Basic Math Examples

$P - mg = m v^{2} \div r$

Step 1

Rewrite the equation as $m v^{2} \div r = P - mg$ .

$m v^{2} \div r = P - mg$

Step 2

Multiply both sides by $r$ .

$m v^{2} \div r r = (P - mg) r$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $m v^{2} \div r r$ .

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Step 3.1.1.1

Rewrite the division as a fraction.

$\frac{m v^{2}}{r} r = (P - mg) r$

Step 3.1.1.2

Cancel the common factor of $r$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{m v^{2}}{r} r = (P - mg) r$

Step 3.1.1.2.2

Rewrite the expression.

$m v^{2} = (P - mg) r$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $(P - mg) r$ .

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Step 3.2.1.1

Apply the distributive property.

$m v^{2} = P r - mg r$

Step 3.2.1.2

Simplify with commuting.

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Step 3.2.1.2.1

Reorder $P$ and $r$ .

$m v^{2} = r P - mg r$

Step 3.2.1.2.2

Reorder $- mg$ and $r$ .

$m v^{2} = r P + r (- mg)$

Step 4

Divide each term in $m v^{2} = r P + r (- mg)$ by $v^{2}$ and simplify.

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Step 4.1

Divide each term in $m v^{2} = r P + r (- mg)$ by $v^{2}$ .

$\frac{m v^{2}}{v^{2}} = \frac{r P}{v^{2}} + \frac{r (- mg)}{v^{2}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $v^{2}$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{m v^{2}}{v^{2}} = \frac{r P}{v^{2}} + \frac{r (- mg)}{v^{2}}$

Step 4.2.1.2

Divide $m$ by $1$ .

$m = \frac{r P}{v^{2}} + \frac{r (- mg)}{v^{2}}$

Step 5

Simplify each term.

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Step 5.1

Factor out negative.

$m = \frac{r P}{v^{2}} + \frac{- r mg}{v^{2}}$

Step 5.2

Move the negative in front of the fraction.

$m = \frac{r P}{v^{2}} - \frac{r mg}{v^{2}}$

Step 5.3

Rewrite the expression.

$m = \frac{r P}{v^{2}} - \frac{r}{v^{2}} mg$