To determine the gravitational attraction between two objects, we can use Newton's law of universal gravitation, which states that the gravitational force \( F \) between two objects is given by:
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} , \text{N m}^2/\text{kg}^2 \)),
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two masses.
Since the distance is the same (1 m) for all the pairs of objects you're considering, the gravitational attraction will depend primarily on the masses of the objects involved.
- Book and Sarah: Assuming Sarah has a mass roughly similar to an average person (let's say around 60 kg) and a book has a mass of about 1 kg.
- Paperclip and Penny: A paperclip might weigh around 1 gram (0.001 kg), and a penny weighs around 2.5 grams (0.0025 kg).
- Small Pot and Book: If we assume a small pot weighs around 0.5 kg and the book is 1 kg.
- Penny and Small Pot: The penny is approximately 0.0025 kg, and the small pot is approximately 0.5 kg.
Now let's consider the approximate forces:
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Book and Sarah: \[ F \approx 6.674 \times 10^{-11} \frac{60 \times 1}{1^2} \approx 6.674 \times 10^{-10} \text{N} \]
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Paperclip and Penny: \[ F \approx 6.674 \times 10^{-11} \frac{0.001 \times 0.0025}{1^2} \approx 1.67 \times 10^{-16} \text{N} \]
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Small Pot and Book: \[ F \approx 6.674 \times 10^{-11} \frac{0.5 \times 1}{1^2} \approx 3.337 \times 10^{-11} \text{N} \]
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Penny and Small Pot: \[ F \approx 6.674 \times 10^{-11} \frac{0.0025 \times 0.5}{1^2} \approx 8.3425 \times 10^{-14} \text{N} \]
Summary:
- Book and Sarah: \( \approx 6.674 \times 10^{-10} \text{N} \)
- Paperclip and Penny: \( \approx 1.67 \times 10^{-16} \text{N} \)
- Small Pot and Book: \( \approx 3.337 \times 10^{-11} \text{N} \)
- Penny and Small Pot: \( \approx 8.3425 \times 10^{-14} \text{N} \)
The gravitational attraction is greatest between the book and Sarah.
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