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Chapter 1: Introduction to Statics

Overview

• Faculty of Engineering and the Built Environment

• Department of Mechanical and Mechatronics Engineering

• Focus on Engineering Mechanics Statics, Ninth Edition

Module Outcomes

At the end of this chapter, students should be able to:

• Express Forces: Represent forces using unit vectors and perpendicular components; perform vector addition and subtraction.

• State Newton's Laws: Understand and articulate the three laws governing motion.

• Units Conversion: Convert units between SI and US customary systems.

• Methodology: Describe the approach to formulate and solve statics problems.

Basic Concepts in Statics

• Mechanics studies the effect of forces on objects:

  • Statics: Concerns the equilibrium of bodies under forces.

  • Dynamics: Deals with the motion of bodies.

Key Terms

• Space: The three-dimensional expanse in which objects and events occur.

• Time: A measure of the duration of events.

• Mass: A measure of the amount of matter in an object.

• Force: An interaction that changes the motion of an object.

• Particle: An object with mass but negligible size.

• Rigid Body: An idealization of a solid body in which deformation is neglected.

Scalars and Vectors

Scalar Quantities

• Defined by magnitude only.

• Examples:

  • Time

  • Volume

  • Density

  • Speed

  • Energy

  • Mass

Vector Quantities

• Defined by both magnitude and direction.

• Must follow the parallelogram law of addition.

• Examples:

  • Displacement

  • Velocity

  • Acceleration

  • Force

  • Moment

  • Momentum

Working with Vectors

• Vector addition:

  • Formula: V = V1 + V2

  • Graphically represented using the triangle or parallelogram method.

• Vector subtraction:

  • Formula: V = V1 - V2

  • Includes reversing the direction of the vector being subtracted.

Newton's Laws of Motion

1. First Law (Law of Inertia): A particle remains at rest or continues to move at constant velocity if no unbalanced force acts on it.

2. Second Law: The acceleration of a particle is proportional to the vector sum of forces acting on it and occurs in the direction of this sum.

3. Third Law: For every action, there is an equal and opposite reaction.

Units of Measurement

SI Units

• Mass (M): Kilogram (kg)

• Length (L): Meter (m)

• Time (T): Second (s)

• Force (F): Newton (N)

U.S. Customary Units

• Mass: Slug

• Length: Foot (ft)

• Time: Second (sec)

• Force: Pound (lb)

Problem Solving in Statics

Steps for Problem Formulation

1. Formulate the Problem

   • State given data.

   • State the desired result.

   • State assumptions and approximations.

2. Develop the Solution

   • Draw the Free Body Diagram (FBD).

   • State governing principles to apply.

   • Make calculations.

   • Verify that answers are reasonable.

   • Draw conclusions.

Review

• Sample problems are located on pages 15 to 16 of the textbook.

• Suggested problems available on Mytutor within the tutorial folder.