The given formula is:

$E = \frac{1}{2}mv^2$

You are asked to isolate $m$ (mass) from this equation. Here's the step-by-step manipulation:

1. Start with the original formula:

$E = \frac{1}{2}mv^2$

2. To remove the fraction, multiply both sides of the equation by 2:

$2E = mv^2$

3. Finally, to isolate $m$, divide both sides of the equation by $v^2$:

$m = \frac{2E}{v^2}$

Thus, the formula for $m$ is:

$m = \frac{2E}{v^2}$

Would you like more details or have any questions?

Here are some related questions:

1. How do you isolate $v$ in the same formula?
2. What is the physical interpretation of $E$, $m$, and $v$ in this equation?
3. How is this formula derived from Newtonian mechanics?
4. How would the formula change if the velocity $v$ is doubled?
5. What are the SI units for energy $E$, mass $m$, and velocity $v$?

Tip: Always check the units of each variable when manipulating formulas to ensure they are consistent.