EML 3004 C CHAPTER 9 Statics Dynamics and

EML 3004 C CHAPTER 9 Statics, Dynamics, and Mechanical Engineering Namas Chandra Introduction to Mechanical engineering Chapter 9 -1

EML 3004 C Objectives Understand the concept of a Vector Write a vector in component form Understand the concepts of a couple and moment Construct a free-body diagram of a physical system Sections 9. 1 9. 2 9. 3 9. 4 9. 5 9. 6 Introduction The Concept of a Vector Forces, Couples, and Moments Equilibrium and Free-body Diagrams Frictional Forces Motion of a Rigid Body Namas Chandra Introduction to Mechanical engineering Chapter 9 -2

EML 3004 C 9. 1 Introduction § Statics deals with bodies (Solid, Liquid, Gases) that are in equilibrium with applied forces. At static equilibrium, a body is at rest or in constant motion (no acceleration). § Newton’s Law ü First: A body is at rest or in uniform motion (constant velocity) along a straight-line unless acted upon by some external (unbalanced) forces. ü Second: Every body accelerates in the direction of external forces. The acceleration is proportional to the magnitude of the force. ü Third: For every action, there is an equal and opposite reaction. § Statics is critical in the study of bodies under forces in the design. Free body diagram isolates forces/bodies and is a critical tool. Namas Chandra Introduction to Mechanical engineering Chapter 9 -3

EML 3004 C 9. 2 Concept of a Vector § While scalar has only magnitude, e. g. : mass, temperature -vector has magnitude and direction, e. g. velocity, force, moment § The above is a geometric representation of the magnitude of the vector is unity, it is called a unit vector Namas Chandra Introduction to Mechanical engineering Chapter 9 -4

EML 3004 C 9. 2. 1 Component of Vector Namas Chandra Introduction to Mechanical engineering Chapter 9 -5

EML 3004 C 9. 2. 2 Component of Vector Namas Chandra Introduction to Mechanical engineering Chapter 9 -6

EML 3004 C 9. 2. 3 Direction Cosines of Vector Namas Chandra Introduction to Mechanical engineering Chapter 9 -7

EML 3004 C 9. 2. 4 Addition/Subtraction of Vectors § Since vectors have magnitude and directions only components can be added Namas Chandra Introduction to Mechanical engineering Chapter 9 -8

EML 3004 C 9. 3 Forces, Couples, and Moments § Magnitude of a couple: M = Fd § Moment of a force M = Force x Lever arm § The direction of the moment is normal to the plane containing the force and the arm. Namas Chandra Introduction to Mechanical engineering Chapter 9 -9

EML 3004 C 9. 4 Equilibrium and Free-Body Diagram § For static equilibrium, using Newton’s Second Law § Free body diagrams show all the forces and boundary conditions on a given body. Use the following steps üIsolate the body from surroundings and draw a simple sketch üPick the right coordinate system (2 D, 3 D, Cartesian, Cylindrical) üAdd all extreme forces (right direction) and internal forces üLabel all known quantities (magnitude/direction) Namas Chandra Introduction to Mechanical engineering Chapter 9 -10

EML 3004 C 9. 5 Frictional forces § A body on a surface (horizontal or sloped) is acted upon by weight acting vertically down and a reaction normal to the surface Using Coloumb’s Law for Static case § For bodies in motion, Namas Chandra Introduction to Mechanical engineering Chapter 9 -11

EML 3004 C 9. 5. 2 Frictional Forces Given 15 Kg crate up 30 degree slope with Namas Chandra Introduction to Mechanical engineering Chapter 9 -12

EML 3004 C 9. 5. 2 Frictional Forces. . 2 Given 15 Kg crate up 30 degree slope with Namas Chandra Introduction to Mechanical engineering Chapter 9 -13

EML 3004 C 9. 6 Motion of Rigid Body Namas Chandra Introduction to Mechanical engineering Chapter 9 -14

EML 3004 C 9. 6. 1 Crate Problem Revisited If the friction =0. 3 compute the dynamics of motion? Namas Chandra Introduction to Mechanical engineering Chapter 9 -15

EML 3004 C CHAPTER 9…concludes Statics, Dynamics, and Mechanical Engineering Namas Chandra Introduction to Mechanical engineering Chapter 9 -16