id216_fall2011_wk5_mechanics_II - Product Design...

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Week 5: Mechanics II - Dynamics Seok-Hyung Bae (seokhyung.bae@kaist.ac.kr) Product Design Engineering ID216 KAIST
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Product Design Engineering ID216 KAIST Contents Beer, Johnston Jr., Clausen, Vector Mechanics for Engineers: Dynamics , McGraw Hill, 2007 1
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Product Design Engineering ID216 KAIST Dynamics Deals with the analysis of bodies in motion. Includes: 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. 2
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Product Design Engineering ID216 KAIST Curvilinear Motion of Particles Particle moving along a curve other than a straight line Position vector r of a particle at time t Cf. Instantaneous velocity Instantaneous speed Instantaneous acceleration 3 dt d t t r r v 0 lim dt ds t s v t 0 lim t t at r r r dt d t t v v a 0 lim
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Product Design Engineering ID216 KAIST Derivative of the vector function: Derivative of vector sum: Derivative of product of scalar and vector functions: Derivative of scalar product and vector product: Rate of change of a vector: a function of time Derivatives of Vector Functions 4     u u u u u du d u u P P P P 0 0 lim lim   du d du d du d Q P Q P   du d f du df du f d P P P     du d du d du d du d du d du d Q P Q P Q P Q P Q P Q P ; P P dt d
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Product Design Engineering ID216 KAIST Rectilinear Components Position vector Velocity vector Acceleration vector 5 k j i r z y x k j i k j i k j i v z y x v v v z y x dt dz dt dy dt dx k j i k j i k j i a z y x a a a z y x dt z d dt y d dt x d 2 2 2 2 2 2
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Product Design Engineering ID216 KAIST Problem 1 A projectile is fired from the edge of a cliff. Neglecting air resistance, find (a) the horizontal distance from the gun to the point where the projectile strikes the ground, (b) the greatest elevation above the ground reached by the projectile. 6
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Product Design Engineering ID216 KAIST Motion Relative to a Frame in Translation Designate one frame as the fixed frame of reference; all other frames not rigidly attached to the fixed reference frame are moving frames of reference. The frame of reference
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id216_fall2011_wk5_mechanics_II - Product Design...

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