Ok, my Physics professor gave us this to do uncertainty propagation with these equations. Can some please show me some examples on each of these so I know I'm doing them right?
Uncertainty Propagation
Since raw data includes uncertainty, all calculations include uncertainty. You are required to propagate uncertainty in your calculations unless specified otherwise in the lab instructions or by your instructor. Use the following method for uncertainty propagation:
1) Find the minimum value, maximum value, and best estimate for all raw data.
2) Perform one mathematical operation at a time.
3) If you are adding, then do the following:
a. c = a + b
b. cmax = amax + bmax
c. cmin = amin + bmin
4) If you are subtracting, then do the following:
a. c = a – b
b. cmax = amax – bmin
c. cmin = amin – bmax
5) If you are multiplying, then do the following:
a. c = a*b
b. cmax = amax*bmax
c. cmin = amin*bmin
6) If you are dividing, then do the following:
a. c = a/b
b. cmax = amax/bmin
c. cmin = amin/bmax
7) If you are using exponents (including square root), then do the following:
a. c = ab
b. cmax = amaxb_max
c. cmin = amin*bmin
on 7, do you mean c= a^b?
if so, the cmax=amax^bmax
and cmin=amin^bmin
others ok.
Sure! I can show you some examples on each of these uncertainty propagation methods. Let's start with addition:
Example 1: Addition
Suppose we have two measurements with uncertainties:
Measurement A: Value = 10 +/- 0.5
Measurement B: Value = 5 +/- 0.3
To find the sum of these measurements, we can use the following formulas:
c = a + b
cmax = amax + bmax
cmin = amin + bmin
Using the given values, we can substitute them into the formulas:
c = 10 + 5 = 15
cmax = (10 + 0.5) + (5 + 0.3) = 15.8
cmin = (10 - 0.5) + (5 - 0.3) = 14.2
So, the result of the addition is c = 15 +/- (0.8 to 0.2).
Next, let's move on to subtraction:
Example 2: Subtraction
Using the same measurements as before:
Measurement A: Value = 10 +/- 0.5
Measurement B: Value = 5 +/- 0.3
The formulas for subtraction are:
c = a - b
cmax = amax - bmin
cmin = amin - bmax
Substituting the given values:
c = 10 - 5 = 5
cmax = (10 + 0.5) - (5 - 0.3) = 5.8
cmin = (10 - 0.5) - (5 + 0.3) = 4.2
The result of the subtraction is c = 5 +/- (0.8 to 0.2).
Moving on to multiplication:
Example 3: Multiplication
Let's consider two measurements with uncertainties:
Measurement A: Value = 3 +/- 0.2
Measurement B: Value = 4 +/- 0.1
The formulas for multiplication are:
c = a * b
cmax = amax * bmax
cmin = amin * bmin
Plugging in the given values:
c = 3 * 4 = 12
cmax = (3 + 0.2) * (4 + 0.1) = 12.6
cmin = (3 - 0.2) * (4 - 0.1) = 11.4
The result of the multiplication is c = 12 +/- (0.6 to 0.4).
Finally, let's look at division:
Example 4: Division
Using the same measurements as before:
Measurement A: Value = 3 +/- 0.2
Measurement B: Value = 4 +/- 0.1
The formulas for division are:
c = a / b
cmax = amax / bmin
cmin = amin / bmax
Substituting the values:
c = 3 / 4 = 0.75
cmax = (3 + 0.2) / (4 - 0.1) = 0.83
cmin = (3 - 0.2) / (4 + 0.1) = 0.68
The result of the division is c = 0.75 +/- (0.15 to 0.07).
I hope these examples have helped you understand how to propagate uncertainties using these equations! If you have any more questions, feel free to ask.