A length is measured as 15.0 m with an uncertainty of ±0.3 m. What is the total

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Question: A length is measured as 15.0 m with an uncertainty of ±0.3 m. What is the total length if two such lengths are added?

Options:

Correct Answer: 30.6 m

Solution:

Total length = 15.0 + 15.0 = 30.0 m; Total uncertainty = ±0.3 + ±0.3 = ±0.6 m.

A length is measured as 15.0 m with an uncertainty of ±0.3 m. What is the total length if two such lengths are added?

A length is measured as 15.0 m with an uncertainty of ±0.3 m. What is the total length if two such lengths are added?

Step 1: Identify the length of one measurement, which is 15.0 m.
Step 2: Identify the uncertainty of one measurement, which is ±0.3 m.
Step 3: To find the total length when adding two measurements, add the lengths together: 15.0 m + 15.0 m.
Step 4: Calculate the total length: 15.0 + 15.0 = 30.0 m.
Step 5: To find the total uncertainty when adding two measurements, add the uncertainties together: ±0.3 m + ±0.3 m.
Step 6: Calculate the total uncertainty: ±0.3 + ±0.3 = ±0.6 m.
Step 7: Combine the total length and total uncertainty: The total length is 30.0 m with an uncertainty of ±0.6 m.

Measurement and Uncertainty – Understanding how to add measurements and their associated uncertainties.
Propagation of Uncertainty – Applying the rules for combining uncertainties when adding measurements.