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
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 Fall '09
 Luna
 Physics, ∆x, qbest

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