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A £2 coin has a diameter of 28 mm and a mass of 12 grams - AQA - A-Level Maths Pure - Question 14 - 2022 - Paper 2
Question 14
A £2 coin has a diameter of 28 mm and a mass of 12 grams. A uniform rod AB of length 160 mm and a fixed load of mass m grams are used to check that a £2 coin has th... show full transcript
Worked Solution & Example Answer:A £2 coin has a diameter of 28 mm and a mass of 12 grams - AQA - A-Level Maths Pure - Question 14 - 2022 - Paper 2
Step 1
Given that the rod is horizontal and rests in equilibrium, find m.
Answer
To find the mass m of the load at B, we will consider the moments about the midpoint of the rod, which we'll denote as point O. First, we find the distance from O to the point of load, which is the full length of the rod divided by 2 (i.e., 160 mm / 2 = 80 mm).
Next, we calculate the moment created by the £2 coin. The radius of the coin is half of the diameter, which is 28 mm / 2 = 14 mm. Therefore, the distance from point O to the centre of the £2 coin is 80 mm - 14 mm = 66 mm.
Using the principle of moments, we can set up the equation:
Here, 12 grams is the mass of the £2 coin and 66 mm is the distance from the center of the coin to the support (O).
Solving for m:
Step 2
State an assumption you have made about the £2 coin to answer part (a).
Answer
The assumption made about the £2 coin is that it is uniform, meaning that its mass is evenly distributed throughout its volume. This allows us to consider the center of mass of the coin when calculating moments.