Sure! Let's solve the equation [tex]\( F = \frac{s M v^2}{r} \)[/tex] for [tex]\( v \)[/tex].
1. Start with the given equation:
[tex]\[
F = \frac{s M v^2}{r}
\][/tex]
2. Isolate [tex]\( v^2 \)[/tex]:
Multiply both sides of the equation by [tex]\( r \)[/tex]:
[tex]\[
F \cdot r = s M v^2
\][/tex]
3. Solve for [tex]\( v^2 \)[/tex]:
Divide both sides by [tex]\( s M \)[/tex]:
[tex]\[
v^2 = \frac{F \cdot r}{s \cdot M}
\][/tex]
4. Take the square root of both sides to solve for [tex]\( v \)[/tex]:
It’s important to consider both positive and negative roots when taking the square root:
[tex]\[
v = \pm \sqrt{\frac{F \cdot r}{s \cdot M}}
\][/tex]
Therefore, the solution for [tex]\( v \)[/tex] is:
[tex]\[
v = \pm \sqrt{\frac{F \cdot r}{s \cdot M}}
\][/tex]
