# The Big Mo, Force and Momentum

## Example 7: my weight.

**The Question:**  If I weigh 200 pounds on Earth, what is my mass in slugs (Okay. I lied. One slugs reference.) and in kilograms? Let's do the actual conversion manipulation. Pretend that Mr Google is out for now.

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**The Answer:**

Let's write the Second law just for me and my weight:

$$
\begin{align*}
w_{\text{me }} &= m_{\text{me }}g \\
m_{\text{me }}   &= \frac{w_{\text{me }}}{g} \\
&= \frac{200 \text{ lb}}{32.2 \text{ ft/s$^2$}} \\
m_{\text{me }}   &= 6.2 \text{ slugs.}
\end{align*}
$$

In order to convert to kilograms, we can do conversions within the correct quantities using the table above. So let's do $w_{\text{me }}$(English)$\to$ $w_{\text{me }}$ (metric):

$$
\begin{align*}
w_{\text{me }}(\text{metric, in N}) & = w_{\text{me }}(\text{English, in lb})  \frac{4.45 \text{ N}}{1 \text{ lb}} \\
w_{\text{me }}(\text{metric}) & = 200 \times 4.45 = 889.6 \text{ N}
\end{align*}
$$

Now calculate the mass in kilograms like before:

$$
\begin{align*}
w_{\text{me }} &= m_{\text{me }}g \\
m_{\text{me }} &= \frac{w_{\text{me }}}{g} \\
&= \frac{889.6 \text{ N}}{9.8 \text{ m/s}^2} \\
m_{\text{me }} &= 90.8 \text{ kg}
\end{align*}
$$

Mr Google's back, so you can check that this is what he would have said.