Physics 2

At the end of this learning unit, the student is able to :

Contribution of the course to the program objectives:

Regarding the learning outcomes of the program of Bachelor in Engineering Sciences, this course contributes to the development and the acquisition of the following learning outcomes:

• LO 1.1, 1.2
• LO 3.2
• LO 4.1, 4.4, 4.5

Specific learning outcomes of the course:

The learning outcomes marked by (*) are initiated in LFSAB1202 and applied for FSA11BA students, in the framework of the project LFSAB1502.
At the end of the course, he student will be able :
1. for the part on electricity:
LO 1.1, LO 1.2: to use basic law of electromagnetism to solve simple problems in electromagnetism or electromechanics
and  more specifically, will be able to:

• Use vector formalism to express interaction forces, in vacuum, between a magnetic field and moving particles or a current, or between currents.
• Use Biot-Savart and Ampere laws in vacuum to calculate the magnetic field produced by currents travelling in geometrically simple structures. (*)
• Calculate the trajectory of a charged particle through a uniform and constant magnetic field
• Distinguish the magnetic properties of various materials (dia-,para-,ferro-magnetic) based on their magnetic permeability. (*)
• Explain and interpret the effect on a coil inductance when a ferromagnetic core is introduced(*)
• Explain the hysteresis phenomenon of magnetic materials, and use the magnetic permeability in the derivation of inductances or simple magnetic circuits containing linear or non-linear magnetic materials. (*)
• Explain the origin of energy losses in a conducting or ferromagnetic material for AC regime
• Explain and justify the boundary conditions for B and H at the interface between two different media
• Define the inductance and mutual inductance of simple structures with and without a ferromagnetic core(*)
• Explain the Lenz-Faraday law expressing the e.f.m induced by a variable magnetic flux and use it for the calculation of AC generators with geometrically simple structures(*)
• Calculate the magnetic energy stored in simple circuits or structures
• Explain how simple electromechanical systems like a DC motor, a AC generator, an ideal transformer, an electromagnet work by exploiting the notion of magnetic flux
• Write and explain Maxwell equations for the EM field in their integral formulation limited to the static case

2. for the part on mechanics of the rigid body:
LO 1.1, LO 1.2 to express in vector form the equations of motion of one or several interconnected rigid bodies; to derive the equations describing the dynamics of a single rigid body (Newton-Euler equations); to manipulate generalized coordinates to model multiple rigid bodies dynamics (by means of) and to derive their equations of motion as well as the constraint forces via the Virtual Power Principle.
and  more specifically, will be able to:

•  use the tools associated to the geometrical space allowing to manipulate vectors in the 3D space
• Use the systematic procedure to calculate, in a general frame, the successive temporal derivatives of a vector in a mobile base.
• Describe in the 3D space, the instantaneous configurations of one or several interconnected rigid bodies
• Specify the variables describing the dynamic behavior of a body modeled as a continuous medium (mass center, momentum, angular momentum, kinetic energy) with an application to the rigid body case
• Use and manipulate the concept of the inertial matrix of a rigid body to mathematically express its angular momentum and kinetic energy
• Exploit various properties (symmetry, planes figures, ¿) to easily derive the mass center position as well as the inertial matrix of a geometrically simple body or combination of various geometrically simple bodies
• express the vector motion equations of a rigid body submitted to various forces (Newton-Euler equations)
• For a rigid body first, then for a system of interconnected rigid bodies, make a justified choice of a set of generalized coordinates allowing an optimized description of the configurations of the system (in 3D /2D space)
• For a rigid body first, then for a system of interconnected rigid bodies, express the constraints ¿ holonomic and non-holonomic ¿ involving the generalized coordinates (or velocities), and verify their independence
• Determine the number of degrees of freedom of a mechanical system
• Make the inventory of forces (and torques) influencing the dynamic behavior of such a system
• Write the motion equations for such a system as a function of generalized coordinates and their derivatives
• Make use of the virtual power principle to derive the differential equations describing the behavior of rigid systems, avoiding the calculation of link forces
• Explain the various kinds of links or static supports, and related degrees of freedom and constraints

• une version récente du livre de H. D. Young et R. A. Freedman, University Physics with Modern Physics, Addison Wesley: San Francisco. Avec ce livre, les étudiants ont droit à une licence leur permettant également un accès en ligne (sur www.masteringphysics.com) à des exercices supplémentaires, des tests et des questions à choix multiples gérés par l'enseignant.
• Symbolic Modeling of Multibody Systems, Jean-Claude Samin et Paul Fisette, Kluwer Academic Publisher, 2003.