Photo AI
A simple pendulum performs oscillations of period T in a vertical plane - AQA - A-Level Physics - Question 1 - 2020 - Paper 3
Question 1
A simple pendulum performs oscillations of period T in a vertical plane. Figure 1 shows views of the pendulum at the equilibrium position and at the instant of relea... show full transcript
Worked Solution & Example Answer:A simple pendulum performs oscillations of period T in a vertical plane - AQA - A-Level Physics - Question 1 - 2020 - Paper 3
Step 1
Explain why you chose this position.
Answer
The chosen position of the fiducial mark is central to the pendulum's arc at equilibrium. This is important because:
-
Maximizing Measurement Accuracy: The mark should align with the bob's vertical path to minimize parallax error when measuring the length of the pendulum (l) from the pivot to the center of mass of the bob.
-
Kinetic Energy Consideration: At this equilibrium position, the pendulum possesses maximum kinetic energy, meaning that any timing measured here provides greater consistency for period calculations since the pendulum moves fastest at this point.
Step 2
Describe a suitable procedure to determine A₀, the amplitude of the pendulum as it is released.
Answer
To determine the amplitude A₀ of the pendulum:
-
Set Up the Experiment: Place the pendulum such that it hangs freely and is able to oscillate without obstructions.
-
Mark the Initial Position: Pull the pendulum bob to one side and mark its initial height using a ruler or the fiducial card. This height represents A₀, the maximum displacement from equilibrium.
-
Release and Measure: Release the pendulum without pushing it. Allow it to swing and observe the height to which it rises on the opposite side. This will serve as verification of A₀.
-
Record Measurements: Use a stop watch to time several oscillations to ensure consistent values for T and investigate any changes in amplitude before and after the release.
Step 3
Estimate, using Figure 3, the expected percentage increase in T when A₀ increases.
Answer
Using Figure 3, observe the trend of the graph that plots T against A₀. The graph indicates that T increases as A₀ increases, suggesting a non-linear relationship:
-
Sample Points: For specific values of A₀ (e.g., A₀ = 0.2 and A₀ = 0.4), measure the corresponding T values from the graph.
-
Calculate Percentage Increase: Use the following formula to estimate the percentage increase:
\[ ext{Percentage Increase} = rac{T_{A_0=0.4} - T_{A_0=0.2}}{T_{A_0=0.2}} imes 100 \]
-
Present Result: Provide the calculated percentage increase based on your values.