Experiment 3 Addition of VectorsRev: 8/24/2019OBJECTIVESWhen 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 are to 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. Since this lab is to be done at home, only the Graphical and, Analyticalparts are to be done. Do these on paper, take nice pictures, andupload with your report. Parts not to do have been changed to redfont.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.11. RulerTHEORY 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 so that the vector graph fits nicely on the graph paper. See Fig 1a, where R = A + B. The magnitude Rof the resultant vector is proportional to the length of the diagonal arrow and the direction of the resultant vector is that ofthe diagonal arrow R. The direction of R may be specified 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.RBABARFigure 1aFigure 1b

Polygon 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.