In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? E = mc² for m

Verified step by step guidance

1. Identify the formula given: \(E = mc^2\). This is Einstein's mass-energy equivalence formula, which relates energy (\(E\)) to mass (\(m\)) and the speed of light (\(c\)).
2. The goal is to solve the formula for the variable \(m\), which means isolating \(m\) on one side of the equation.
3. Start by dividing both sides of the equation by \(c^2\) to isolate \(m\): \(\frac{E}{c^2} = \frac{mc^2}{c^2}\).
4. Simplify the right side since \(c^2\) divided by \(c^2\) is 1, leaving \(\frac{E}{c^2} = m\).
5. Rewrite the equation to express \(m\) explicitly: \(m = \frac{E}{c^2}\). This shows mass as energy divided by the square of the speed of light.

Key Concepts

Solving Formulas for a Specified Variable

This involves rearranging an equation to isolate the desired variable on one side. It requires using algebraic operations such as addition, subtraction, multiplication, division, and sometimes roots or exponents to rewrite the formula in terms of the specified variable.

Understanding the Formula E = mc²

This famous formula, derived by Albert Einstein, expresses the relationship between energy (E), mass (m), and the speed of light (c). It shows that energy equals mass times the speed of light squared, highlighting the equivalence of mass and energy.

Physical Constants and Their Roles in Formulas

The speed of light (c) is a constant approximately equal to 3 × 10^8 meters per second. Recognizing constants helps in solving formulas and understanding their physical meaning, as constants remain fixed while variables can change.