How do we calculate energy of food?

Question

Here is the problem, according to me:

In a classic hamburger, according to my internet research, approximately 906 kJ are contained.

Now take a car of 1 000 kilograms, and push it to 30 m/s. It has a certain kinetic energy, which is: 1 000 * 30² = 900 kJ

So does it mean that the work (in a physical sense) needed to stop the car is equivalent to the energy brought by the hamburger, so a human just have to eat an hamburger to be able to stop the car?

It is very hard to imagine, as even with the strength of an human and the possibility to brake the car very slowly, I think a human will need a lot of energy.

So how it is possible to compare the energy brought by food and the mechanical/kinetic energy?

Because on the other hand, it could also mean that with the energy brought by one hamburger (approximately 15% of the food energy is used by the human body, and the value I gave take into account this 85% factor), I am able to put push a car to 30 m/s!

Answer 1

A calorimeter is a device that you can use to measure the energy of food. You put a small amount of the food in a calorimeter. Then you submerge the calorimeter in a known quantity of water. Now you burn the food and measure the increase in temperature of the water. By careful measurements, one can determine the energy required to heat the water. That amount of heat is the caloric content of that food.

Once you know the energy of the food you can compare it to other material objects just by calculating the energy of the objects. Kinetic energy is just $$(1/2) mv^2$$

Answer 2

It isn't so far fetched as it might appear. A gallon of gas will accelerate the car to speed and keep it there for perhaps 30 miles. The energy in gas comes from chemical bonds. The bonds in gas are not totally different from the bonds in a hamburger.

Burning a gallon of gas produces 132,000 BTU, or $1.39 \times 10^8$ J. That is ~150 times more than the 900,000 J from burning a hamburger. Given the relative sizes, it sounds like gas has more energy per pound. So a hamburger has enough energy to run a car for about 0.2 miles.

Eating a hamburger for lunch produces enough energy to run a human until dinner. Over the course of an afternoon, a human could do enough work to push the car up to speed. Perhaps he could pedal a bicycle connected to a generator, and store the energy in batteries. Then the batteries might well have enough charge to get an electric car up to speed.

Answer 3

There's something you're overlooking that makes the whole thing somewhat counter-intuitive: the maximum force the human can exert on the car.

In order to reach the kinetic energy of $450\mathrm{kJ}$ that same amount of work $W$ has to be done on the car by the human, according to:

$$W=K$$

where:

$$\mathbf{d}W=F\mathbf{d}x$$

Here $F$ is the force exerted by the human (we'll assume it constant, for simplicity's sake) on the car and $\mathbf{d}x$ the displacement (linear, for simplicity's sake). Integrating we get:

$$W=F\Delta x$$

and:

$$F\Delta x=\frac12 mv^2$$

Or:

$$\Delta x=\frac{m v^2}{2F}$$

Obviously if $F$ is relatively small compared to $mv^2$, $\Delta x$ will be large. However that doesn't mean the human won't get the car up to speed: it just takes quite a long time.

That time can be calculated from Newton's second Law:

$$F=ma \to a=\frac{F}{m}$$

and:

$$v=a\Delta t \to \Delta t=\frac{v}{a}$$

So:

$$\Delta t=\frac{mv}{F}$$

It's similar if we made the car tow a fully loaded $20$ tonnes HGV: the car can do it but it would take an impractical amount of time because the maximum amount of force it can deliver is small compared to that of an HGV tractor.

Answer 4

The whole scenario seems to be implausible when you consider that in order for the person to accelerate the vehicle to a speed of 30 m/s at the end the person would have to run at a pace of 70 mph!

A more reasonable speed to push the car is about 10 mph or 4.5 m/s which is a kinetic energy of about 10 kJ. That’s only 10% of your hamburger’s calories.

By the way, according to one site an average person's straight pushing force is 60-80 N. At 80 N assuming negligible friction the car's acceleration would be 0.08$\frac{m}{s^2}$. So If would take about a minute to reach 4.5 m/s.

Hope this helps.

Answer 5

I am able to put push a car to 30 m/s!

You are ignoring the inefficiency of your body burning those 900 kJ here, your actual mechanical output will be much lower.

Ok, so let's assume that you can actually produce 25 % of the burned energy as mechanical work, then, yes, you can accelerate the car to 15 m/s (half the speed, quarter the energy). If the car is suspended frictionlessly in vacuum, that is. It'll take you a while, because you will be feeding this energy into the car at about 200 to 250 watts, so it'll take you about $225\ \mathrm{kWs}/225\ \mathrm W = 1000\ \mathrm s = 16\ \mathrm{min} + 20\ \mathrm s$ to get the car up to speed.

Unfortunately, car's loose much more than the 250 watts that you can output to wind resistance when going 54 km/h, so you won't reach that speed without the vacuum. You'll only reach the speed at which the losses to friction and wind resistance match your energy input, which is a rather meager figure. Better get on your bike and ride about 7 km at 25 km/h with the energy your hamburger provided.