Physics Examples

$F = m a$

$F$	$=$	$6 N$
$m$	$=$	$?$
$a$	$=$	$3 \frac{m}{s^{2}}$

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 $6 N$ for $F$ .

$m = \frac{6 N}{a}$

Step 2.2

Substitute $3 \frac{m}{s^{2}}$ for $a$ .

$m = \frac{6 N}{3 \frac{m}{s^{2}}}$

$m = \frac{6.00 N}{3.00 \frac{m}{s^{2}}}$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $6.00$ and $3.00$ .

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Step 3.1.1

Factor $3.00$ out of $6.00 N$ .

$m = \frac{3.00 (2 N)}{3.00 \frac{m}{s^{2}}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $3.00$ out of $3.00 \frac{m}{s^{2}}$ .

$m = \frac{3.00 (2 N)}{3.00 (1 \frac{m}{s^{2}})}$

Step 3.1.2.2

Cancel the common factor.

$m = \frac{3.00 (2 N)}{3.00 (1 \frac{m}{s^{2}})}$

Step 3.1.2.3

Rewrite the expression.

$m = \frac{2 N}{1 \frac{m}{s^{2}}}$

Step 3.2

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

$m = \frac{2 (kg \frac{m}{s^{2}})}{1 \frac{m}{s^{2}}}$

Step 3.3

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

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Step 3.3.1

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

$m = \frac{2 (kg \frac{m}{s^{2}})}{1 \frac{m}{s^{2}}}$

Step 3.3.2

Divide $2 (kg)$ by $1$ .

$m = 2 (kg)$

$m = 2 kg$

Step 4

Round to $3$ significant figures.

$m = 2.00 kg$

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