PPH 0095 Mechanics Foundation in Engineering

ONLINE NOTES

Chapter 2 Kinematics

FOSEE , MULTIMEDIA UNIVERSITY (436821-T) MELAKA CAMPUS, JALAN AYER KEROH LAMA, 75450 MELAKA, MALAYSIA. Tel 606 252 3594 Fax 606 231 8799 URL: http://fosee.mmu.edu.my/~asd/

PPH0095

MECHANICS

Contents 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 Introduction Definitions of Linear Motion Distance Displacement Speed and Velocity Average Velocity Instantaneous Velocity Average Acceleration Instantaneous Acceleration Equations of Linear Motions Motion Graphs Free Falling Objects under gravity Projectile Motion Uniform Circular Motion

ASD 2011/12

KINEMATICS

1/23

PPH0095

MECHANICS

Mind Map

ASD 2011/12

KINEMATICS

2/23

PPH0095

MECHANICS

OBJECTIVES

Upon completion of this chapter, you should be able to: 1) 2) 3) 4) 5) define distance, displacement, velocity, acceleration. know how to apply all the equation for linear motion with constant acceleration. draw graph velocity versus time , distance versus time and explain them. understand the concept of free fall and should be able to solve the problem. understand the concept of projectile motion and uniform circular motion and should be able to solve the problem.

2.0

INTRODUCTION

Kinematics is the branch of mechanics which studies the motion of objects without considering the forces that cause the motion. Vector quantities such as displacement, velocity, and acceleration are involved. The study of the motion of objects under the action of forces is called dynamics. The study of the motion of objects, and the related concepts of force and energy, form the field called mechanics. Mechanics is customarily divided into two parts i.e. kinematics and dynamics. • Kinematics : the description of how objects move. Kinematics in one dimension : describing an object that moves along a straight line path, which is one dimensional motion. Kinematics in two dimensions : the description of the motion of objects that move in paths in two (or three) dimensions. • Dynamics : deals with force and why objects move as they do. In this part we will solve the following questions : What makes an object at rest begin to move ? What causes a body to accelerate or decelerate ? What is involved when an object moves in a circle ? We can answer in each case that a FORCE is required.

2.1

• •

DEFINITIONS of LINEAR MOTION

Linear motion is motion along a straight line. Three types of motion: • Translational • Rotational • Vibrational

ASD 2011/12

KINEMATICS

3/23

PPH0095

MECHANICS

•

Figure 1 • • We only discuss objects that move without rotating (Figure 1a) Motion in straight line; • Vertical • Horizontal • Slanting

Reference Frames • • Any measurement of position, distance or speed must be made with respect to a frame of reference. It is always important to specify the frame of reference when stating a speed. In everyday life, we usually mean "with respect to the Earth".

Position • For one-dimensional motion, we often choose the x axis as the line along which the motion takes place. • The position of an object at any moment is given by its x coordinate. • If the motion is vertical, as for a dropped object, we usually use the y axis.

2.2

• • •

DISTANCE

The length of the actual path or total path length. It depends on the frame of reference, for example, Ipoh is 200 km away from Kuala Lumpur. A set of coordinate axes represents a frame of reference.

ASD 2011/12

KINEMATICS

4/23

PPH0095

MECHANICS

2.3

• •

DISPLACEMENT

The change in position of the object, i.e. displacement is how far the objects is from its starting point. For example : A change from an initial position xi to the final position xf, the displacement is, ∆x = xf - xi. The symbol ∆ (delta) means "change in". So ∆x means the change in x which...