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This question is about an experiment with a linear air track - AQA - A-Level Physics - Question 3 - 2017 - Paper 3
Question 3
This question is about an experiment with a linear air track. A block is used to raise one end of the track. A bumper fitted with a rubber cord is attached at the l... show full transcript
Worked Solution & Example Answer:This question is about an experiment with a linear air track - AQA - A-Level Physics - Question 3 - 2017 - Paper 3
Step 1
Deduce this value of p using Figure 13 and Figure 15.
Answer
From Figure 13, we can see that the glider starts at the zero mark at the bottom of the track. In Figure 15, the highest position of the glider recorded is at the 198.4 cm mark. Therefore, the value of p corresponding to n = 0 is p = 198.4 cm.
Step 2
Deduce x for all the values of p using Figure 14.
Answer
Using Figure 14, we can determine the distance x for each position p. This yields the following results:
- For n = 0, x = 0 cm.
- For n = 2, x = 174.6 cm.
- For n = 4, x = 125.4 cm.
- For n = 6, x = 101.3 cm.
- For n = 9, x = 75.4 cm.
- For n = 13, x = 53.8 cm.
Step 3
Plot on Figure 16 a graph of ln(x/cm) against n.
Answer
To plot the graph of ln(x/cm) against n, first calculate ln(x) for each of the values determined:
- For n = 0: ln(198.4) = 5.278
- For n = 2: ln(174.6) = 5.164
- For n = 4: ln(125.4) = 4.832
- For n = 6: ln(101.3) = 4.615
- For n = 9: ln(75.4) = 4.223
- For n = 13: ln(53.8) = 3.977
Next, plot these points on Figure 16. Ensure that the data points form a linear graph, confirming an exponential decay relationship.
Step 4
Explain why the graph you plotted confirms that x decreases exponentially with n.
Answer
The graph is linear with a negative gradient. This straight-line relationship indicates that as n increases, x decreases exponentially. The relationship can be expressed in the form x = Ae^{-kn} where A and k are constants, which fits the definition of exponential decay.
Step 5
Step 6
Describe and explain two procedures the student should take to reduce uncertainty in the measurements of p.
Answer
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Use a digital measuring device: Implement a digital ruler or sensor to measure the position p of the glider. Digital devices provide more precise readings than manual measurement, reducing human errors.
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Repeat measurements: Take multiple measurements of p at the same position under identical conditions and calculate the average value. This procedure helps to smooth out anomalies and minimizes random errors in the data collection process.