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: $F=\frac{GMm}{r^2}$.
2. To solve for $m$, first isolate $m$ by multiplying both sides of the equation by $r^2$ to eliminate the denominator: $F{r}^2=GMm$.
3. Next, divide both sides of the equation by $GM$ to solve for $m$: $m=\frac{F{r}^2}{GM}$.
4. Ensure that the variables $G$, $M$, and $r$ are not zero, as they appear in the denominator.
5. The formula is now rearranged to express $m$ in terms of $F$, $G$, $M$, and $r$.

Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as addition, subtraction, multiplication, and division applied to both sides of the equation. Understanding how to manipulate equations is crucial for solving for a variable, especially in formulas where multiple variables are present.

Understanding Variables

In the context of the formula F = GMm/r², each letter represents a variable with a specific physical meaning: F is the gravitational force, G is the gravitational constant, M is the mass of one object, m is the mass of another object, and r is the distance between their centers. Recognizing the role of each variable helps in understanding how to isolate the variable of interest, in this case, m.

Denominator Restrictions

When solving equations, it is essential to consider restrictions on the variables, particularly those in the denominator. In this formula, r cannot be zero, as division by zero is undefined. Acknowledging these restrictions ensures that the solutions derived from the manipulation of the equation are valid and applicable in real-world scenarios.