Mechanics II

Code:

EM0018

Acronym:

M II

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2009/2010 - 2S

Active?	Yes
Web Page:	http://www.fe.up.pt/~jchousal/2/mecanica2.htm
Responsible unit:	Applied Mechanics Section
Course/CS Responsible:	Master in Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEIG	160	Syllabus since 2006/2007	2	-	7	70	187

Teaching language

Portuguese

Objectives

1. To understand and to apply the essential concepts of KINEMATICS which are related with the motion of RIGID BODIES. To determine its velocity and acceleration.
2. To know how to determine velocity fields and contemporaneous accelerations in absolute or relative motions of the various mechanism components in an arbitrary 3D motion.
3. To identify what happens on a solid due to its motion (mass and inertia).
4. To know how to determine the dynamic balance of mechanical systems through vector theorems, energy theorems, impulse theorem and quantity of movement.

By the end of the semester, students should know how to analyze kinematic and dynamic behaviours of bi dimensional and tri dimensional mechanisms.

Program

Kinematics of a point

Trajectory
Position vectors, velocity vectors and acceleration vectors.
Vector’s components in intrinsic coordinates and in various Cartesian coordinates (steady or movable)
Vector treatment of rotation motion
“Angular velocity” vector or “rotation” vector
“Angular acceleration” vector

Kinematics of a solid

Velocity fields
Connection between velocities and two points of a solid: 1st Mozzi equation Elementary motions of a solid: translational and rotational
Some particular motions: plain motion, polar motion and helical motion
“General” motion: from “tangent” motion to helical motion.
Absolute velocity, relative velocity and transport velocity
Absolute acceleration, relative acceleration, transport acceleration and complementary (Coriolis) acceleration
Solid motion on permanent contact
Slip acceleration
Velocity fields on constant contact
Particular cases: pure rolling, pure twist, pure slip
Rotation motion from the place where two motion solids meet and constant contact solids
Instantaneous axis of rotation in an arbitrary motion of a solid
Rotation motion of that axis
Axoid surfaces


Mass Kinematics

Torsor motion
Torsor acceleration
Kinematic energy in a material system


Dynamics- Force, Mass and Acceleration

Dynamics of a material point
The elementary principles of dynamics
Equations of motion
Inertial force
Kinematic momentum variation of a material point
Equation of dynamics
Dynamics of a solid: Method of analysis, motion of the center of mass, motion around the center of mass, dynamic balance, particular motions and applications.

Dynamics- Work and Energy
Work and energy: work of a force and binary work
Work of conservative and non-conservative forces
Work and kinematic energy
Work and total energy mechanics
The principal of conservation of total energy mechanics
Theorem of virtual work: virtual dislocation, theorem of virtual work.

Mandatory literature

Jorge H. O. et al; Dinâmica do ponto material e do corpo rígido, Jorge Seabra, SMAp, DEMEGI, FEUP, 2004
Marcelo Moura et al; Cinemática, Marcelo Moura, SMAp, DEMEGI, FEUP, 2004

Complementary Bibliography

Meriam, J. L.; Dynamics. ISBN: 0-471-24167-9(Vol. 2)
Beer, Ferdinand P; Vector mechanics for engineers. ISBN: 0-07-118306-X

Teaching methods and learning activities

Classes per week: theoretical: 2 hours per week; practical: 4 hours per week
Theoretical classes- 24 h
Practical classes- 46 h

Students can meet professors outside class time (office time will be scheduled by each professor)

keywords

Physical sciences > Physics > Classical mechanics > Kinetics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	73,00
	Total:	-	0,00

Eligibility for exams

According to General Evaluation Rules of FEUP.
Besides students have to reach a minimum mark of 6 out of 20 in the mid-term test, to be admitted to exams.

Calculation formula of final grade

1. Students will have to attend to two exams
2. The first exam will exclusively test the concepts of kinematics.
3. The second exam will test the themes taught on the second part of the semester (dynamics).
4. Both exams are worth 50% of the final mark.
5. Students will have to achieve a minimum mark of 7 (6.50) out of 20 on each of the exams.
6. Students who:
-did not reach an average mark of 10 out of 20 in both exams
- reached an average mark of 10 out of 20 but did not follow the rule of item 5
- missed one of the exams
Will have a chance to attend to the recurso exam (resit), which will cover all themes of the course (kinematics and dynamics).
7. All students will be admitted to recurso exam (resit), even the ones who completed the course but want to improve their mark.

Examinations or Special Assignments

Test

Special assessment (TE, DA, ...)

Test

Classification improvement

Students have to attend to recurso exam (resit) to improve their marks.