# Problem-Solving: Laboratory Practice

Physics I · Principles of Laboratory Practice · https://tryals.app/learn/physics-i/problem-solving-laboratory-practice

## Pre-Lab and Execution

Effective laboratory work combines experimental skill with rigorous data analysis. The goal is not to force a "right answer," but to demonstrate honest analysis and physical understanding.

**Before the experiment**, read the theory and predict the expected result. Identify which variables to control, vary, and measure, then estimate required precision to choose appropriate instruments.

**During the experiment**, record raw data immediately in a table with units and note any anomalies. Always take at least $5$ repeated measurements for each data point to capture variability.

**Common pitfalls** include discarding "bad" data without statistical justification, confusing single-measurement uncertainty with the uncertainty of the mean, and omitting units during calculations.

## Post-Lab and Agreement

**After the experiment**, follow these core steps for data processing and evaluation:

| Step | Action |
| --- | --- |
| 1 & 2 | Calculate means/errors and plot with error bars |
| 3 & 4 | Fit a line/curve and extract physical quantities |
| 5 & 6 | Propagate uncertainties and compare with accepted values |

**Assessing agreement**: Two results $A \pm \delta A$ and $B \pm \delta B$ agree if:

$$|A - B| \leq 2\sqrt{(\delta A)^2 + (\delta B)^2}$$

**Common pitfall**: Comparing bare central values (like declaring $9.79$ wrong because a handbook says $9.81$) ignores error analysis. Results disagree only if their uncertainty intervals fail to overlap.

## Practice questions

9 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Complete the statement with the correct term.

**Answer:** A **factorial** experiment tests the effect of two or more factors by varying them in all possible combinations.

**Why:** Factorial design tests all combinations of factor levels, allowing detection of interactions.

Page: https://tryals.app/practice/physics-i/problem-solving-laboratory-practice/complete-the-statement-with-the-correct-term

### 2. Two measurements of $g$: $9.80 \pm 0.10$ and $9.90 \pm 0.20$ m/s$^{2}$. What is the weighted mean? (Weights $= 1/\sigma^{2}$.)

**Answer:** 9.82 (within ±0.01)

**Why:** $w_{1} = 1/0.01 = 100, w_{2} = 1/0.04 = 25$. Weighted mean = (100$\times9.80 + 25 \times9.90)/125 = 9.82$.

Page: https://tryals.app/practice/physics-i/problem-solving-laboratory-practice/two-measurements-of-g-9-80-0-10-and-9-90-0-20-m-s-what-is-the

### 3. Match each problem-solving strategy to its description.

**Answer:**

- Dimensional analysis → Check that units are consistent on both sides of an equation
- Order-of-magnitude estimate → Rough calculation to check if a result is reasonable
- Limiting cases → Verify a formula by checking extreme parameter values
- Sensitivity analysis → Determine which variable contributes most to the total uncertainty

**Why:** These strategies help catch errors and build confidence in results.

Page: https://tryals.app/practice/physics-i/problem-solving-laboratory-practice/match-each-problem-solving-strategy-to-its-description

### 4. Which are good practices for maintaining a laboratory notebook?

A. Rewrite data neatly on a separate sheet and discard the original
B. Cross out errors with a single line (don't erase or white out)
C. Date and sign each page
D. Record data in pen directly in the notebook during the experiment

**Answer:** B. Cross out errors with a single line (don't erase or white out); C. Date and sign each page; D. Record data in pen directly in the notebook during the experiment

**Why:** Lab notebooks are legal and scientific records; originals must be preserved, errors crossed out (not erased).

Page: https://tryals.app/practice/physics-i/problem-solving-laboratory-practice/which-are-good-practices-for-maintaining-a-laboratory-notebook

### 5. Complete the following passage by choosing the correct terms from the word bank.

**Answer:** Before conducting an experiment, you should write a **hypothesis** that predicts the outcome and identify the **confounding** variables to control.

**Why:** A clear hypothesis and identification of confounding variables are essential for good experimental design.

Page: https://tryals.app/practice/physics-i/problem-solving-laboratory-practice/complete-the-following-passage-by-choosing-the-correct-terms-from-the

### 6. Sort each activity into the planning or analysis phase of an experiment.

**Answer:**

- Planning phase: Formulating the hypothesis, Choosing controlled variables, Designing the data collection table
- Analysis phase: Calculating the chi-squared statistic, Plotting residuals, Propagating uncertainties to the final result

**Why:** Good experiments require careful planning before and rigorous analysis after data collection.

Page: https://tryals.app/practice/physics-i/problem-solving-laboratory-practice/sort-each-activity-into-the-planning-or-analysis-phase-of-an

### 7. Two labs measure the same constant. Lab A: $9.79 \pm 0.02$. Lab B: $9.90 \pm 0.15$. The accepted value is 9.81. Which statement is the **correct reading** of these results?

A. The labs disagree with each other, so at least one blundered
B. Lab B failed: 9.90 is farther from 9.81
C. Lab A failed: its interval is suspiciously narrow
D. Both are consistent with 9.81 within their error bars

**Answer:** D. Both are consistent with 9.81 within their error bars

**Why:** Both intervals embrace 9.81, so both measurements are consistent with it. B is merely less **precise**, not wrong. Results are statements of ranges, not single numbers; comparing bare central values without their uncertainties is the cardinal sin of data interpretation.

Page: https://tryals.app/practice/physics-i/problem-solving-laboratory-practice/two-labs-measure-the-same-constant-lab-a-9-79-0-02-lab-b-9-90

### 8. An experimental result is reported as $9.79 \pm 0.05$ m/s². Why is the uncertainty part of the result rather than an admission attached to it?

A. Because it shows the experimenters were careful
B. Because without it the number cannot be compared with anything
C. Because journals require uncertainties to be quoted
D. Because the uncertainty can be used to correct the central value later

**Answer:** B. Because without it the number cannot be compared with anything

**Why:** Agreement is a statement about intervals. The same central value agrees or disagrees depending on the uncertainty, so the uncertainty IS the claim.

Page: https://tryals.app/practice/physics-i/problem-solving-laboratory-practice/an-experimental-result-is-reported-as-9-79-0-05-m-s-why-is-the

### 9. Systematic errors can be reduced by simply taking more measurements and averaging.

**Answer:** False

**Why:** Averaging reduces random error but not systematic error; systematic errors require calibration or redesign.

Page: https://tryals.app/practice/physics-i/problem-solving-laboratory-practice/systematic-errors-can-be-reduced-by-simply-taking-more-measurements