# The Addition and Resolution of Vectors: The Force Table TLSAMP 2005.

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The Addition and Resolution of Vectors: The Force Table TLSAMP 2005

Group Members Jazmon Malone Christian Mallet Kristen Williams Janna Lipford Rhonda Laird

Force At Work

Group Two

Objective To analyze different methods of vector addition.

Hypothesis We believe that the sum of two vectors is not equal to the sum of their magnitude.

Group Two At Work

Materials  Three Weights  Calibrator  Thread  Force Table  Scissors  Calculator  Pulleys  Washer

Methods  Collected all materials  Make all pulleys parallel to the force table  Next you will cut the thread and attach it to each weight  Attach each weight to the washer  After attaching each weight to the washer, place one weight on 30 degrees and the other weight on 120 degrees.  With the remainder weight you will attempt to balance the washer.  When the washer is balanced you will record the degree and the weight that it took to balance the other two weights

Methods (Continued)  The weight is the magnitude of the resultant force, and degree is 180 degrees different from the direction of the resultant force  Input your results into the following formula  Record your results on a table.  Repeat this experiment three more times.  Compare the results and come to a conclusion

Data F1F2 ANGLE 1 IN DEGREES ANGLE 1 IN RADIANS ANGLE 2 IN DEGREES ANGLE 2 IN RADIANS 50 300.52361202.0944 50 200.34911001.7453 50 00.0000901.5708 50 100.1745951.6581 50 0.87271602.7925 50 1001.7453300.5236 50 1152.0071400.6981 50 350.61091452.5307

Data (Continued) cos(a1)cos(a2)sum(Fx)sin(a1)sin(a2)sum(Fy) 0.866025-0.518.301270190.50.86602540468.30127019 0.939693-0.1736538.302222160.3420201430.98480775366.34139482 16.13E-175001 0.984808-0.0871644.882600510.1736481780.99619469858.49214379 0.642788-0.93969-14.845250550.7660444430.34202014355.40322932 -0.173650.86602534.618861310.9848077530.574.24038765 -0.422620.76604417.171309070.9063077870.6427876177.45476984 0.819152-0.8191500.573576436 57.35764364

Data (Continued) R Balancing ForceTHETA IN RADIANS THETA IN DEGREES 70.71068701.30899693975 76.60444801.04719755160 70.71068450.78539816345 73.7277352.50.91629785753 57.3576475-1.308996939-75 81.915264.9951.13446401465 79.3353377.51.3526301778 57.35764000

Data Continued cos(a1)cos(a2)sum(Fx)sin(a1)sin(a2)sum(Fy) 0.866025-0.518.301270190.50.86602540468.30127019 0.939693-0.1736538.302222160.3420201430.98480775366.34139482 16.13E-175001 0.984808-0.0871644.882600510.1736481780.99619469858.49214379 0.642788-0.93969-14.845250550.7660444430.34202014355.40322932 -0.173650.86602534.618861310.9848077530.574.24038765 -0.422620.76604417.171309070.9063077870.6427876177.45476984 0.819152-0.8191500.573576436 57.35764364

Data Continued Theoretical Force Empirical Force 70.7106870 76.6044480 70.7106845 73.7277352.5 57.3576475 81.915264.995 79.3353377.5 57.357640

Hypothesis Testing Ho: Theoretical Force = Empirical Force Ha: Theoretical Force is not equal to the Empirical Force By using the Paired t-Test we found that the p-value is equal to By using the Paired t-Test we found that the p-value is equal to 0.157964475 The p-value is less than 0.05, so we failed to reject the null hypothesis.

Data Continued t-Test: Paired Two Sample for Means Theoretical ForceBalancing Force Mean70.9649199958.124375 Variance85.69359314701.3294674 Observations88 Pearson Correlation0.528446146 Hypothesized Mean Difference0 df7 t Stat1.580675693 P(T<=t) one-tail0.078982238 t Critical one-tail1.894577508 P(T<=t) two-tail0.157964475 t Critical two-tail2.36462256

Group Two with the Force Table

Conclusion Our Empirical Result supports the theoretical result. The theoretical result is the sum of the forces and magnitude. Our Empirical Result supports the theoretical result. The theoretical result is the sum of the forces and magnitude.