Id216_fall2011_wk4_m - Product Design Engineering ID216 KAIST Week 4 Mechanics I Statics Seok-Hyung Bae(seokhyung.bae@kaist.ac.kr Product Design

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Week 4: Mechanics I - Statics 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., Eisenberg, Vector Mechanics for Engineers: Statics /Dynamics, McGraw Hill, 2007 1
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Product Design Engineering ID216 KAIST What’s Mechanics Science that describes and predicts the conditions of rest or motion of bodies under the action of forces Mechanics is an applied science - it is not an abstract or pure science; mechanics is the foundation of most engineering sciences and is an indispensable prerequisite to their study. Categories of Mechanics: Rigid bodies: Statics & Dynamics Deformable bodies Fluids 2
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Product Design Engineering ID216 KAIST Vectors Vector: parameters possessing magnitude and direction which add according to the parallelogram law (e.g., displacements, velocities, accelerations) Scalar: parameters possessing magnitude but not direction (e.g., mass, volume, temperature) Equal vectors have the same magnitude and direction. Negative vector of a given vector has the same magnitude and the opposite direction. 3
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Product Design Engineering ID216 KAIST Addition of Vectors Parallelogram rule for vector addition Triangle rule for vector addition Law of cosines: Law of sines: Vector addition is commutative C.f. Multiplication of a vector by a scalar C.f. Vector subtraction 4 B PQ Q P R cos 2 2 2 2 P C Q P B Q A sin sin sin B C
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Product Design Engineering ID216 KAIST Problem 1 The two forces act on a bolt at A. Determine their resultant. 5
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Product Design Engineering ID216 KAIST Problem 2 A barge is pulled by two tugboats. If the resultant of the forces exerted by the tugboats is 5000 N directed along the axis of the barge, determine: (a) the tension in each of the ropes for = 45 , (b) the value of for which the tension in rope 2 is a minimum. 6
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Product Design Engineering ID216 KAIST Rectangular Components of a Vector A vector can be resolved into perpendicular components so that the resulting parallelogram is a rectangle. Perpendicular unit vectors: parallel to the x and y axes Vector components may be expressed as products of the unit vectors with the scalar magnitudes of the vector components. 7 y x F F F sin , cos ; F F F F F F y x y x j i F j i ,
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Product Design Engineering ID216 KAIST Vector Addition by Summing Components 8           j i j i j i j i j i S Q P R y x y y y x x x y x y x y x R R S Q P S Q P S S Q Q P P x y y x R R R R R 1 2 2 tan
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Problem 3 Four forces act on bolt A as shown. Determine the resultant of the force on the bolt. 9
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This note was uploaded on 12/06/2011 for the course ID 216 taught by Professor Bae during the Fall '11 term at Korea Advanced Institute of Science and Technology.

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Id216_fall2011_wk4_m - Product Design Engineering ID216 KAIST Week 4 Mechanics I Statics Seok-Hyung Bae(seokhyung.bae@kaist.ac.kr Product Design

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