Tham khảo tài liệu 'sat ii physics (sn) episode 1 part 2', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The vector is called the x-component of A and the is called the y-component of A. In this book we will use subscripts to denote vector components. For example the x-component of A is and the y-component of vector A is . The direction of a vector can be expressed in terms of the angle by which it is rotated counterclockwise from the x-axis. Vector Decomposition The process of finding a vector s components is known as resolving decomposing or breaking down a vector. Let s take the example illustrated above of a vector A with a magnitude of A and a direction above the x-axis. Because and A form a right triangle we can use trigonometry to solve this problem. Applying the trigonometric definitions of cosine and sine we find Vector Addition Using Components Vector decomposition is particularly useful when you re called upon to add two vectors that are 26 neither parallel nor perpendicular. In such a case you will want to resolve one vector into components that run parallel and perpendicular to the other vector. EXAMPLE Two ropes are tied to a box on a frictionless surface. One rope pulls due east with a force of . The second rope pulls with a force of at an angle 30Â west of north as shown in the diagram. What is the total force acting on the box To solve this problem we need to resolve the force on the second rope into its northward and westward components. Because the force is directed 30 west of north its northward component is and its westward component is Since the eastward component is also the eastward and westward components cancel one another out. The resultant force is directed due north with a force of approximately . You can justify this answer by using the parallelogram method. If you fill out the half-completed parallelogram formed by the two vectors in the diagram above you will find that the opposite corner of the parallelogram is directly above the corner made by the tails of those two vectors. 27 Vector Multiplication There are two .
