# Mechanics

Áreas Científicas |

Classificação |
Área Científica |

OFICIAL |
Solid Mechanics |

## Ocorrência: 2023/2024 - 1S

### Ciclos de Estudo/Cursos

Sigla |
Nº de Estudantes |
Plano de Estudos |
Anos Curriculares |
Créditos UCN |
Créditos ECTS |
Horas de Contacto |
Horas Totais |

LTE |
50 |
Plano de Estudos |
1 |
- |
6 |
75 |
162 |

### Docência - Responsabilidades

### Língua de trabalho

Portuguese

### Objetivos

The student should be able to understand and apply the fundamental laws of newtonian mechanics; apply a specific methodology for problem solving; perform experiments and analyse the results obtained and identify deviations from expected results critically.

### Resultados de aprendizagem e competências

1.The student should have a basic knowledge about mechanics, its concepts, fundamental principles and its importance in engineering sciences. Knowledge of units: International and imperial systems of units. Knowledge about the methods of resolution of problems in mechanics. The student should be aware of the sensitivity of the solution to the numerical precision used in the calculations. 2.Knowledge of how the forces act on a given particle and how to calculate the resultant force on that same particle. Knowledge of how to represent the free-body diagram and obtain the equilibrium equations of the particle through the use of Newton’s first and third laws of motion. The student should be able to resolve a force in space given its intensity and two points of its line of action. Equilibrium of forces in space. 3.The student should understand the effect of a force on a rigid body and the reason why that same force acting on that same rigid body can be considered a sliding vector. The student should know how to calculate the moment of a force about a point and about a given axis using vector product, scalar product and mixed triple product. The student should understand the concept of a force couple and know how to reduce a system of forces to one force and one couple. 4.The student should be able to draw the free-body diagram of a rigid body. Knowledge of the various types of supports and the reactions they produce. The student should be able to establish the equilibrium equations of a rigid body and identify over constrained and under constrained situations. 5.The student should know the laws of dry friction and how to determine the friction coefficients through the friction angles. Knowledge of how to obtain the solution of problems involving dry friction. 6.The student should be able to find the geometrical centre of plane figures and lines, and the centre of mass of plates and wires, through integration or by decomposition. 7.The student should be able to establish the equations of displacement, velocity and acceleration of a particle over time in uniform rectilinear motion and in uniformly accelerated rectilinear motion. Understanding of the dependent motion of various particles and of their relative velocity and acceleration. Knowledge of the equations of curvilinear motion of particles. Tangential and normal components of the velocity and acceleration vectors. 8.Write the dynamic equilibrium equations of a particle using Newton’s second law of motion.

### Modo de trabalho

Presencial

### Programa

1. Introduction Fundamental concepts, notation and systems of units. Review of the mathematical tools needed in thecurricular unit.

2. Static of particles Forces in a plane and forces in space. Addiction of vectors, resolution of forces into components. Equilibrium of a particle.

3. Rigid bodies: Equivalent systems of forces Moment of a force about a point. Moment of a force about a given axis. Couples. Equivalent systems of forces.

4. Equilibrium of rigid bodies. Free-body diagram. Equilibrium of a rigid body in two dimensions. Equilibrium of a rigid body in threedimensions.

5. Friction Laws of dry friction, coefficients of friction.

6. Distributed Forces Centroids of areas and lines. Centre of gravity of two dimensional bodies. First and second moments of areas.

7. Kinematics of particles Rectilinear and curvilinear motion of particles.

8. Dynamics of particles Newton’s second law of motion. Linear momentum of a particle. Dynamic equilibrium.

### Bibliografia Obrigatória

Beer & Johnston; Mecânica Vectorial para Engenheiros - Estática, Mc Graw-Hill

Beer & Johnston; Mecânica Vectorial para Engenheiros - Dinâmica, Mc Graw-Hill

### Métodos de ensino e atividades de aprendizagem

Theoretical-practical lessons: explanatory concepts and principles of the mechanics of particles and rigid bodies followed by problem solving; Laboratory classes: experiments with specific guides and exercises.

### Tipo de avaliação

Distributed evaluation without final exam

### Componentes de Avaliação

Designation |
Peso (%) |

Teste |
80,00 |

Trabalho laboratorial |
20,00 |

**Total: ** |
100,00 |

### Componentes de Ocupação

Designation |
Tempo (Horas) |

Frequência das aulas |
75,00 |

Estudo autónomo |
87,00 |

**Total: ** |
162,00 |

### Obtenção de frequência

Distributed assessment or final exame.

### Fórmula de cálculo da classificação final

Final Classification (NF) is given by:

**NF=0,80 *T+0,20*RL (Distributed assessment)**

NF=1*EF

where:

T is the is classification average of the tests

RL is classification average of the laboratory reports

The student is approved in distributed assessment when T≥8,5 e NF≥9,5