Physics Examples

$F = m a$

$F$	$=$	$20 N$
$m$	$=$	$?$
$a$	$=$	$1.33 \frac{m}{s^{2}}$

Step 1

Solve for $m$ .

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Step 1.1

Rewrite the equation as $m a = F$ .

$m a = F$

Step 1.2

Divide each term in $m a = F$ by $a$ and simplify.

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Step 1.2.1

Divide each term in $m a = F$ by $a$ .

$\frac{m a}{a} = \frac{F}{a}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $a$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{m a}{a} = \frac{F}{a}$

Step 1.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{F}{a}$

Step 2

Substitute the given values into $m = \frac{F}{a}$ .

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Step 2.1

Substitute $20 N$ for $F$ .

$m = \frac{20 N}{a}$

Step 2.2

Substitute $1.33 \frac{m}{s^{2}}$ for $a$ .

$m = \frac{20 N}{1.33 \frac{m}{s^{2}}}$

$m = \frac{20.0 N}{1.33 \frac{m}{s^{2}}}$

Step 3

Simplify the right side.

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Step 3.1

Rewrite $N$ as $kg \frac{m}{s^{2}}$ .

$m = \frac{20.0 (kg \frac{m}{s^{2}})}{1.33 \frac{m}{s^{2}}}$

Step 3.2

Cancel $\frac{m}{s^{2}}$ .

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Step 3.2.1

Cancel $\frac{m}{s^{2}}$ .

$m = \frac{20.0 (kg \frac{m}{s^{2}})}{1.33 \frac{m}{s^{2}}}$

Step 3.2.2

Rewrite the expression.

$m = \frac{20.0 (kg)}{1.33}$

Step 3.3

Rewrite the expression.

$m = 15.03759398 \frac{1 kg}{1}$

Step 3.4

Combine fractions.

$m = 15.03759398 kg$

Step 4

Round to $3$ significant figures.

$m = 15.0 kg$

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