Does a Snickers candy bar (65g,325kcal) provide enough energy to climb from Zermatt (elevation 1660m) to the top of the Matterhorn (4478m), or might you need to stop at Hdrnli Hut (3260m) to eat another one? Imagine that you and your gear have a mass of 75 kg, and that all of your work is done against gravity (that is, you are just climbing straightup). Remember from your introductory physics course the equation below where g is acceleration due to gravity (9.8m/sec2). One joule (J) is 1kg m^2/sec^2 and there are 4.l kJ per kcal. What assumptions made here will greatly underestimate how much candy you need?

One will have to stop at Hdrnli Hut to eat another candy bar, and a total of 1.55 bars of candy is needed to complete this climb.

Explanation:

Snickers candy bar energy content = 325 kcal

1 kcal = 4.1 kJ

therefore, 325 kcal = 4.1 x 325 = 1332.5 kJ

Elevation of Zermatt = 1660m

Elevation of Matterhorn = 4478m

Total mass of you and your climbing gears m = 75 kg

elevation from Zermatt to Matterhorn h = 4478 - 1660 = 2818 m

acceleration due to gravity g = 9.8 m/s^2

The work that will be done against the potential energy in climbing up this height = mgh

==> 75 x 2818 x 9.8 = 2071230 J = 2071.23 kJ

A snickers bar will not provide enough energy to go straight from Zermatt to Matterhorn, so one needs to stop at Hdrnli Hut to eat another one.

The total number of bars that will be needed is

==> (total energy needed)/(total energy in a candy bar)

==> 2071.23/1332.5 = 1.55 bars of candy