d by a gravitational force of 9.3 N. What will the force of attraction be if the distance between the two masses e final answer to four decimal places.) ill be 148.8 ON.

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Chapter1: Units, Trigonometry. And Vectors
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**Question:**

Two masses are attracted by a gravitational force of 9.3 N. What will the force of attraction be if the distance between the two masses is quadrupled? (Round the final answer to four decimal places.)

**Incorrect Response Given:**

The force of attraction will be \(148.8\) N.

**Explanation:**

The gravitational force between two masses is governed by Newton's Law of Universal Gravitation, which is mathematically expressed as:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

Where:
- \( F \) is the gravitational force between the masses,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses,
- \( r \) is the distance between the centers of the two masses.

When the distance \( r \) is quadrupled, the force \( F \) becomes:

\[ F' = \frac{G \cdot m_1 \cdot m_2}{(4r)^2} = \frac{G \cdot m_1 \cdot m_2}{16r^2} = \frac{1}{16} \cdot F \]

So the new force \( F' \) is \( \frac{1}{16} \) of the original force.

Given the original force \( F = 9.3 \) N, the new force is:

\[ F' = \frac{9.3}{16} \approx 0.5813 \, \text{N} \]
Transcribed Image Text:**Question:** Two masses are attracted by a gravitational force of 9.3 N. What will the force of attraction be if the distance between the two masses is quadrupled? (Round the final answer to four decimal places.) **Incorrect Response Given:** The force of attraction will be \(148.8\) N. **Explanation:** The gravitational force between two masses is governed by Newton's Law of Universal Gravitation, which is mathematically expressed as: \[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \] Where: - \( F \) is the gravitational force between the masses, - \( G \) is the gravitational constant, - \( m_1 \) and \( m_2 \) are the masses, - \( r \) is the distance between the centers of the two masses. When the distance \( r \) is quadrupled, the force \( F \) becomes: \[ F' = \frac{G \cdot m_1 \cdot m_2}{(4r)^2} = \frac{G \cdot m_1 \cdot m_2}{16r^2} = \frac{1}{16} \cdot F \] So the new force \( F' \) is \( \frac{1}{16} \) of the original force. Given the original force \( F = 9.3 \) N, the new force is: \[ F' = \frac{9.3}{16} \approx 0.5813 \, \text{N} \]
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