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Figure 1 shows a fairground ride - AQA - A-Level Physics - Question 1 - 2022 - Paper 6
Question 1
Figure 1 shows a fairground ride. Figure 1 The ride consists of a rotor that rotates in a vertical circle about a horizontal axis. The rotor has two rigid arms. A ... show full transcript
Worked Solution & Example Answer:Figure 1 shows a fairground ride - AQA - A-Level Physics - Question 1 - 2022 - Paper 6
Step 1
Determine the mean angular velocity of the rotor during the 12 s period.
Answer
To find the mean angular velocity ar{ heta} over the 12 s period, we will calculate the area under the angular velocity-time graph in Figure 2, dividing that area by the total time of 12 s.
The angular displacement in radians can be calculated by summing the areas of the trapezoids created in the graph, and using the formula:
ar{ heta} = \frac{\Delta \theta}{t_{total}}
where ar{ heta} is the mean angular velocity, is the angular displacement, and is the total time.
Calculating the areas, we find: [\bar{\omega} = 1.75 \text{ rad s}^{-1}]
Step 2
Calculate the power output of the driving mechanism during the first 2 s shown in Figure 2.
Answer
Power output (P) is calculated using the formula:
Where T is the torque and is the angular velocity. We need to use the value of torque obtained in the previous section, alongside the maximum angular velocity achieved during the first 2 s, to calculate:
[ P = 546 \text{ W} ]
Step 3
Calculate the maximum torque applied by the driving mechanism to the rotor during the 12 s period.
Answer
To find the maximum torque T_max, we analyze the relationship:
Where I is the moment of inertia and is the angular acceleration. Considering the highest angular acceleration obtained in the graph can be related with the torque equation.
Thus, applying known values: [ T_{max} = 990 ext{ N m} ]
Step 4
Step 5
Which graph best shows the variation of the torque T applied to the rotor for the 12 s period? Tick (✓) one box.
Answer
Upon reviewing the torque variation over the time period displayed in the graphs, the correct graph demonstrates the expected characteristic changes in torque corresponding to the angular velocity changes in the given time. The correct option is ticked on the provided graph.