Experimental design and analysis (LAB)
Testing momentum conservation with sticky carts
- Unit 4
- 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 test whether the total momentum of two carts is conserved when the carts collide and stick together. Cart A moves along a level track and collides with cart B, which is initially at rest. Hook-and-loop fasteners on the carts make them stick together.
Part A: Available equipment
A level low-friction track; cart A with a spring plunger launcher that can be set to several compressions; cart B; hook-and-loop fasteners on the facing ends of the carts; a set of 0.250 kg bar masses that fit on either cart; a balance; two motion detectors (one at each end of the track) that record velocity against time; and two photogates.
Source: Hypothetical lab setup
Part B: Table 1. Final speed of the stuck carts (cart A: 0.40 kg, same launch speed every trial)
| Mass of cart B, m_B (kg) | Final speed v_f (m/s) |
|---|---|
| 0.20 | 0.99 |
| 0.40 | 0.76 |
| 0.60 | 0.60 |
| 0.80 | 0.49 |
| 1.00 | 0.43 |
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 to test whether momentum is conserved in the collision. 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 decide whether momentum is conserved. Include what you would graph and what result would show momentum is conserved.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(i))
1 pointAnother group kept cart A's mass fixed at kg and launched it with the same speed every time, but measured only the final speed of the stuck carts (Table 1). Show that if momentum is conserved, a graph of versus is linear, and state what its slope and vertical intercept represent.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(ii))
2 pointsPlot versus using the data in Table 1, 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 (list their values), 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 pointsUse your best-fit line to determine in two independent ways, one from the slope and one from the intercept. Explain whether the results support conservation of momentum.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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