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PHYS 1301 1L2Ex. 4 The Addition and Resolution of Vectors: The Force Table
I.ObjectivePhysical quantities are classified as either scalar or vector quantities. The distinction is simple. A scalar quantity is one with magnitude only—for example, speed and temperature. A vector quantity, on the other hand, has both magnitude and direction. Such quantities include displacement, velocity, acceleration, and force—for example, a velocity of 15 m/s north or a force of 10 N along the + x-axis. Vectors are generally written using a boldface capital letter with an over arrow, for example, ⃗F. A nonboldface letter, F, indicates a magnitude. Because. Vectors have the property of direction, the common method of addition, that is scalar addition, is not applicable to vector quantities. To find the resultant or vector sum of two or more vector, special methods of vector addition are used, which may be graphical and/or analytical. The chief methods of there will be described, and the addition of force vectors will be investigated. The results of graphical and analytical methods will be compared with the experimental results obtained from a force table. The experimental arrangements of force will physically illustrate the principles of the methods of vector addition.II.TheoryA.Methods of Vector Addition: GraphicalTriangle MethodThe vectors are placed “head-to-tail which would be ⃗R=⃗A+ ⃗BAs long as the direction stays pointed in the same way, the vectors may movearound. ⃗Rwould be the vector sum and the magnitude of it would be relativeto the length of the vector arrow. The direction would be at the angle that isproportional to ⃗A. Polygon MethodWhen three vectors are being added, ⃗R=⃗A+⃗B+⃗C. This method is basicallythe head to tail method twice applied. To find the length and the angle can bedetermined by the resultant of the vector ⃗Rand in order to get that a graphical