Aim for FivePhysics C: Mechanics

Experimental design and analysis (LAB)

Measuring g with a meterstick pendulum

  • Units 5 and 7
  • 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 acceleration due to gravity g using a uniform meterstick as a physical pendulum. Small holes have been drilled along the meterstick's center line every 5.0 cm, so the meterstick can hang from a horizontal nail through any hole and swing freely. For small oscillations, the period of a physical pendulum is T=2πIMgdT = 2\pi\sqrt{\dfrac{I}{Mgd}}, where I is the rotational inertia about the pivot, M is the mass, and d is the distance from the pivot to the center of mass. The students do not know the meterstick's rotational inertia about its center, IcmI_{\text{cm}}, and do not want to assume a value for it.

Part A: Available equipment

A uniform meterstick with holes drilled along its center line every 5.0 cm, a horizontal nail fixed to a stand that fits through the holes, a stopwatch, a protractor, a balance, and a second meterstick.

Source: Hypothetical lab setup

Part B: Table 1. Period of the meterstick pendulum for different pivot holes (small amplitude)

Distance from pivot to center d (m)Period T (s)
0.101.95
0.151.68
0.201.58
0.301.52
0.401.57
0.451.60

Source: Hypothetical data

Suggested time: 27 minutes

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Part (A(i))

3 points

Using only the equipment listed in the setup, describe an experimental procedure you could use to collect data that would allow you to determine g. 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 points

Describe how you would use your data to determine g without knowing IcmI_{\text{cm}}. 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 point

Another group collected the data in Table 1. Indicate which quantities you would graph to produce a straight line that could be used to determine g. Calculate the values you would plot.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (B(ii))

2 points

Plot 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 points

Using your best-fit line, calculate an experimental value for g.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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