Meriam, Kraige & Bolton — Statics of Particles: Problem 2_15

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/15 Determine the - and -components of the tension which is applied to point of the bar . Neglect the effects of the small pulley at . Assume that and are known. Problem 2/15 1. Define the Coordinate System and Point Locations We establish a rectangular coordinate system with the origin at the pivot . Based on the geometric information provided in the diagram: Bar : The bar has a length . The angle is measured from the horizontal -axis to the bar . Therefore, the coordinates of point are: Pulley : The dimensions show that pulley is located at a horizontal distance from the -axis and a vertical distance from the -axis. Thus, the coordinates of point are: 2. Determine the Force Vector Direction The tension is applied to point through a cable that passes over the pulley at . Neglecting the pulley's size, the force acts on point in the direction from toward . We can define the position vector from to : Substituting the coordinates: 3. Calculate the Length of the Cable Segment The magnitude of the vector (the distance between and ) is calculated using the Pythagorean theorem: xyTA OABrθ O(0,0) OArθx OAA x = A rcosθ,y = A rsinθ BBr yrxB x = B r,y = B r TAB AAB ABAB = AB(x − B x )i+ A (y − B y )j A = AB(r−rcosθ)i+(r−rsinθ)j=r(1−cosθ)i+r(1−sinθ)j AB ABAB Using the trigonometric identity : 4. Derive the - and -components of Tension The tension vector can be expressed as its magnitude multiplied by the unit vector in the direction of : The