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.
The Answer:
Let’s write the Second law just for me and my weight:
\[\begin{split}
\begin{align*}
w_{\text{me }} &= m_{\text{me }}g \\
m_{\text{me }} &= \frac{w_{\text{me }}}{g} \\
&= \frac{200 \text{ lb}}{32.2 \text{ ft/s$^2$}} \\
m_{\text{me }} &= 6.2 \text{ slugs.}
\end{align*}
\end{split}\]
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):
\[\begin{split}
\begin{align*}
w_{\text{me }}(\text{metric, in N}) & = w_{\text{me }}(\text{English, in lb}) \frac{4.45 \text{ N}}{1 \text{ lb}} \\
w_{\text{me }}(\text{metric}) & = 200 \times 4.45 = 889.6 \text{ N}
\end{align*}
\end{split}\]
Now calculate the mass in kilograms like before:
\[\begin{split}
\begin{align*}
w_{\text{me }} &= m_{\text{me }}g \\
m_{\text{me }} &= \frac{w_{\text{me }}}{g} \\
&= \frac{889.6 \text{ N}}{9.8 \text{ m/s}^2} \\
m_{\text{me }} &= 90.8 \text{ kg}
\end{align*}
\end{split}\]
Mr Google’s back, so you can check that this is what he would have said.