Vector Addition of Forces

Purpose: To study vector addition by:
1) Graphical means and by
2) Using components.
A circular force table is used to check results.

Equipment: Circular force table, masses, massholders, string, protractor, four pulleys.

Procedure: 1. Your instructor will give each group three masses in grams (which will
represent the magnitude of three forces) and three angles. Choose a scale of
1 cm = 20 grams, make a vector diagram showing these forces, and
graphically find their resultant. Determine the magnitude (length) and
direction (angle) of the resultant force using a ruler and protractor.

mass 1. 100g 0 degree
mass 2. 100g 335 degree
mass 3. 100g 270 degree

2. Make a second vector diagram and show the same three forces again. Find
the resultant vector again, this time by components. Show the components of
each vector as well as the resultant vector on your diagram. Draw the force
(vector) you would need to exactly cancel out this resultant.

                                           scaled vectors and their vector addition steps 1 and2

                                             results from calculating the angle at 180 degrees
                                               opposite from resulting angle of first 30 vectors
                                                (step 3)

3. Mount three pulleys on the edge of your force table at the angles given
above. Attach strings to the center ring so that they each run over the pulley
and attach to a mass holder as shown in the figure below. Hang the
appropriate masses (numerically equal to the forces in grams) on each string.
Is the ring in equilibrium? Set up a fourth pulley and mass holder at 180
degrees opposite from the angle you calculated for the resultant of the first
three vectors. Record all mass and angles. If you now place a mass on this
fourth holder equal to the magnitude of the resultant, what happens? THE RING WAS IN EQUILIBRIUM right in the middle not touching the center point. Ask
your instructor to check your results before going on.

                                                            force table set up
4. Confirm your results via simulation:
http://phet.colorado.edu/en/simulation/vector-addition
Add the vectors and obtain a resultant.

                                              results are verified thru simulation
Errors:human error in correctly lining up the masses with their respected angles on the table and also error in the  vector addition calculations.the table not being properly leveled.
conclusion: we were able to learn how to study vector addition by both graphically and by components, we found out that the results are more accurate when using vector components you just have to be careful that the math is done right or else u wont get equilibrium when the results are checked on a force table.