Mechanics 2

Code:

L.EC012

Acronym:

M2

Keywords
Classification	Keyword
OFICIAL	Basic Sciences

Instance: 2023/2024 - 1S

Active?	Yes
Responsible unit:	Department of Civil Engineering
Course/CS Responsible:	Bachelor in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EC	237	Syllabus	2	-	6	52	162

Teaching language

Portuguese
Obs.: Português

Objectives

JUSTIFICATION:
The fundamental concepts of kinematics and dynamics and their generalization to three-dimensional space strongly contribute to a better understanding of the surrounding environment and the phenomena that condition and determine it.

OBJECTIVES:
This curricular unit aims teaching and developing the ability to solve problems related to the kinematics and kinetics of particles, systems of particles and rigid bodies, by introducing theoretical concepts and practical methodologies.

Learning outcomes and competences

COMPETENCES AND LEARNING OUTCOMES:
Knowledge: Define and demonstrate knowledge in areas of basic science. Identify key concepts related to kinematics and dynamics of systems.
Comprehension: Interpret and identify the phenomena associated with movement of systems and the causes that produce nuclear knowledge in engineering. Interpret the phenomena in the light of empirical knowledge.
Application: Develop knowledge in fundamental sciences. Apply the concepts of kinematics and dynamics in the resolution of practical cases.
Analysis: Analyze the relationship between kinematics and systems dynamics. Understand the difference between particle and system of particles and the implications in the response. 

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

The students are required to have basic knowledge on Mathematics and Physics acquired before entering at FEUP, complemented with the Mathematical Analysis and Algebra courses of the 1st year.

Program

Chapter 1 – KINEMATICS OF A PARTICLE
Description of the motion of a particle; Position, velocity and acceleration vectors; Dimensions and units; Motion osculator plane; Graphical representation of kinematics quantities; Classification of the particle’s motion; Uniform rectilinear motion; Uniformly accelerated motion; Angular velocity and angular acceleration; Circular motion; Rotation vector or Angular velocity vector.

Chapter 2 – KINEMATICS OF A SYSTEM OF PARTICLES
Translation motion; Rotation motion; Rotation operator; General motion of a solid; Plane motion of a solid; Theorem of velocities projection; Instantaneous centre of zero velocity; Kinematics of the relative motion; Theorem of the composition of velocities; Theorem of the composition of accelerations or Theorem of Coriolis; Newton’s principle of relativity.

Chapter 3 - GEOMETRY OF MASSES
Centre of geometry, centre of mass and centre of gravity of a two dimensional body; Centroids of areas and lines; First moments of areas and lines; Theorems of Pappus- Guldinus; Second moment, or moment of inertia, of an area and of a mass; Parallel axes theorem or Steiner’s theorem; Polar moment of inertia; Radius of gyration; Products of inertia; Principal axes and principal moments of inertia; Graphical determination of moments and products of inertia: Land’s circle and Mohr’s circle.

Chapter 4 – DYNAMICS OF PARTICLES
Fundamental principles of dynamics; Linear momentum; Rate of change of linear momentum – Linear impulse; Notion of field; Work of a force; Theorem of kinetic energy; Potential energy – Conservative fields; Principle of conservation of mechanical energy; Power and efficiency; Angular momentum; Rate of change of angular momentum; Central forces – Motion under a central force; Newton’s law of gravity; Trajectory of a particle under a central force; Principle of D’Alembert.

Chapter 5 – DYNAMICS OF A SYSTEM OF PARTICLES
General equations of motion; Centre of mass theorem; Linear momentum; Rate of change of linear momentum; Principle of conservation of linear momentum; Impact – Direct central impact and Oblique central impact; System of particles with variable mass; Angular momentum; Rate of change of angular momentum; Principle of conservation of angular momentum; Kinetic energy; Theorem of kinetic energy; Rotation of a solid about a fixed axis; Extension to the principle of D’Alembert.

Chapter 6 – VIBRATION OF DISCRETE SYSTEMS WITH ONE DEGREE OF FREEDOM
Characterization of discrete systems with one degree of freedom (DS1); Formulation of the DS1 equations of motion; Motion of DS1 without damping in free vibration and when subjected to harmonic actions; Motion of DS1 with damping in free vibration and when subjected to harmonic actions.

Scientific content – 80% 
Technological content – 20% 

DEMONSTRATION OF THE SYLLABUS COHERENCE WITH THE CURRICULAR UNIT'S OBJECTIVES:
The fundamental concepts of kinematics and dynamics and its generalization to three-dimensional space contribute significantly to a better perception of the surrounding environment and phenomena that condition it.

Mandatory literature

Henriques, A.A.R.; Guedes, J.P.M.; Apontamentos de Mecânica 2, 2002
Beer, Ferdinand P; Mecânica vetorial para engenheiros. ISBN: 85-86804-49-5
Meriam, J. L.; Mecânica - Dinâmica. ISBN: 85-216-1176-5

Complementary Bibliography

Shames, Irving H.; Engineering Mechanics. ISBN: 0-13-356924-1
Timoshenko, S.; Advanced Dynamics
Spiegel, Murray R.; Schaum.s outline of theory and problems of theoretical mechanics with an introduction to Lagrange.s
Pestel, Eduard C.; Dynamics

Teaching methods and learning activities

All subjects of the course are discussed in the theoretical and practical classes. Exposition and explanation of concepts, principles and methods, complemented and illustrated with the resolution of some of the problems proposed at the exercises sheets, are done in the theoretical classes. In the practical classes it is promoted the discussion of the problems proposed at the exercises sheets, being the students asked to solve them individually or in group.

DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:
Students are encouraged to apply the concepts of kinematics and dynamics in the resolution of practical cases, to analyze and relate kinematics and dynamics of systems, to understand the difference between particle and system of particles and the implications for the response.

keywords

Physical sciences > Physics > Classical mechanics > Structural mechanics
Physical sciences > Physics > Classical mechanics > Kinetics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	70,00
Participação presencial	10,00
Teste	20,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Frequência das aulas	47,00
Total:	47,00

Eligibility for exams

Achieving a final classification requires the attendance of the Curricular Unit (CU), as established in the FEUP evaluation rules. A student is considered to have attended a CU if, after been regularly enrolled, he does not exceed the limit number of absences that corresponds to 25% of the expected number of face-to-face classes.

Calculation formula of final grade

The final classification is defined through a distributed evaluation component (consisting of one test to be carried out during the class period and by the evaluation of the student's participation in the theoretical classes) and a final exam. The distributed evaluation is optional. All the evaluation components are expressed on a scale of 0 to 20 values.

The final classification is computed using the following formula:

CF = max {CT ; EF}

Where:

CT = PP x CPT + PA x CAD + PF x EF 

With:

CPT - average classification of participation in theoretical classes by answering to online questionnaires during these classes: correct answer to 50% of the total of the questions asked in questionnaire "i" implies CPTi =20, otherwise, CPTi = 0;
CAD - classification of the evaluation test to be carried during the class period;
EF - classification of the final exam (ordinary and/or appeal seasons).

And PP, PA and PF the weights associated to the classifications CPT, CAD and EF:

PP = 0,10 (10%)
PA = 0,20 (20%)
PF = 0,70 (70%)

NOTE 1: The evaluations associated to CPT and CAD are optional. If a student does not participate in any of them, the corresponding weights are added to PF.

NOTE 2: The formulation is valid for all the students registered in this curricular unit.

NOTE 3: The classification of the distributed evaluation obtained in previous school years won’t be valid in the present school year.

NOTE 4: The final maximum grade that any student can obtain through the presented formula (CF) is 17. To obtain a grade of 18 or higher, the student must take an oral exam. Only students with a CF of 18 or higher are admitted to an oral exam.

Examinations or Special Assignments

Optionally, students can participate in the questionnaires to be carried out in the theoretical classes (CPT – See "Fórmula de cálculo da classificação final") that will constitute the component of the distributed evaluation of the curricular unit. This evaluation will be considered in the final classification only if it is obtained during the current school year.

Special assessment (TE, DA, ...)

See NOTE 2 of item "Fórmula de cálculo da classificação 
final".

Classification improvement

Tests to improve the classification of the distributed evaluation are not foreseen, but improving the classification of the final exam of the ordinary season is possible by perfomring the final exam of the appeal season.

Observations

Estimated working time outside classes: 3 hours/week.