Experimental design and analysis (LAB)
Measuring the charge on a hanging ball
- Units 8 and 9
- 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. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator and equation sheet allowed. The CED suggests 25–30 minutes.
The question and its sources
Students want to determine the charge q on a small, charged conducting ball. The ball hangs from a light, insulating thread midway between two large, vertical, parallel metal plates. When a potential difference is applied across the plates, the ball is pushed sideways and the thread hangs at an angle θ from the vertical. Assume the ball's charge stays the same throughout and the field between the plates is uniform. Use g = 9.8 m/s².
Part A: Available equipment
The charged ball (mass 0.50 g) hanging from an insulating thread about 0.10 m long; two large, vertical, parallel metal plates on insulating stands; an adjustable high-voltage supply (0 to 10,000 V) with a built-in voltmeter; a protractor mounted behind the thread; a meterstick; and a camera.
Source: Hypothetical lab setup
Part B: Table 1. Another group's data (plates 0.20 m apart; thread 0.10 m long; ball mass 0.50 g)
| Potential difference across the plates ΔV (V) | Angle of thread from vertical θ (°) |
|---|---|
| 2000 | 6.0 |
| 4000 | 11.4 |
| 6000 | 17.0 |
| 8000 | 22.0 |
| 10,000 | 27.2 |
Source: Hypothetical data
Suggested time: 27 minutes
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Part (A(i))
3 pointsDescribe an experimental procedure you could use, with only the equipment listed, to collect data that would allow you to determine q. Include what you would measure, what you would change, and any steps 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 q. Include what you would graph and how the graph would give you q.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(i))
1 pointUsing the data in Table 1, indicate which quantities you would graph to produce a straight line that could be used to determine q. 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 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 (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 calculate an experimental value for q.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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