Ok, my Physics professor gave us this to do uncertainty propagation with these e

Question

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:

Find the minimum value, maximum value, and best estimate for all raw data.

Perform one mathematical operation at a time.

If you are adding, then do the following:

c = a + b

cmax = amax + bmax

cmin = amin + bmin

If you are subtracting, then do the following:

c = a – b

cmax = amax – bmin

cmin = amin – bmax

If you are multiplying, then do the following:

c = a*b

cmax = amax*bmax

cmin = amin*bmin

If you are dividing, then do the following:

c = a/b

cmax = amax/bmin

cmin = amin/bmax

If you are using exponents (including square root), then do the following:

c = ab

cmax = amaxb_max

cmin = amin*bmin

This is the raw data that I'm using.

Trial at 10% Mass Difference: 38.0 ± 0.1 g

Trial #

Time

1

2.84

2

3.06

3

2.75

4

2.95

5

2.90

Trial at 15% Mass Difference: 43.7 ± 0.1 g

Trial #

Time

1

1.99

2

2.01

3

2.03

4

1.96

5

1.97

Trial at 20% Mass Difference: 45.6 ± 0.1 g

Trial #

Time

1

1.79

2

1.89

3

1.83

4

1.82

5

1.78

Trial at 25% Mass Difference: 47.5 ± 0.1 g

Trial #

Time

1

1.58

2

1.56

3

1.59

4

1.60

5

1.63

Trial #

Time

1

2.84

2

3.06

3

2.75

4

2.95

5

2.90

Explanation / Answer

It’s not clearly mentioned what to with the tabulated data you have provided. For the stated equations involving max and min, the logic is very simple, namely that one should consider the maximum and minimum error that can be there in a particular mathematical operation. For all the basic operations like addition, multiplication, exponential only maximum(minimum) numbers should be involved to have maximum(minimum) resultant value, with the exceptions in cases of subtraction and division, where to obtain maximum(minimum) resultant one should subtract the min(max) from max(min) or divide max(min by min(max).

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