1 / 23

Chap13

Chap13. Kinetics of a particle : Force and Acceleration. 13.1 Newton’s law of motion. 1.Newton’s 2 nd law of motion. (1) A particle subjected to an unbalanced force. experiences an acceleration. having the same. and a magnitude that is directly. direction as. proportional to the force.

tola
Download Presentation

Chap13

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chap13 Kinetics of a particle : Force and Acceleration.

  2. 13.1 Newton’s law of motion 1.Newton’s 2nd law of motion (1) A particle subjected to an unbalanced force experiences an acceleration having the same and a magnitude that is directly direction as proportional to the force. =m m = mass of a particle =a quantitative measure of the resistance of the particle to a change in its velocity.

  3. r m1 m2 acting on the particle is (2) The unbalanced force proportional to the time rate of change of the particle’s linear momentum. (if m=constant) 2. Newton’s Law of Gravitational Attraction

  4. G = universal constant of gravitation = r = distance between centers of two particles Weight of a particle with mass m1 = m =mg m2 : mass of the earth r = distance between the earth center and the particle

  5. g= = acceleration due to gravity measured at a point on the surface of the =9.81 earth at sea level and at a latitude of

  6. 13-2 The equations of motion p • Equations of motion of a particle subjected to more than one force.

  7. Kinetic diagram of particle p. p Free body diagram of particle p. p ………...equation of motion

  8. D’A lembert principle inertia force vector Dynamic equilibrium diagram p (慣性力) 若 則此狀態為靜平衡 +

  9. (1) Inertial frame y p path p x o y p path p x o 2. Inertial frame of reference (newtonian) A coordinate system is either fixed or translates in a given direction with a constant velocity. (2) Noninertial frame

  10. 13-3 Equation of motion for a system of particle z i y xyz: Inertial Coordinate System x Equation of motion of particle i. Dynamic equilibrium diagram of particle i. i

  11. resultant external force resultant internal force Equation of motion of a system of particles.

  12. By definition of the center of mass for a system of particles. Position vector of the center of mass G. Total mass of all particles. Assume that no mass is entering or leaving the system.

  13. Hence： This equation justifies the application of the equation of motion to a body that is represented as a single particle.

  14. 13-4 Equations of motion：Rectangular z path y Rectangular Coordinate system. Coordinate x Equation of motion of particle P. In rectangular components

  15. scalar eqns. Analysis procedure • Free Body Diagram. • (1) Select the proper inertial coordinate system. • (2) Draw the particle’s F.B.D. • 2. Equation of motion • (1) Apply the equations of motion in scalar form • or vector form. or

  16. (2) Friction force (3) Spring force 3. Equations of kinematics Apply for the solutions

  17. 13.5 Equation of Motion:Normal and Tangential Curve path =Tangential unit vector b =Normal unit vector n t =Binormal unit vector = P Coordinates Curve path of motion of a particle is known.

  18. = = = 0 Equation of motion Or scalar form

  19. Analysis procedure 1. Free body diagram Identify the unknowns in the problem. 2. Equation of motion Apply the equations of motion using normal and tangential coordinates. 3. Kinematics Formulate the tangential and normal components of acceleration.

  20. 13.6 Equation of Motion :Cylindrical coordinate z r Equation of motion in cylindrical coordinates

  21. and Cylindrical or polar coordinates are suitable for a problem for which Data regarding the angular motion of the radial line r are given, or in Cases where the path can be conveniently expressed in terms of these coordinates.

  22. Normal and Tangential force If the particle’s accelerated motion is not completely specified, then information regarding the directions or magnitudes of the forces acting on the particle must be known or computed. Now, consider the case in which the force P causes the particle to move along the path r=f(q) as shown in the following figure. r=f(q) :path of motion of particle P:External force on the particle F:Friction force along the tangent N:Normal force perpendicular to tangent of path

  23. + positive direction of - negative direction of rd dr Direction ofF & N The directions of F and N can be specified relative to the radial coordinate r by computing the angle y. Angle y is defined between the extended radial line and the tangent to the path. dr :radial component rdq :transverse component ds:distance

More Related