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Climbing a Mountain with Hamburger Energy
Climbing a Mountain
with Hamburger Energy
Obviously, when you climb a mountain, the energy that you use comes from the
food that you eat. But how tall a mountain could you climb with the energy you get from a
quarter-pound hamburger which has about 400 Calories?
The ph’.isical energy needed to climb a mountain is given as the change in
gravitational potential energy, which is given as:
where PEis the potential energy, m is the mass cf the-object, g is the acceier[ior du jo
gravity (9.8 m/sec
), and h is the change in height. The units of energy in this equation are
2
joules or N—m (the work accomplished by one newton acting through a distance of one
meter.) Because units of joules and calories are used, a conversion from one kind of unit
to the other is needed. The Calorie (or kilocalorie) equals 4,180 joules, and represents
the energy required to raise 1 kilogram of water 1 degree centigrade. (Some textbooks
use the calorie, th a small “c”.) One calorie equals 4.18 joules and is the amount of
energy needed to raise 1 gram of water 1 degree centigrade. The Calorie, with a capital
“C”, equals 1,000 calories.
,
As a high school physics student, this confusion between “Calories” and “calo
ries” caused me some real difficulties. I tried to calculate how much food I would have to
eat to climb a mountain. I found that the amount of food needed worked out to a couple
of hundred hamburgers which, of course, would not fit in my stomach! I thought, “This
number sounds strange,” so I checked my assumptions. I then realized that the Calorie
supplied 4,180 joules rather than the 4.18 joules that a calorie provides. Then, my answer
seemed reasonable. Checking my assumptions when my answer seemed strange (more
than ten hamburgers sounds strange, let alone a couple of hundred) allowed me to get a
correct answer. A “check with reality” is very important and may allow you to arrive at a
correct answer in the end.
Let us calculate the number of quarter-pound hamburgers that a person would
need to eat in order to get up Mount Marcy (the highest mountain in New York State),
starting from Lake Colden. Lake Colden is 840 meters above sea level (2,764 feet), and
Mt. Marcy is 1,630 meters above sea level (5,344 feet). The climber’s mass is about 78
kilograms. The energy needed to climb Marcy is found by using the equation:
mgh
PE
PE
=
=
(78 kg)
>
Energy Needed
(9.8 m/sec
)
2
6.0
(1630 m
—
840 m);
joules;
x
This could be written as: 6.0
x
x
10 joules/climb.
© 1985 J. Weston Waich, Publisher
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Climbing a Mountain with Hamburger Energy
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The hamburger has about 400 Calories, which can be expressed: 1 hamburger/4J
Calories. Using the conversion factor (6.0 X 10 joules/climb), and the fact that there are
4,180 joules/Calorie, the number of hamburgers needed to fuel the climb up Mount
Marcy can be found:
1 hamburç
400 Calories
-
-
>
1 Calorie
4180 joules
x
6.0
x 10
joules
climb
=
.36 hamburgers
climb
The above calculation shows that about one-third of a quarter-pound hamburger is
needed to climb Mount Marcy, the hiqhest mountain in New -L
07 °f fron :i’c t
V
base. This does not
ii
food! Ac’aiaiiy, tvoud take more energ. than
one-third of ahamburger because the human hncy is on!y about 30 cfficnt
“converting foci intbënery. Same nergy is needed to digest the food. Also, muscles do
not work with 100% efficiency. Therefore, because only about one-third of the food’s
energy is changed into useful energy, humans need to consume about three times more
food energy than is required by the work alone (in this case, the climb). 3 x .36
hamburgers equals about 1 full burger.
© 985 J. Weston Walch, Publisher
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/ Climbing a Mountain with Hamburger Energy
NAME_____________________________ DATE
Climbinq a Mountain
with Hamburger Energy
Questions and Problems
1. How much energy in joules would you need to climb from Leadville, Colo
rado, about 3,050 meters above sea level, to the top of Mount Elbert, the highest
mountain in Colorado, which rises about 4,330 meters above sea level? (There are about
2.2 pounds/kilogram. Use your own mass.)
2. How many quarter-pound hamburgers (400 Cal/burger) would you need to
eat if you wanted to climb to the top of Mount Elbert, given the efficiency of the human
body?
3. How much energy in joules would a 50 kg person need to climb from Lake
Colden to Mount Marcy, a vertical distance of 790 meters?
4. How many eggs, having about 75 Calories each, would the person in problem 3
need to eat, given that the human body is only 30% efficient?
5.
What makes the human body less than 100% efficient?
6. You go on a bicycle ride and climb ten hills, each 200 meters high. Using your
own mass, how many quarter-pound hamburgers would you need to eat to supply your
body with the energy needed for the trip? (Use the data in problem 1.)
7. As you ride down the last hill to your house, then stop, you have neither
kinetic energy nor potential energy. Where did all the energy from the hamburgers go?
© 1985 J. Weston Waich, Publisher
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