Dr. Lee’s student is measuring the beam deflection according to the weight of coins. Number of Experiment Coin Weight [Kg] Beam Deflection [mm]
1 0.00 1.00
2 0.20 1.22
3 0.40 1.49
4 0.60 1.82
5 0.80 2.23
6 1.00 2.72
7 1.20 3.32
We found the deflection is somehow proportional to the coin weight. If the linear fit curve is determined as Y [mm]=a [mm/Kg] × X [Kg]+b [mm], calculate the total uncertainty (ut) of the beam deflection when ua (uncertainty of a) = 0.10 mm/Kg and ub (uncertainty of b) = 0.05 mm. Please use the equation below:
ut = √((f/a)X=Xmax × ua)2 + (f/b × ub)2