THEORYMECHANICS902Chapter13 Theorem ofkinetic energyCollege of Mechanical and VehicleEngineering王晓君
College of Mechanical and Vehicle Engineering 王晓君 Chapter13 Theorem of kinetic energy THEORY MECHANICS
Work of forceThe kinetic energy of the particleand its systemTheorem of kinetic energyExamples of comprehensiveapplication of universal theorem
• Work of force • The kinetic energy of the particle and its system • Theorem of kinetic energy • Examples of comprehensive application of universal theorem
LntroductionThe first two chapters established the relationship between thephysical activity change of particle and particles system and theexternal force and acting time.Based on work and kinetic energy, this chapter establishes therelationship between the change of kinetic energy of a particle orsystem of particles and the work of the force, namely kinetic energytheorem.Differentfrom the momentum theorem and the moment ofmomentum theorem, the kinetic energy theorem is more convenientand effective to analyze the dynamics of particles and particlesystems from the perspective of energy. It also can establish theconnection between the mechanical movement and other forms ofmovement.Before the introduction to the kinetic energy theorem, firstintroduced the relevant physical quantities: work with kinetic energy
Introduction The first two chapters established the relationship between the physical activity change of particle and particles system and the external force and acting time. Based on work and kinetic energy, this chapter establishes the relationship between the change of kinetic energy of a particle or system of particles and the work of the force, namely kinetic energy theorem. Different from the momentum theorem and the moment of momentum theorem, the kinetic energy theorem is more convenient and effective to analyze the dynamics of particles and particle systems from the perspective of energy. It also can establish the connection between the mechanical movement and other forms of movement. Before the introduction to the kinetic energy theorem, first introduced the relevant physical quantities: work with kinetic energy
I .The concept of work1,The work of the normal force13.1Suppose the object travels along a straight方Work of forcepath S under the action of constant forceFLM' M.α αas shown in the figure, then the work doneby the force Wis defined asW=Fcosα.s= F.3Work is algebraic quantity. It represents the cumulativeeffect of a force over a distance, so work is the cumulativeeffect.In the SI system of units, the unit of work is J(Joule). 1J = 1N . mM2A2, The work of the variable forcedsaijaMLet the particle M move along the curveunder the action of variable force F, as shown万in the figure, and the work done by the force F[M,on the tiny arc is called the element work ofthe force, denoted as SwW
Ⅰ.The concept of work M1 M2 s F F 1、The work of the normal force Suppose the object travels along a straight path S under the action of constant force , as shown in the figure, then the work done by the force W is defined as F W F s F s = cos = Work is algebraic quantity. It represents the cumulative effect of a force over a distance, so work is the cumulative effect. In the SI system of units, the unit of work is J (Joule). 1J =1N m 2、The work of the variable force M1 M M2 M F dsdr Let the particle M move along the curve under the action of variable force , as shown in the figure, and the work done by the force on the tiny arc is called the element work of the force, denoted as F F W 13.1 Work of force
I .The concept of workLet the displacement of the correspondingM,small arc ds be dr then the expression ofdsVaaMelement work of the force is W = F.drFW, M .dr--- adus ctor ethodMJM,SW = Fcosα·ds = F:dsM?Mn? Fcosα·ds :Wi2 =F.ds ---- The natural methodJM,JM,dr = dxi + dyi + dzkSuppose: F = Xi +Yi+ ZkSW = Xdx + Ydy + ZdzMWi2 =Xdx + Ydy + ZdzJMRectangularcoordinate method
W F ds F ds M M M M = = 2 1 2 1 cos 1 2 M1 M M2 M F dsdr Suppose： F Xi Yj Zk = + + dr dxi dyj dzk = + + W = Xdx +Ydy + Zdz = + + 2 1 1 2 M M W Xdx Ydy Zdz W = F ds = F ds cos = 2 1 12 M M W F dr Let the displacement of the corresponding small arc be , then the expression of element work of the force is ds dr W F dr = - The natural method - Radius vector method - Rectangular coordinate method Ⅰ.The concept of work