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Unformatted text preview: Chapter 11 Chapter 11 Kinematics of Particles Kinematics of Particles EMEC 3730 Fall 2007 niversity of Nebraska University of Nebraska 1 11.1 Introduction Definitions: i ti d f th t f ti Ki ti i d t Kinematics : study of the geometry of motion. Kinematics is used to relate displacement, velocity, acceleration, and time without reference to the cause of motion. Kinetics : study of the relations existing between the forces acting on a body, the mass of the body, and the motion of the body. Kinetics is used to predict the motion caused by given forces or to determine the forces required to produce a given motion. Rectilinear motion: position, velocity, and acceleration of a particle as it moves along a straight line. Curvilinear motion : position, velocity, and acceleration of a particle as it moves along a curved line in two or three dimensions. 2 11.2 Rectilinear Motion: Position, Velocity &amp; Acceleration , y Particle moving along a straight line is said be in ctilinear motion to be in rectilinear motion . Position coordinate of a particle is defined by positive or negative distance of particle from a fixed origin on the line. The motion of a particle is known if the p position coordinate for particle is known for every value of time t . Motion of the particle may be expressed in the form of a function, e.g., 3 2 6 t t x = or in the form of a graph x vs. t . 3 11.2 Rectilinear Motion: Position, Velocity &amp; Acceleration , y Consider particle which occupies position P at time and P at + Dt , t x = Average velocity Instantaneous velocity may be positive or egative Magnitude of velocity is referred t x v t = = lim Instantaneous velocity negative. Magnitude of velocity is referred to as particle speed . From the definition of a derivative, dt dx t x v t = = lim e.g., 3 2 6 t t x = 4 2 3 12 t t dt dx v = = 11.2 Rectilinear Motion: Position, Velocity &amp; Acceleration , y Consider particle with velocity v at time t nd t t and v at t + Dt , Instantaneous acceleration t v a t = = lim Instantaneous acceleration may be: positive: increasing positive velocity or decreasing negative velocity- negative: decreasing positive velocity or increasing negative velocity. g g y 5 11.2 Rectilinear Motion: Position, Velocity &amp; Acceleration , y From the definition of a derivative, dt x d dt dv t v a t g lim 2 2 2 = = = t dt dv a t t v 6 12 3 12 e.g....
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