ErrorPropagation2A - Error Propagation The analysis of uncertainties(errors in measurements and calculations is essential in the physics laboratory For

1 The analysis of uncertainties (errors) in measurements and calculations is essential in the physics laboratory. For example, suppose you measure the length of a long rod by making three measurement x = x best ± ∆ x, y = y best ± ∆ y, and z = z best ± ∆ z. Each of these measurements has its own uncertainty ∆ x, ∆ y, and ∆ z respectively. What is the uncertainty in the length of the rod L = x + y + z? When we add the measurements do the uncertainties ∆ x, ∆ y, ∆ z cancel, add, or remain the same? Likewise , suppose we measure the dimensions b = b best ± ∆ b, h = h best ± ∆ h, and w = w best ± ∆ w of a block. Again, each of these measurements has its own uncertainty ∆ b, ∆ h, and ∆ w respectively. What is the uncertainty in the volume of the block V = bhw? Do the uncertainties add, cancel, or remain the same when we calculate the volume? In order for us to determine what happens to the uncertainty (error) in the length of the rod or volume of the block we must analyze how the error (uncertainty) propagates when we do the calculation. In error analysis we refer to this as error propagation . There is an error propagation formula that is used for calculating uncertainties when adding or subtracting measurements with uncertainties and a different error propagation