When we add or subtract two quantities, their uncertainties must always added to

Question

When we add or subtract two quantities, their uncertainties must always added to obtain the uncertainty ao 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 (13) = (x + y) plusminus (Delta x = Delta y)m (14) = (z plusminus Delta z)m (15) You measure X = 7.4 plusminus 0.05m and Y = 3.6 plusminus 0.02m. Find X + Y and X - Y. Decompose the vector r = 12 plusminus 0.1cm 30 degree into its components rx plusminus Delta rx and ry 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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