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chap24 - Addition of a System of Coplanar Forces Vector...

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Addition of a System of Coplanar Forces Vector Notation In many problems it will be necessary to resolve a force into 2 components that are perpendicular to each other. y j ˆ i ˆ x O 2 vectors, i ˆ and j ˆ that have the direction shown and magnitude 1 - unit vectors. The i ˆ and j ˆ provide direction! -suppose I want a vector 4 units long in the x -direction i V ˆ 4 = -a vector 5 units long in the negative y -direction ( 29 j j V ˆ 5 ˆ 5 - = - = Is j i P ˆ 8 . 0 ˆ 6 . 0 + = a unit vector? Yes 1 8 . 0 6 . 0 2 2 = + = P j Suppose we have a force, with magnitude F x , that lies on the x -axis. i F F x x ˆ = and one on the y -axis i F F y y ˆ = . What is the resultant, F j ? j F i F F F F y x y x ˆ ˆ + = + = Remember: y x F F j j , and x F j are vectors y x F F , and F are magnitude of vectors, which are scalars What does F j look like? y What is the magnitude of F j ? 2 2 y x F F F + = y F j F j What is θ ? = - x y F F 1 tan θ j ˆ θ i ˆ x F j x
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Given F j what is x F j and y F j i F F x ˆ cos θ = j F F y ˆ sin θ = What is Υ F
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