Determine the value of e=mc²
Understand the Problem
The question is asking for the value of the equation e=mc², which describes the relationship between energy (e), mass (m), and the speed of light (c). In this equation, e represents energy, m represents mass, and c represents the speed of light in a vacuum, approximately 299,792,458 meters per second. To determine a specific value, a mass will need to be provided.
Answer
$e \approx 8.987551787 \times 10^{16} \text{ joules}$ for $m = 1 \text{ kg}$.
Answer for screen readers
The energy $e$ for a mass of $1 \text{ kg}$ is approximately $8.987551787 \times 10^{16} \text{ joules}$.
Steps to Solve
- Identify Variables
We need to identify the variables involved in the equation. Let's denote the mass as $m$ and the speed of light as $c$. In this case, we will use the approximate value of the speed of light:
$$ c \approx 299,792,458 \text{ m/s} $$
- Plug in the Mass
To find the energy $e$, we need the mass $m$. Suppose we have a mass value, for example, $m = 1 \text{ kg}$. Now we can substitute this mass into the equation:
$$ e = mc^2 $$
- Calculate Energy
Now we will calculate the energy using our values. For $m = 1 \text{ kg}$, we substitute into the equation:
$$ e = 1 \text{ kg} \times (299,792,458 \text{ m/s})^2 $$
- Evaluate the Expression
Finally, we calculate the square of the speed of light and then multiply it by the mass:
$$ c^2 = (299,792,458 \text{ m/s})^2 \approx 8.987551787 \times 10^{16} \text{ m}^2/\text{s}^2 $$
$$ e = 1 \text{ kg} \times 8.987551787 \times 10^{16} \text{ m}^2/\text{s}^2 \approx 8.987551787 \times 10^{16} \text{ joules} $$
The energy $e$ for a mass of $1 \text{ kg}$ is approximately $8.987551787 \times 10^{16} \text{ joules}$.
More Information
This well-known equation $e=mc^2$ was formulated by Albert Einstein and illustrates how mass can be converted into energy. This principle is fundamental in nuclear physics and has various applications, including nuclear power and weapons.
Tips
- Not using the correct value for the speed of light. Ensure you use $c \approx 299,792,458 \text{ m/s}$.
- Forgetting to square the speed of light when substituting in the formula.
- Miscalculating the final energy value, especially when handling large numbers in scientific notation.
