FRQ 3 – Experimental Design

Overview

• Question 3 of 4 in Section II
• Worth 10 points (12.5% of your total exam score)
• Suggested time: 25-30 minutes
• Calculator allowed
• Tests skills: Creating quantitative graphs (1.B), Calculations and functional dependence (2.B, 2.D), Experimental design (3.A)

The Experimental Design and Analysis question uniquely assesses your ability to think like an experimental physicist. You'll design procedures to answer scientific questions, identify what to measure and how to analyze data, then work with provided data to extract meaningful results. This question emphasizes that physics isn't just about solving textbook problems – it's about investigating the real world systematically.

Strategy Deep Dive

LAB questions combine experimental design with data analysis. These complementary sections assess your ability to plan investigations and interpret results.

The Experimental Mindset

Unlike other FRQs where the scenario is completely defined, the LAB question puts you in charge. You decide what to measure, how to measure it, and how to analyze results. This freedom is both liberating and challenging. The key is thinking systematically about experimental design.

Effective experiments require variable isolation. Change only the quantity under investigation while maintaining all other conditions constant. This fundamental principle demands careful put in placeation. If investigating how mass affects period of oscillation, you can't just use different springs for different masses – that changes two variables. You need the same spring with different masses.

Designing Procedures

When writing procedures, balance detail with efficiency. You're not writing a lab manual, but you need enough detail to show you understand experimental realities. Include:

• What quantities you'll measure and how
• What you'll vary and what you'll keep constant
• How you'll minimize uncertainty (multiple trials, averaging, etc.)
• What equipment you'll use (be realistic about high school labs)

Replace vague instructions with specific procedures. Rather than "measure the force," write "Use a spring scale to measure the force required to maintain constant block velocity." Specificity demonstrates practical understanding.

Data Analysis Planning

Before you even see data, you should know how you'll analyze it. Linearization transforms complex relationships into analyzable forms. Physics relationships are often non-linear (quadratic, inverse, etc.), but linear graphs are easiest to analyze. Plan what to plot to get a straight line.

For example, if investigating how period depends on length for a pendulum, plotting T vs. L gives a curve. But physics tells us T = 2π√(L/g), so T^2 = (4π^2/g)L. Plotting T^2 vs. L gives a straight line with slope 4π^2/g. This planning before seeing data demonstrates physics understanding.

Working with Provided Data

The second part provides experimental data for a related investigation. This tests whether you can apply your analytical thinking to real data with all its imperfections. Key skills:

• Choosing appropriate quantities to graph
• Creating clear, accurate graphs
• Extracting information from slopes and intercepts
• Connecting results back to physics principles

Real data isn't perfect. Points won't fall exactly on lines. Your job is finding the trend and extracting physics meaning despite the scatter.

Common Experimental Scenarios

Certain experimental setups appear repeatedly because they offer rich opportunities for investigation while being feasible in high school labs.

Motion on Inclines

Investigating acceleration on ramps allows varying angle, mass, surface friction, or rotation. Common investigations:

• How does angle affect acceleration?
• How does the shape of a rolling object affect its acceleration?
• How can we determine coefficient of friction?

Key insight: Some quantities (like mass) don't affect acceleration on frictionless inclines, while others (like angle) do. Your procedure must recognize these relationships.

Oscillation Systems

Springs and pendulums offer numerous variables to investigate:

• Period vs. mass (springs yes, pendulums no)
• Period vs. amplitude (neither, for small oscillations)
• Period vs. spring constant or length
• Damping effects

These systems are excellent because relationships are well-defined but non-linear, requiring thoughtful analysis.

Fluid Pressure Experiments

Pressure investigations might involve:

• Pressure vs. depth in fluids
• Flow rate vs. pressure difference
• Buoyancy vs. object density

These connect to everyday experiences while requiring careful measurement technique.

Collision Investigations

While harder to control, collision experiments might investigate:

• Energy loss vs. material
• Coefficient of restitution vs. drop height
• Momentum conservation verification

The challenge is designing procedures that yield reproducible results despite the rapid nature of collisions.

Rubric Breakdown

Understanding the scoring helps you focus effort where it matters most. The 10 points typically divide between design and analysis sections.

Design Section (5 points typical)

Procedure (2-3 points):

• 1 point for identifying correct quantities to measure
• 1 point for describing a method that could work
• 1 point for addressing experimental uncertainties

What earns credit: Specific, realistic procedures that would actually answer the question. Mentioning multiple trials, averaging, or other uncertainty-reduction methods. Using appropriate equipment available in high school labs.

What loses credit: Vague procedures lacking specific measurements. Unrealistic equipment (laser interferometers, etc.). Procedures that wouldn't actually test the relationship in question.

Analysis Method (2 points):

• 1 point for describing what graph to create
• 1 point for explaining how to extract the answer from the graph

What earns credit: Specifying exact quantities to plot (including any mathematical transformations). Explaining whether slope, intercept, or another feature provides the answer. Showing understanding of linearization if needed.

What loses credit: Vague statements like "graph the data." Not explaining how the graph answers the question. Suggesting graphs that wouldn't reveal the relationship being investigated.

Analysis Section (5 points typical)

Graph Creation (3 points):

• 1 point for proper axes labels with units
• 1 point for accurate plotting with appropriate scale
• 1 point for best-fit line when appropriate

What earns credit: Clear labels including units. Scales that spread data across most of the graph. Points plotted accurately. Best-fit lines that reasonably represent the trend (not connecting dots).

What loses credit: Missing units. Compressed scales that waste graph space. Forcing lines through origin without justification. Connecting dots instead of finding best fit.

Calculation/Extraction (2 points):

• 1 point for correct slope/intercept calculation
• 1 point for correct interpretation with units

What earns credit: Using points from the best-fit line (not data points) for slope. Including units in calculations. Correctly relating slope/intercept to physical quantities.

What loses credit: Using data points instead of best-fit line. Arithmetic errors. Missing or incorrect units. Not relating mathematical results to physics.

Time Management Reality

30 minutes requires efficient work across both sections. Here's a practical timeline:

Minutes 0-3: Understanding Both Parts Read the entire question. Note what physical relationship you're investigating in design and what data you'll analyze. This overview prevents designing experiments that don't connect to the analysis.

Minutes 3-8: Experimental Design Write your procedure efficiently. Use numbered steps if that helps organize thoughts. Focus on what varies, what's measured, and what's constant. Don't write paragraphs – clear, concise statements earn full credit.

Minutes 8-12: Analysis Method Describe your graphing plan. If linearization is needed, show the mathematical reasoning briefly. Explain clearly how the graph will answer the question. This connects your experimental design to actual results.

Minutes 12-20: Creating the Graph This is where precision matters. Take time to:

• Choose scales that use the full graph
• Label axes completely with units
• Plot points carefully
• Draw best-fit line thoughtfully (it doesn't have to go through every point)

Minutes 20-27: Analysis and Calculation Extract the requested information from your graph. Show your calculation clearly. Include units throughout. Interpret what your result means physically.

Minutes 27-30: Review Check graph labels and units. Verify your procedure would actually work. Ensure your analysis answers the question asked. Add clarifying notes if needed.

Specific Experimental Design Strategies

Different types of investigations require different approaches. Here's how to handle common scenarios:

Direct Relationship Investigations

When investigating how quantity A affects quantity B:

1. Identify what to vary (A) and what to measure (B)
2. List what must stay constant (everything else)
3. Plan at least 5 data points across a reasonable range
4. Describe measurement tools realistically

Example: Investigating how angle affects acceleration down a ramp:

• Vary: ramp angle (using protractor or trigonometry)
• Measure: acceleration (using photogate timer or video analysis)
• Constant: same ramp surface, same object, release from rest
• Range: 10° to 60° in 10° increments

Verification Experiments

When verifying a physics principle:

1. Identify what relationship should hold
2. Plan measurements to test this relationship
3. Describe how agreement/disagreement would appear
4. Include uncertainty considerations

Example: Verifying conservation of momentum:

• Measure: masses and velocities before/after collision
• Method: video analysis or photogates
• Analysis: calculate total momentum before and after
• Success: values agree within experimental uncertainty

Determination Experiments

When finding an unknown quantity:

1. Identify what known relationship includes this quantity
2. Plan to measure everything else in that relationship
3. Describe how to isolate the unknown
4. Consider multiple methods if possible

Example: Determining local g value:

• Use pendulum: measure period and length, calculate from T = 2π√(L/g)
• Multiple lengths give multiple data points
• Graph T^2 vs. L, slope relates to g
• Average multiple trials at each length

Data Analysis Mastery

The analysis section tests whether you can extract physics from real data. Key strategies:

Choosing What to Graph

The question usually hints at the relationship, but you must decide exactly what to plot. Consider:

• What makes a straight line? (easier to analyze)
• What quantities were actually measured?
• What transformations might be needed?

If position was measured but you need acceleration, you might need to plot x vs. t^2. If investigating inverse relationships, plotting y vs. 1/x linearizes the data.

Creating Quality Graphs

Graph creation is a skill that earns easy points when done right:

• Use graph paper lines as guides
• Make scales that are easy to read (multiples of 1, 2, 5, 10)
• Spread data across at least 75% of each axis
• Label everything: axes, units, title if helpful
• Plot points clearly (visible dots, not tiny specks)

Best-Fit Lines

Your line should represent the trend, not connect dots:

• Balance points above and below the line
• Consider whether the line should go through origin (only if physics demands it)
• Extend line to cover the full data range
• Use a ruler for straight lines

Extracting Information

When calculating slope:

• Use points from your best-fit line, not data points
• Choose points far apart for accuracy
• Show the calculation: m = (y₂ - y₁)/(x₂ - x₁)
• Include units in the calculation

When using intercepts:

• Extend your line if necessary
• Read carefully from the graph
• Consider whether physics predicts zero or non-zero intercept

Common Pitfalls and How to Avoid Them

The LAB question has unique challenges. Here's how to navigate them:

Unrealistic Procedures

Students often describe procedures that wouldn't work in practice. Instead of "measure the velocity," specify "use a motion sensor to record position vs. time, then calculate velocity from the slope." This shows practical understanding.

Forgetting Controls

In excitement to vary one quantity, students forget to specify what stays constant. Always include a statement about controls. This demonstrates understanding of variable isolation.

Poor Graph Scales

Choosing scales like 0-100 when your data ranges from 2-8 wastes graph space and makes reading difficult. Choose scales that frame your data nicely while using convenient divisions.

Missing Linearization

If the relationship is non-linear, you must transform variables to create a linear graph. Don't plot curved relationships and try to analyze them – the slope of a curve isn't constant and doesn't give useful information.

Incomplete Analysis

Calculating slope isn't enough – you must connect it to physics. If slope equals 4π^2/g, state this and show how you'd extract g. The physical interpretation matters as much as the mathematical result.

Final Thoughts

The Experimental Design and Analysis question celebrates physics as an experimental science. It recognizes that real physics happens in labs, not just on paper. This question tests whether you can think like an experimental physicist: designing systematic investigations, controlling variables, analyzing messy real-world data, and extracting meaningful results.

Develop experimental thinking throughout your studies. For every physics relationship, consider how to verify it experimentally. When viewing data, identify the underlying physics principles it reveals. This thinking transforms you from a problem-solver to an investigator.

This question reflects authentic scientific practice. Research physicists primarily design experiments and analyze data rather than solving predetermined problems. By mastering this question type, you're developing real scientific skills that extend far beyond the AP exam. Approach it with curiosity and systematic thinking, and those 10 points will follow naturally.