Vectors in Multiple Directions

1. Balance forces.

1. On the force table, set up two pulleys with the same mass facing opposite directions (180° difference in angle).
2. 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.
3. Notice that if the components of the vectors associated with these forces are added, the resultant vector will have zero magnitude. This is how to determine that all forces are in equilibrium.

2. Analytical calculations.

1. This lab will consist of three forces in equilibrium. Two forces will be known, while the third will be found-first analytically, using the theory of vectors, and then experimentally. For this lab, keep at 0° for the duration.
2. Note that if and  are known and , when added to the system, causes the two forces to be in equilibrium, then is of equal magnitude but in the opposite direction to the sum (  +  ).
3. Calculate the magnitude of and . Use the fact that and that 1 Newton (N) is a unit of force equal to .
4. Using the theory of vectors, calculate what magnitude  would be if it was the sum (  +  ).
5. Using the theory of vectors, calculate what angle would be if it was the sum (  +  ).

3. Experiment.

1. Following the values on the first line of Table 1 for  and , set up the two forces on the force table. Remember to keep  at 0°.
2. Set up the third force, , by adding weights and changing the angle until equilibrium is reached. Record these values in Table 2.
3. Repeat step 3.2 for each of the four cases.
4. Determine the percent difference from the analytical result by calculating the . Complete Table 2 with these calculated values.