Vectors in Multiple Directions
Source: Nicholas Timmons, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA
This experiment demonstrates how vectors add and subtract in multiple directions. The goal will be to analytically calculate the addition or subtraction of multiple vectors and then to experimentally confirm the calculations.
A vector is an object with both magnitude and direction. The magnitude of a vector is simply denoted as the length, while the direction is typically defined by the angle it makes with the x-axis. Because forces are vectors, they can be used as a physical representation of vectors. By setting up a system of forces and finding which additional force will create an equilibrium between the forces, a system of vectors can be experimentally verified.
1. Balance forces.
- On the force table, set up two pulleys with the same mass facing opposite directions (180° difference in angle).
- The force of each will be equal to
. Check whether the two forces are equal and opposite by examining the ring at the center of the force table, which should not move. - Notice that if the components of the vectors associated with these forces are added, the resultant vector will have zero
The results of the lab are shown in Table 1 and Table 2.
Table 1. Setup.
at 0° for the duration.
are known and 
, when added to the system, causes the two forces to be in equilibrium, then 
.
. Complete Table 2 with these calculated values.
