Physics II workshop_Part_20

# Physics II workshop_Part_20 - Error analysis for the...

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42 Error analysis for the horizontal and the tilted projectile experiments. Refer to the propagation of uncertainties handout for the rules used below. From the horizontal shot , we got a value for the initial velocity of the ball, v 0 , using measurements of h and L . The equation for v 0 in this case is v 0 = L 2 h g We need to calculate the uncertainty in v 0 . Since we can assume that g is known to high precision, we only have to consider the uncertainties in L and h . First consider the 2 h g term. Since this is essentially constant × h 1/2 , the relative uncertainty is Δ 2 h g ( ) 2 h g = 1 2 Δ h h The relative uncertainty in L is just Δ L / L . Now we can use the error propagation rule for multiplication and division to get the relative uncertainty on v 0 : Δ v 0 v 0 = Δ L L + Δ 2 h g ( ) 2 h g = Δ L L + 1 2 Δ h h . The absolute error on v 0 is then Δ v 0 = v 0 Δ L L + 1 2 Δ h h Note: base your estimates of Δ L , Δ h , on the spread in the measurements, not the uncertainty on individual measurements.

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