https://file.aiquickdraw.com/mathbot/file/1727469486676w4fk3exq.jpg

The given formula in the image is Newton's Law of Gravitation:

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

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

We are asked to solve for \( m_1 \).

### Steps to solve for \( m_1 \):

1. Start with the original equation:
   \[
   F = G \frac{m_1 m_2}{d^2}
   \]

2. To isolate \( m_1 \), first multiply both sides by \( d^2 \) to remove the denominator:
   \[
   F d^2 = G m_1 m_2
   \]

3. Next, divide both sides by \( G m_2 \) to solve for \( m_1 \):
   \[
   m_1 = \frac{F d^2}{G m_2}
   \]

Thus, the formula for \( m_1 \) is:

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

Would you like more details or further clarification?

Here are 5 related questions to deepen your understanding:
1. How does increasing the distance \( d \) between two objects affect the gravitational force?
2. What happens to \( m_1 \) if the force \( F \) doubles while all other variables remain constant?
3. How would you use this formula to calculate the gravitational force between two objects, given their masses and distance?
4. Can the gravitational force ever be negative? Why or why not?
5. How does the gravitational constant \( G \) influence the calculation of gravitational force?

**Tip**: When working with physical formulas, always ensure you are using consistent units, such as meters for distance and kilograms for mass, to avoid errors.

Newton's Law of Gravitation is given by the formula F = G(m1*m2/d^2). Solve the formula for m1.

Learn how to solve for m1 in Newton's Law of Gravitation using the formula F = G(m1*m2/d^2). This guide breaks down the algebra involved in solving the equation and explores the physical concepts of gravitational force, suitable for students in Grades 9-12.

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