1. VECTOR MECHANICS Rules for Graphical Vector Addition Ms. Peace

2. Introduction  In this chapter you will Study the effects of forces acting on a particle Learn how to replace two or more forces acting on a particle by a single force having the same effect Resultant Develop the relations which exist among the various forces acting on a particle in equilibrium

3. 2.2 Forces in a Plane  Forces on a Particle: the action of one body on another Characterized by  Point of Application  Magnitude  Direction Forces on a given particle have the same point of application so we will completely define by magnitude and direction

4. 2.2 Forces in a Plane  Magnitude Characterized by a certain number of units  N newton  kN kilonewton  lb pound  kip kilopound  Direction Defined by the line of action and the sense of the force

5. 2.2 Forces in a Plane  Infinite straight line = line of action 10 lb 30° A

6. 2.2 Forces in a Plane  Resultant Two forces acting on a particle can be replaced by a single force P Q R A

7. 2.4 Vectors  Vectors Mathematical expressions possessing magnitude and direction and add according to the parallelogram law and triangle law Displacements Velocities Accelerations Momenta

8. 2.4 Vectors  Scalar Physical quantities that do not have direction  Volume  Mass  Energy

9. 2.4 Vectors  Represented by arrows In text by boldface Letter with an arrow above it Underlined letter  Magnitude of a vector Defines the length of a vector used to represent it

10. 2.4 Vectors  Fixed Vectors (Bound) Well-defined point of application  The particle itself  Free Vectors Freely moved in space  Couples  Sliding Vectors Forces acting on a rigid body slid along line of action

11. 2.3 Vectors  Equal vectors have same magnitude and direction P P

12. 2.3 Vectors  Negative vector of a given vector P is defined as a vector having same magnitude as P and direction opposite to that of P P -P P + (-P) = 0 equal and opposite vectors

13. 2.4 Addition of Vectors  P + Q = Q + P  Addition of Vectors is Commutative  Laws/Rules to find resultant graphically Parallelogram Law Polygon Method/ Triangle Law Component Method