Hypothesis: I can successfully add vectors.
Introduction: A vector is a quantity that has magnitude (speed, force, and/or length) and direction. For example, if a person is traveling East at 60 mph, then s/he is traveling in the direction East and at a magnitude of 60 mph. A scalar is a quantity with only a magnitude. Common scalars include currency, mass, time, and acceleration. It wouldn’t make sense to say the sweater costs $38.00 southwest, so we leave off the direction. The magnitude symbol ( ), an arrow, can express direction by its angle on a coordinate plane and its length, which is usually offered. In this lab, I also use the directional measurement unit of Azimuth (Az), which is conducted by starting at North and rotating clockwise to the desired angle, most probably the angle of the vector. Adding vectors, either two positive, two negative, or one of each is done most easily by resolving, or finding each vectors’ (A, B,C,…) x and y components. Here is an example of how to resolve then add vectors:











Procedure: See lab book.
Data:     

Trial 1     Magnitude (g)     Direction (Az)     X (N)     Y (N)
A     100.00     0     0     1.00
B     100.00     93.00     .998     -.052
C     100.00     177.00     .052     -.998
D     100.00     270.00     -1.00     0




Trial     Percent Error (%)
1     5.0
2     1.0
3     38.2
4     11.8

Trial 2     Magnitude (g)     Direction (Az)     X (N)     Y (N)
A     120.00     332.00     -.563     1.06
B     100.00     75.00     .966     .259
C     100.00     150.00     .500     -.866
D     100.00     234.00     -.809     -.588



Trial 3     Magnitude (g)     Direction (Az)     X (N)     Y (N)
A     170.00     277.00     -1.687     .207
B     200.00     60.00     1.732     1.00
C     100.00     148.00     .530     -.848
D     110.00     215.00     -.631     -.901
                         




Trial 4     Magnitude (g)     Direction (Az)     X (N)     Y (N)
A     120.00     315.00     -.849     .849
B     200.00     339.00     -.717     1.867
C     300.00     138.00     2.007     -2.229
D     110.00     265.00     -1.096     -.096






Sample Calculations:            (Trial 2)










                                         

                                                       
                                             
Conclusion: I successfully added three out of four vectors with a percent error of 12% or less, in which the acceptable percent error was 20% or less.
Analysis: Friction between the string and the pulley can have an effect on the lab because it makes the forces unnaturally low. To solve this problem, nullify friction by vibrating the force table. Another source of error may come when someone is putting the weights on the hooks of the pulleys and neglects to add the 50 grams of the hooks to their total force pulling on that particular string. This may throw off all calculations. Make sure to calculate and include all factors and measurements. Be careful to use cosine, sin, and tangent carefully or one miscalculation may cause more mistakes to be made unintentionally as well.