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A student carried out an investigation to determine the spring constant of a spring - AQA - GCSE Physics - Question 2 - 2018 - Paper 1
Question 2
A student carried out an investigation to determine the spring constant of a spring. Table 1 gives the data obtained by the student. Table 1 | Force in N | Extens... show full transcript
Worked Solution & Example Answer:A student carried out an investigation to determine the spring constant of a spring - AQA - GCSE Physics - Question 2 - 2018 - Paper 1
Step 1
Describe a method the student could have used to obtain the data given in Table 1.
Answer
To obtain the data in Table 1, the student could follow this method:
- Set Up the Apparatus: The student should first set up a clamp stand with a clamp to hold the spring securely from a fixed point.
- Use a Ruler: Place a ruler vertically beside the spring, ensuring it is fixed in position to avoid parallax errors while taking measurements.
- Record Initial Position: For each force applied, record the initial position of the bottom of the spring without any loads added.
- Apply Weights: Weigh the spring down progressively with weights (2 N, 4 N, etc.), starting from 0 N up to 10 N.
- Measure Extensions: After adding each weight, measure the new position of the bottom of the spring and calculate the extension by taking the difference from the initial position.
- Repeat Measurements: Repeat the measurements for each force applied to ensure accuracy.
- Identify Possible Errors: Possible inaccuracies could come from not holding the ruler vertically, misjudging the spring's position, or failing to clamp the ruler at the right angle.
Step 2
Suggest why.
Answer
The student measured the extension for five different forces to identify any anomalous results and to reduce the effect of random error. By measuring the extension for various forces, the student could establish a more accurate average for the spring constant and ensure that the spring behaves linearly within the elastic limit.
Step 3
Complete Figure 2 by plotting the missing data from Table 1.
Answer
To plot the missing data:
- Draw the graph with force on the x-axis (N) and extension on the y-axis (cm).
- Plot the following points based on Table 1:
- (0, 0.0)
- (2, 3.5)
- (4, 8.0)
- (6, 12.5)
- (8, 16.0)
- (10, 20.0)
- Draw a straight line of best fit that passes through the origin (0,0) and through (10,20).
Step 4
Step 5
Calculate the spring constant of the spring that the student used.
Answer
To calculate the spring constant (k), we can use the formula derived from Hooke’s Law:
- Choose one force and its corresponding extension from the data. For instance, using the force of 10 N and the extension of 20 cm:
- Convert extension to meters: 20 cm = 0.2 m
- Substitute the values into the formula:
Therefore, the spring constant is:
Spring constant = 50 N/m.
Step 6
Explain how the data supports the student's conclusion.
Answer
The data supports the student's conclusion that the spring obeyed Hooke's Law because:
- Linear Relationship: The plot of force against extension produced a straight line, indicating a linear relationship. This suggests that the extension is directly proportional to the force applied, which is a key aspect of Hooke's Law.
- Origin Intersection: The line of best fit passes through the origin, confirming that when no force is applied, the extension is zero and aligns with the principles of elasticity.
- Consistent Results: Each recorded extension correlates with the respective force applied, demonstrating consistency across multiple trials, which validates the linearity of the spring's response under the tested conditions.