Dynamics Northern Illinois Universiy动力学北伊利诺斯大学.pptVIP

Dynamics Kinematic Vectors Kinematic quantities refer to the motion only. Position Velocity Acceleration Kinematic vectors of velocity and acceleration are coplanar. Force and Mass Two particles can influence each other. Masses related to accelerations Momentum is defined be mass and velocity. Derivative is force Defines equations of motion Forces on One Particle There is a net force on each particle in an object. This corresponds to the particle’s acceleration. Forces on a System For N particles in a system the forces add. Particles of constant mass Some forces are internal and some are external to the system. Internal forces cancel Center of Mass The weighted average of the positions of the particles is the center of mass. The system acts like a single particle. Force at center of mass Translational change at center of mass Sliding Inclined Plane The block and inclined plane are both free to move. Two frictionless surfaces The coordinates should point along the surface. Normal force is the force of constraint The motion will be along the surface Acceleration from plane and block relative to plane Motion of Plane The inclined plane has two forces from constraints. Upward from table Reaction from block The system of linear equations are solved for the accelerations. Newtonian Mechanics The result compares to the simple problem of a fixed plane. There were four unknowns in the problem. Two accelerations Two forces of constraint The constraint forces can be eliminated by using work. * * x2 x1 mA mB mr mr M m q M m q M next m q M