Mechanics 1 - Lecture 1 Overview

Mechanics 1 - Lecture 1

• Course: Mechanics 1, Fall 2024, Lecture 1
• Instructor: Dr. Neveen Abd El-Fattah El-Shamy, Assistant Professor, Mathematical and Engineering Physics Department, Faculty of Engineering, Mansoura University
• Aim: Apply knowledge of mathematics to solve fundamental mechanical engineering problems.
• Reference: R. C. Hibbeler, "Engineering Mechanics: Statics and Dynamics," Fourteenth Edition, Pearson Prentice Hall, New Jersey, 2016.
• Evaluation:
  • Final exam (50 marks)
  • Mid-term exam (20 marks)
  • Semester work (30 marks):
    • Quizzes (10 marks)
    • Scientific Day (10 marks)
    • Activities in Tutorials (5 marks)
    • Attendance (5 marks)
  • Total: 100 marks

Intended Learning Outcomes

• Recognize the types of forces, moments, and equilibrium of rigid bodies. Select appropriate solutions to simplify systems of forces and moments to equivalent systems.
• Identify support reactions and subjects of centroids and evaluate the characteristics of complete free-body diagrams.
• Apply mathematics to write appropriate equilibrium equations from the free-body diagram, including support reactions on a structure.
• Use computational facilities to analyze simple structures, frames, and machines.

Contents

• Vectors in 3D
• Equilibrium of Particle
• Systems of Forces and Moments
• Equilibrium of Rigid Body
• Frames and Machines
• Center of Gravity and Centroid
• Friction

Week-by-Week Schedule

• Week 1: Introduction (Vectors in 2D), Vectors in 3D, Equilibrium of Particle in 3D, Quiz 1
• Week 2-3: Systems of Forces and moments, Equilibrium of Rigid Body in 2D
• Week 4: Midterm Exam
• Week 5-6: Equilibrium of Rigid Body in 2D cont.
• Week 7: Frames and Machines, Quiz 2
• Week 8-9: Center of Gravity and Centroid, Friction
• Week 10-11: Scientific Day
• Week 12: Final Exam

Mechanics Summary

• Mechanics: A branch of physical science dealing with the effects of forces on objects.
  • Rigid-Body Mechanics: Deals with the behavior of objects that do not deform under applied forces.
  • Statics: Focuses on equilibrium, where forces balance, and bodies are either at rest or moving at a constant velocity.
  • Dynamics: Deals with accelerated motion of bodies.
• Scalar: A quantity characterized by a single number (e.g., mass, temperature).
• Vector: A quantity with both magnitude and direction (e.g., velocity, force).

Coordinate Systems

• Two-dimensional coordinates system defined using x and y axes.
• Three-dimensional coordinates system defined using x, y, and z axes.

Units of Measurement

• US Customary units: Utilizes units like pounds (lb) for force, slugs for mass, feet for length, and seconds for time.
• SI units: Employs units like Newtons (N) for force, kilograms (kg) for mass, meters (m) for length, and seconds (s) for time.

Vector Representation

• A vector is graphically represented using a line with an arrow (with magnitude and direction).

  • Magnitude: Length of the line, denoted as |V|
  • Direction: Angle (θ) from a reference line, describing the vector's orientation.

• Cartesian Rectangular Components break down a vector into x and y (or x, y, and z components) for calculation ease. These components are usually along coordinate axes).

• Vector component calculations using trigonometric functions such as cosine and sine.