Experimental design and analysis (LAB)

Spring constant of a toy launcher

Unit 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. 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 want to determine the spring constant k of the spring inside a toy launcher that shoots a small ball straight up. They do not have a force sensor. Use g = 9.8 m/s² (answers that use g = 10 m/s² are also accepted).

Part A: Available equipment

The launcher (its compression can be set to different measured amounts), a small ball, an electronic balance, a meterstick, and a video camera that can record the ball against a wall marked in centimeters.

Source: Hypothetical lab setup

Part B: Table 1. Another group's data (ball mass 0.080 kg; h = maximum height reached, measured from the ball's position when the spring is compressed)

Spring compression x (m)	Maximum height h (m)
0.020	0.17
0.030	0.36
0.040	0.66
0.050	1.01
0.060	1.48

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 k. Include what you would measure and how.

Your answer to part (A(i))

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Part (A(ii))

2 points

Describe how you would use your data to determine k.

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 whose slope can be used to determine k, 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 calculate the spring constant k.

Your answer to part (B(iii))

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