L3-Vector Addition.doc - PHYSICS-1 ADDITION OF VECTORS Experiment 2 Addition of Vectors QUAN NGUYEN Phys 1401 DATE PHYSICS-1 ADDITION OF VECTORS

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PHYSICS-1 ADDITION OF VECTORS Experiment 2: Addition of Vectors QUAN NGUYEN Phys 1401 DATE: 10/11/2017
PHYSICS-1 ADDITION OF VECTORS EXPERIMENT-2: Addition of Vectors OBJECTIVES When 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, and 2. To find the resultant of a number of forces acting on a body. APPARATUS 1. Force table 5. Strings for suspending the masses 2. Four weight holders 6. A ring 3. Four pulleys 7. A metal pin 4. Slotted weights 8. A protractor 9. A compass 10. Sheets of plain or graph paper. THEORY OF VECTOR ADDITION A. Graphical Methods Parallelogram Method Vectors 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 be specified as being at an angle θ relative to A . Triangle Method An 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 method Figure 1 b: Triangle method R A B B A R
PHYSICS-1 ADDITION OF VECTORS Polygon Method If more than two vectors are added, the head-to-tail method forms a 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 the vector D . The length (magnitude) and the angle of orientation of R can be measured from the diagram. Figure 2 B. Analytical Methods Triangle Method The 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: C 2 = A 2 + B 2 – 2AB Cos γ