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Physics Examples

F = m a

$F = m a$

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

Step 1

Solve for

m

$m$ .

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Step 1.1

Rewrite the equation as

m a = F

$m a = F$ .

m a = F

$m a = F$

Step 1.2

Divide each term in

m a = F

$m a = F$ by

a

$a$ and simplify.

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Step 1.2.1

Divide each term in

m a = F

$m a = F$ by

a

$a$ .

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

$a$ .

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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

$1$ .

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

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

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

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

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

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.

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

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

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

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

$1$ .

$m = 2 (kg)$

$m = 2 kg$

$m = 2 kg$

Step 4

Round to

$3$ significant figures.

$m = 2.00 kg$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$