Statics of Particles
Statics of Particles
Contents·Introduction（绪论）·ResultantofTwoForces（两个力的合力）·Vectors（矢量）·AdditionofVectors（矢量加和）·Resultantof SeveralConcurrentForces（多个力的合力）·Rectangular Components ofa Force:Unit Vectors（力的直角坐标分量：单位矢量）·Addition ofForcesbySummingComponents（通过分量相加求合力）·EquilibriumofaParticle（质点平衡条件）·Free-BodyDiagrams（受力简图）2
Contents • Introduction（绪论） • Resultant of Two Forces（两个力的合力） • Vectors（矢量） • Addition of Vectors（矢量加和） • Resultant of Several Concurrent Forces（多个力的合力） • Rectangular Components of a Force: Unit Vectors（力的直角坐标 分量：单位矢量） • Addition of Forces by Summing Components（通过分量相加求 合力） • Equilibrium of a Particle（质点平衡条件） • Free-Body Diagrams（受力简图） 2
Introduction: The objective for the current chapter is to investigate the effects of forceson particles:- replacing multiple forces acting on a particle with a singleequivalent or resultant force,- relations between forces acting on a particle that is in astate of equilibrium.. The focus on particles does not imply a restriction to miniscule bodiesRather, the study is restricted to analyses in which the size and shape ofthe bodies is not significant so that all forces may be assumed to beapplied at a single point.3
Introduction • The objective for the current chapter is to investigate the effects of forces on particles: - replacing multiple forces acting on a particle with a single equivalent or resultant force, - relations between forces acting on a particle that is in a state of equilibrium. • The focus on particles does not imply a restriction to miniscule bodies. Rather, the study is restricted to analyses in which the size and shape of the bodies is not significant so that all forces may be assumed to be applied at a single point. 3
Resultant of Two Forces:force: action of one body on another:characterized by its point of application,101bmagnitude, line of action, and sense.30°A. Experimental evidence shows that thecombined effect of twoforces may berepresented by a single resultant force. The resultant is equivalent to the diagonal ofRa parallelogram which contains the twoforces in adjacent legsA. Force is a vector quantity4
Resultant of Two Forces • force: action of one body on another; characterized by its point of application, magnitude, line of action, and sense. • Experimental evidence shows that the combined effect of two forces may be represented by a single resultant force. • The resultant is equivalent to the diagonal of a parallelogram which contains the two forces in adjacent legs. • Force is a vector quantity. 4
VectorsVector: parameter possessing magnitude and directionwhich add according to the parallelogram law. Examples:displacements, velocities, accelerations.+(: Scalar: parameter possessing magnitude but not directionQExamples: mass, volume, temperature.Vectorclassifications:-Fixed orbound vectors have well defined points ofapplication that cannot be changed without affectingan analysis.-Freevectorsmaybefreelymoved inspacewithoutchanging their effect on an analysis- Sliding vectors may be applied anywhere along theirline of action without affecting an analysisEqual vectors have the same magnitude and direction: Negative vector of a given vector has the same magnitudeand the opposite direction5
Vectors • Vector: parameter possessing magnitude and direction which add according to the parallelogram law. Examples: displacements, velocities, accelerations. • Vector classifications: - Fixed or bound vectors have well defined points of application that cannot be changed without affecting an analysis. - Free vectors may be freely moved in space without changing their effect on an analysis. - Sliding vectors may be applied anywhere along their line of action without affecting an analysis. • Equal vectors have the same magnitude and direction. • Negative vector of a given vector has the same magnitude and the opposite direction. • Scalar: parameter possessing magnitude but not direction. Examples: mass, volume, temperature 5