50%(2)1 out of 2 people found this document helpful
This preview shows page 1 - 4 out of 10 pages.
PHYSICS-1ADDITION OF VECTORSExperiment 2: Addition of VectorsQUAN NGUYENPhys 1401DATE: 10/11/2017
PHYSICS-1ADDITION OF VECTORSEXPERIMENT-2: Addition of VectorsOBJECTIVESWhen a number of forces passing through the same point, act on an object, they may be replaced by a single force which is called the resultant or the sum. The resultant therefore is a single force which is similar in effect to the effect produced by the several forces acting on the body. It is therefore a single force that replaces those forces. The objectives of this lab areto use graphical, analytic and experimental methods to:1. Resolve a force vector into its rectangular components, and2. To find the resultant of a number of forces acting on a body. APPARATUS1. Force table5. Strings for suspending the masses 2. Four weight holders6. A ring3. Four pulleys7. A metal pin4. Slotted weights8. A protractor9. A compass10. Sheets of plain or graph paper.THEORY OF VECTOR ADDITIONA.Graphical MethodsParallelogram MethodVectors are represented graphically by arrows. The length of a vector arrow (drawn to scale on graph paper) is proportional to the magnitude of the vector, and the arrow points in the direction of the vector. The length scale is arbitrary and usually selected for convenience and so that the vector graph fits nicely on the graph paper. See Fig 1a, where R = A + B. The magnitude R of the resultant vector is proportional to the length of the diagonal arrow and the direction of the resultant vector is that of the diagonal arrow R. The direction of R may bespecified as being at an angle θ relative to A.Triangle MethodAn equivalent method of finding R is to place the vectors to be added "head to tail" (head of A to tail of B, Fig. l b). Vector arrows may be moved as long as they remain pointed in the same direction. The length and direction of the resultant is measured from the graph.Figure 1 a: Parallelogram methodFigure 1 b: Triangle methodRABBAR
PHYSICS-1ADDITION OF VECTORSPolygon MethodIf more than two vectors are added, the head-to-tail method formsa polygon (Fig. 2). For four vectors, the resultant R = A + B + C +D is the vector arrow from the tail of the A arrow to the head of thevector D. The length (magnitude) and the angle of orientation of Rcan be measured from the diagram. Figure 2B.Analytical MethodsTriangle MethodThe magnitude of R in Fig. 3 can also be computed by using trigonometry. The Law of Sines and the Law of Cosines are especially useful for this:Law of Sines: A/Sin α = B / Sin β = C / Sin γ. Law of Cosines:C2= A2+ B2– 2AB Cos γ