if two objects with masses of 3kg and 9kg experience a gravitational force of 27N what will the gravitational force be if the mass of the second object is increased to 18kg while the first object remains the same

The gravitational force between two masses is governed by Newton's law of universal gravitation:

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

where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \)),
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the two objects.

Given:
- Initial masses: \( m_1 = 3 \, \text{kg} \) and \( m_2 = 9 \, \text{kg} \),
- Gravitational force between them: \( F = 27 \, \text{N} \).

We are asked to find the new gravitational force when the second mass \( m_2 \) is increased to 18 kg, with \( m_1 \) remaining the same.

### Step 1: Use the ratio of forces
Since the distance \( r \) between the objects and the gravitational constant \( G \) remain the same, we can express the ratio of the forces based on the masses:

\[
\frac{F_{\text{new}}}{F_{\text{old}}} = \frac{m_1 \cdot m_2' }{m_1 \cdot m_2} = \frac{m_2'}{m_2}
\]

Where \( m_2' = 18 \, \text{kg} \) and \( m_2 = 9 \, \text{kg} \).

\[
\frac{F_{\text{new}}}{27} = \frac{18}{9} = 2
\]

### Step 2: Calculate the new force
\[
F_{\text{new}} = 2 \times 27 = 54 \, \text{N}
\]

Thus, the new gravitational force between the two objects is \( \mathbf{54 \, \text{N}} \).

Would you like more details on this? Here are five questions that can extend this topic:

1. How does the gravitational force change if both masses are doubled?
2. How is the gravitational force affected by the distance between the two objects?
3. What happens to the gravitational force if the mass of the first object is also increased?
4. How can we calculate the distance between two objects given their masses and gravitational force?
5. How would the gravitational force change if the distance between the objects was halved?

**Tip:** The gravitational force is directly proportional to the product of the masses and inversely proportional to the square of the distance.

If two objects with masses of 3kg and 9kg experience a gravitational force of 27N, what will the gravitational force be if the mass of the second object is increased to 18kg while the first object remains the same?

Find out how to calculate the new gravitational force when the mass of one object changes. This example starts with a 3kg and 9kg mass experiencing a force of 27N, and shows how to determine the new force when the second mass increases to 18kg. This problem explores Newton's Law of Universal Gravitation and proportional relationships, suitable for students in Grades 9-12.

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