Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. F = GMm/r², for m (force of gravity)

Verified step by step guidance

1. Start with the given formula for the force of gravity: \(F = \frac{GMm}{r^2}\).
2. Our goal is to solve for the variable \(m\). To isolate \(m\), first multiply both sides of the equation by \(r^2\) to eliminate the denominator: \(F \times r^2 = GMm\).
3. Next, to solve for \(m\), divide both sides of the equation by \(G M\) (assuming \(G\) and \(M\) are not zero): \(\frac{F r^2}{G M} = m\).
4. Rewrite the equation to clearly express \(m\) in terms of the other variables: \(m = \frac{F r^2}{G M}\).
5. This is the formula for \(m\) in terms of \(F\), \(G\), \(M\), and \(r\).

Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This includes using inverse operations such as multiplication, division, addition, and subtraction to solve for the desired variable while maintaining equation balance.

Solving for a Variable in a Formula

Solving for a variable means rewriting the formula so that the variable appears alone on one side of the equation. This often requires isolating the variable by performing operations on both sides, especially when the variable is in the numerator or denominator.

Handling Variables in Denominators

When variables appear in denominators, it is important to multiply both sides by the denominator to eliminate fractions. This step simplifies the equation and avoids division by zero, which is undefined, ensuring the solution is valid.