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

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

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Force At Work

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Group Two

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Objective To analyze different methods of vector addition.

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

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Group Two At Work

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Materials Three Weights Calibrator Thread Force Table Scissors Calculator Pulleys Washer

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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

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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

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Data F1F2 ANGLE 1 IN DEGREES ANGLE 1 IN RADIANS ANGLE 2 IN DEGREES ANGLE 2 IN RADIANS

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Data (Continued) cos(a1)cos(a2)sum(Fx)sin(a1)sin(a2)sum(Fy) E

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Data (Continued) R Balancing ForceTHETA IN RADIANS THETA IN DEGREES

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Data Continued cos(a1)cos(a2)sum(Fx)sin(a1)sin(a2)sum(Fy) E

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Data Continued Theoretical Force Empirical Force

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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 The p-value is less than 0.05, so we failed to reject the null hypothesis.

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Data Continued t-Test: Paired Two Sample for Means Theoretical ForceBalancing Force Mean Variance Observations88 Pearson Correlation Hypothesized Mean Difference0 df7 t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail

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Group Two with the Force Table

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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.

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