Experimental design and analysis (LAB)
Spring constant of a cart's plunger
- Units 2 and 3
- 10 points
- About 27 minutes
You can use a calculator on this question, just like on exam day.
A two-part lab question. First you design an experiment to answer a question: what you change, what you measure, the equipment and how you would analyze the data. Then you get a data table from a similar experiment, choose what to graph (often so the points fall on a straight line), plot it and use the slope, the intercept or the graph's shape to answer a question. On the exam: Question 3 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 25–30 minutes. This question type started in May 2025, so Physics C: Mechanics free-response questions from 2024 and earlier are built differently.
The question and its sources
Students want to determine the spring constant k of the spring plunger built into the front of a lab cart. The plunger can be pushed in by up to 6 cm.
Part A: Available equipment
A lab cart with a spring plunger on its front, a level low-friction track with a fixed end stop the plunger can push against, a balance, a ruler marked in millimeters, a set of slotted masses, a motion detector that records velocity against time, a photogate and timer, and a small wooden stop block.
Source: Hypothetical lab setup
Part B: Table 1. Launch speed for different plunger compressions (cart mass 0.50 kg)
| Compression x (m) | Launch speed v (m/s) |
|---|---|
| 0.010 | 0.13 |
| 0.020 | 0.23 |
| 0.030 | 0.37 |
| 0.040 | 0.47 |
| 0.050 | 0.61 |
Source: Hypothetical data
Suggested time: 27 minutes
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Part (A(i))
3 pointsUsing only the equipment listed in the setup, describe an experimental procedure you could use to collect data that would allow you to determine k. Include what you would measure and how, what you would vary, and one step you would take to reduce experimental uncertainty.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (A(ii))
2 pointsDescribe how you would use your data to determine k. Include what you would graph and how you would use the graph.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(i))
1 pointAnother group used a cart of total mass 0.50 kg and collected the data in Table 1. Indicate which quantities you would graph to produce a straight line that could be used to determine k, and justify your choice with an equation.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(ii))
2 pointsPlot the quantities you chose and draw a best-fit line. You can't draw here, so describe the graph you would draw: what goes on each axis (with units), the scale, the points you would plot, and the best-fit line.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(iii))
2 pointsUsing your best-fit line, calculate an experimental value for k.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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