cord passing over the arc CD on the pulley. DEPENDENT MOTION (continued) The negative sign indicates that as A moves down the incline (positive s A direction), B moves up the incline (negative s B direction)....
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This note was uploaded on 02/27/2012 for the course DYNAMICS 440:222 taught by Professor Pengsong during the Spring '11 term at Rutgers.
 Spring '11
 PENGSONG

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