Experimental design and analysis (LAB)

Water streaming from a hole in a bottle

Units 1 and 8
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 allowed. The CED suggests 25–30 minutes.

The question and its sources

Students investigate how the speed of water leaving a small hole near the bottom of a tall plastic bottle depends on the depth h of the hole below the water's surface. The bottle stands on a block so the hole is at a known height above the floor. Use g = 9.8 m/s² (answers that use g = 10 m/s² are also accepted).

Part A: Available equipment

The tall bottle with a small hole near the bottom (covered with tape when not in use), a pitcher of water, a meterstick, a marker, a shallow tray to catch the water, and a stopwatch.

Source: Hypothetical lab setup

Part B: Table 1. Another group's data (hole 0.50 m above the tray; x = horizontal distance from the hole to where the stream lands)

Depth of hole below water surface h (m)	Horizontal landing distance x (m)
0.10	0.43
0.20	0.61
0.30	0.75
0.40	0.86
0.50	0.97

Source: Hypothetical data

Suggested time: 27 minutes

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Part (A(i))

3 points

Describe an experimental procedure, using only the equipment listed, to collect data that would let you determine how the speed of the water leaving the hole depends on h. Include how you would find the speed from your measurements.

Your answer to part (A(i))

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Part (A(ii))

2 points

Torricelli's theorem predicts that the exit speed is v = √(2gh). Describe how you would use your data to test this prediction.

Your answer to part (A(ii))

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Part (B(i))

1 point

Using Table 1, indicate which quantities you would graph to produce a straight line that can be compared with Torricelli's prediction, and calculate the values you would plot.

Your answer to part (B(i))

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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 (list their values), and the best-fit line.

Your answer to part (B(ii))

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Part (B(iii))

2 points

Use your best-fit line to determine whether the data support Torricelli's prediction. If the data differ from the prediction, suggest a physical reason.

Your answer to part (B(iii))

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