Chapter 1

Introductions

1.1 What is Mechanics ?

*Dr. Yiheng Wang

1.1 What is Mechanics ?

*Dr. Yiheng Wang

1.2 Fundamental Concepts & Principles● Space: Position of a point P measured from a reference

point (origin). The given length in specified direction is called Coordinate

● Time: together with position define an event.● Mass: a body property to resist a change in the translational

motion ● Force: An action of one body on another, by actual contact or

at a distance. A vector defined by its point of application, magnitude, and direction.

● Particle: A small amount of matter assume to occupy a single point in space.

● Rigid body: A body with many particles, occupying fixed positions w.r.t. each other.

● Parallelogram Law for Addition of Forces (Vectors)

1.2 Fundamental Concepts & Principles

1.2 Fundamental Concepts & Principles

● Principle of Transmissibility

(Force is a sliding vector)

● Newton's First Law of Motion

1.2 Fundamental Concepts & Principles

*Dr. Yiheng Wang

● Newton's Second Law of Motion

1.2 Fundamental Concepts & Principles

*Dr. Yiheng Wang

● Newton's Third Law of Motion

1.2 Fundamental Concepts & Principles

*Dr. Yiheng Wang

● Newton's Law of Gravitation

1.2 Fundamental Concepts & Principles

*Dr. Yiheng Wang

● Newton's Law of Gravitation

1.2 Fundamental Concepts & Principles

*Dr. Yiheng Wang

1.3 Units:International System of Units (SI Units)

● Basic Units– Length: meter (m)

– Mass: kilogram (kg)

– Time: second (s)

● Derived Uncit– Force: Newton (N)

1.3 Units: SI Units

1.3 Units: SI Units

1.3 Units: US Customary Units

● Basic Units– Length: foot (ft)

– force: pound (lb)

– Time: second (s)

● Derived Unit– Mass: slug

● Only remember conversion factors of base units.● Do calculation for both numbers and units.

– for example

1.4 Conversion of Units

1.4 Conversion of Units

1.5 Method of Problem Solution

● Clear problem statement should be given.● Free-body diagrams (FBD) should be drawn.● Write equations expressing principles related to

the FBDs.● Solve the problem (writing neatly all the steps).● Check your answers carefully.

1.6 Numerical Accuracy

● Accuracy of the solutions should not be more accurate than the accuracy of the given data.

● In engineering problems data are mostly less accurate than 0.2 percent. (100 ± 0.2)

● In general,– Use 4 significant figures if the numbers begin with 1

– Use 3 significant figures, all otherwise.

● For example: – 15 lb → 15.00 lb

– 40 lb → 40.0 lb