When we add or subtract two qualities, their uncertainties must always be added

Question

When we add or subtract two qualities, their uncertainties must always be added to obtain the uncertainty on the computed quantity. For example, the length z plusminus Delta z is the sum of x plusminus Delta x and y plusminus Delta y. Therefore, the uncertainty of the total length is, Length = (x plusminus Delta x)m + (y plusminus Delta y)m = (x + y) plusminus ( Delta x = Delta y)m = (z plusminus Delta z)m You measure X = 7.4 plusminus 0.05m and Y = 3.6 plusminus 0.02m. Find X + Y and X - Y. Decompose the vector rvector = 12 plusminus 0.1cm/30 degree into its components rvectorx plusminus Delta rx and rvectory plusminus Delta ry. If we were given an uncertainty in the angle, how would this complicate the calculation?

Explanation / Answer

a)x + y = 11 + 0.07 m and x-y= 3.8 ± 0.07 m

b) rx ±rx =12cos30 ± 0.1 cm *cos20 =10.39±0.0866 cm

ry ±ry =12sin30 ± 0.1 cm *sin30 =6±0.05 cm

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