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CV2101 Chapt 2 - Force Vectors

# CV2101 Chapt 2 - Force Vectors - Chapter 2 h Force Vectors...

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h Chapter 2 Force Vectors 2-1

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2 1 Scalars & Vectors 2.1 Scalars & Vectors M h i d l ith t ki d f titi Mechanics deals with two kinds of quantities: Scalars - quantities with magnitudes only. eg, mass (kg), length (m), speed (m/s) Vectors - magnitudes, directions and sense eg, force (N), displacement (m), moment (N ڄ m) 2-2 Chapter 2 Force Vectors
2.1 Scalars & Vectors Cont. The magnitude of the vector is the length of the The magnitude of the vector is the length of the arrow, the direction is defined by the angle between a reference axis and the arrow’s line of action, and the sense is indicated by the arrowhead the sense is indicated by the arrowhead. 2-3 Chapter 2 Force Vectors

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Types of Vectors C l t li i th l 1. Coplanar vectors lie in the same plane. 2. Collinear vectors act along the same line of action. 3. Concurrent vectors have lines of action that pass through the same point. 2-4 Chapter 2 Force Vectors
2 2 Vector Operations 2.2 Vector Operations V t dditi R A B B A Vector addition: R = A + B = B + A Vectors obey parallelogram law. The resultant R can also be obtained by the triangle rule. 2-5 Chapter 2 Force Vectors

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2 2 Vector Operations C 2.2 Vector Operations Cont. V t bt ti R’ A B A ( B) Vector subtraction: R’ = A - B = A + (-B) Resolution of a vector A vector may be resolved into two t b d i // components by drawing a //gram. For a given vector, there exist an infinite number of possible sets of components. 2-6 Chapter 2 Force Vectors
Cartesian vector form (2-D) Cartesian vector form (2 D) A f F b l d i t t A force F may be resolved into two components along the x and y axes: F = F x i + F y j where F x = F cos θ ; F y = F sin θ i is a unit vector in the x direction j i it t i th di ti is a unit vector in the y direction We can also represent F with a magnitude: F ( F 2 + F 2 ) and magnitude: F = x + y ) and direction tan θ = F y / F x F’ F’ i F’ j 2-7 F’ = x – F’ y Chapter 2 Force Vectors

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Resultant of several coplanar forces Wh th f i th h th i t it i Where three or more forces passing through the same point, it is convenient to determine their resultant by adding the respective components of all forces to obtain the magnitude and direction of the resultant the resultant. F R = F 1 + F 2 + F 3 = (F 1x - F 2x + F 3x ) i + (F 1y + F 2y - F 3y ) j = (F Rx ) i + (F Ry ) j Magnitude and direction of F R F R = (F Rx 2 + F Ry 2 ); θ = tan -1 (F Ry / F Rx ) 2-8 Chapter 2 Force Vectors
Sine law and Cosine law 2-9 Chapter 2 Force Vectors

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Example 2 1 Example 2.1 T f t th h k Two forces act on the hook. Determine the magnitude and direction of the resultant force direction of the resultant force. Solution: Method 1: Addition by trigonometry Method 1: Method 2: Algebraic solution using x, y components 2-10 Chapter 2 Force Vectors
Example 2 1 C Example 2.1 Cont. Sol tion 1 Addition b t igonomet Solution 1: Addition by trigonometry Construct the force triangle.

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CV2101 Chapt 2 - Force Vectors - Chapter 2 h Force Vectors...

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