Does a Snickers $^{\mathrm{TM}}$ candy bar $(65 \mathrm{g}, 325 \text { kcal })$ provide enough energy to climb from Zermatt (elevation $1660 \mathrm{m}$ ) to the top of the Matterhorn $(4478 \mathrm{m}, \text { Figure } \mathrm{Q} 2-4),$ or might you need to stop at Hörnli Hut $(3260 \mathrm{m})$ to eat another one? Imagine that you and your gear have a mass of $75 \mathrm{kg}$, and that all of your work is done against gravity (that is, you are just climbing straight up). Remember from your introductory physics course that
\[\text { work }(\mathrm{J})=\operatorname{mass}(\mathrm{kg}) \times g\left(\mathrm{m} / \mathrm{sec}^{2}\right) \times \text { height gained }(\mathrm{m})\]
where $g$ is acceleration due to gravity $\left(9.8 \mathrm{m} / \mathrm{sec}^{2}\right) .$ One joule is $1 \mathrm{kg} \mathrm{m}^{2} / \mathrm{sec}^{2}$ and there are $4.18 \mathrm{kJ}$ per kcal.
What assumptions made here will greatly underestimate how much candy you need?