Physics, 21.09.2020 23:01 Adialis

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?

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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

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

Answer from: Quest

you can cut your hand off if your not

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Does a Snickers candy bar (65g,325kcal) provide enough energy to climb from Zermatt (elevation 1660m...

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