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The Addition and Resolution of Vectors:
The Force Table

After completing this lab, you will be able to:
1. Add a set of vectors graphically to find the resultant.
2. Add a set ofvectors analytically to find the resultant.
3. Appreciate the differences between graphical and analytical methods of vector addition.

Physical quantities are generally classifiedas being scalar or vector quantities. The distinction is simple. A scalar quantity is one with a magnitude only for example, speed (55 mph) and time (3 hrs.). A vector quantity on the other hand hasboth magnitude and direction. Such quantities include displacement, velocity, acceleration and force, for example, a velocity of 55 mph north or a force of 20 N along the +y axis. Because vectors havethe property of direction, the common method of addition, scalar addition, is not applicable to vector quantities. To find the resultant or vector sum of two or more vectors, special methods ofvector addition are used, which may be graphical and/or analytical. Two of these methods will be described, and we will investigate the addition of force vectors. The result of graphical and analyticalmethods will be compared with the experimental results obtained from the force table. The experimental arrangement of forces (vectors) will physically illustrate the principles of the methods of vectoraddition.

The force table is an apparatus that allows the experimental determination of the resultant of force vectors. The rim of the circular table is calibrated in degrees.Weight forces are applied to a central ring by means of strings running over pulleys and attached to weight hangers. The magnitude (which is the mass times the acceleration due to gravity) of a force(vector) is varied by adding or removing slotted weights, and direction is varied by moving the pulley. The resultant of two or more forces (vectors) is found by balancing the forces with another force...
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