Scientific inquiry and measurement

Four students measure the width of a notebook with a ruler whose smallest division is 1 mm. Which reported result is the most appropriate?

1. A

   21 cm

2. B

   21.437 cm

3. C

   21.4 cm

4. D

   0.21437 m

1. a

   Select and explain Select the best result, then explain why the other highly precise-looking result is not justified by the ruler.

   3
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   Correct choiceC

   1. 1

      Selects option C, which reports the notebook width as 21.4 cm.

   2. 2

      Recognises that a 1 mm scale supports reporting to about the nearest millimetre, or 0.1 cm.

   3. 3

      Explains that 21.437 cm claims digits that the instrument cannot resolve.

A student times ten complete swings of the same pendulum five times. The stopwatch reads to 0.01 s.

1. a

   Identify Identify the anomalous reading and give one evidence-based reason for your choice.

   2
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   1. 1

      Identifies 19.17 s as anomalous.

   2. 2

      States that it is much farther from the tight cluster 18.36–18.42 s than any other reading.

2. b

   Calculate Exclude the anomaly. Calculate the mean time for one swing and give the answer to an appropriate precision.

   3
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   1. 1

      Finds the mean time for ten swings: (18.42 + 18.36 + 18.40 + 18.38) ÷ 4 = 18.39 s.

   2. 2

      Divides by ten to obtain the period 1.839 s.

   3. 3

      Reports about 1.84 s with a justified precision.

3. c

   Explain Explain why timing ten swings is better than timing only one swing with the same stopwatch.

   2
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   1. 1

      Human reaction-time uncertainty is roughly the same for either timing interval.

   2. 2

      Dividing a longer total time by ten reduces the percentage uncertainty in the period.

A team claims that increasing the release height of a toy car increases its speed at the bottom of a ramp. They have one ramp, a metre rule, two light gates, blocks, and the same toy car.

1. a

   Formulate Write a testable research question and identify the independent and dependent variables.

   3
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   1. 1

      Writes a question that links release height to speed at the bottom for the same car and ramp.

   2. 2

      Identifies release height as the independent variable.

   3. 3

      Identifies speed measured by the light gates as the dependent variable.

2. b

   Design Describe a method that produces enough valid data to test the claim.

   3
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   1. 1

      Uses at least five measured release heights spanning a sensible range and releases the car without a push.

   2. 2

      Keeps relevant controls such as car, ramp surface, gate position, and ramp geometry unchanged.

   3. 3

      Repeats each height, calculates representative speeds, and plots speed against release height.

3. c

   Evaluate The car sometimes veers and misses a light gate. Propose one specific improvement and explain how it improves the evidence.

   2
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   1. 1

      Proposes a realistic guide rail or aligned channel that does not add substantial rubbing.

   2. 2

      Explains that more runs pass through the same part of the gate, reducing lost or inconsistent measurements.