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{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*}

’ $w_{\text{me }}$ $\to$ $w_{\text{me }}$ (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.