4. You and your lab partner added vectors in two ways. One lab partner should ha

Question

4. You and your lab partner added vectors in two ways. One lab partner should have added F1+ F2 and the other lab partner F2+ F1 . Did your results ‘verify’ the commutative law of addition for vectors. Explain your answer. Be sure and include uncertainties.

I understand that our resultant vectors are the same but i do not know 'why' they are the same or how to include the uncertainties.

Two Forces F,4.0000 ± 0.0002) N @ (135.00 ± 0.04) degrees F,=(6.0000 ± 0.0002) N @ 250.00 ± 0.04) degrees Uncertainty of this resultant is 0.0003N and 0.2 degrees Three Forces F.=(4.0000 ± 0.0002) N @ (290.00 ± 0.04) degrees F,3.00004 0.0002) N @ 180.00 ± 0.04) degrees F,=(5.0000 ± 0.0002) N @ 120.00 ± 0.04) degrees Uncertainty of this resultant is 0.0003N and 0.2 degrees

Explanation / Answer

Since forces are vector quantities and vectors follow commutative law therefore F1 + F2 must be equal to F2 + F1. Therefore resultants in both the calculations must be equal.

Now since the results in for the cases are equal therefore the commutative law is verified in the above demonstration.

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