Kinetic Energy vs Burger Energy

[oneiron]

Hello Everyone.

I was teaching a physics class the other day on basic momentum and kinetic energy when I decided, for fun, to work out how fast the kilojoules from a Quarter Pounder could propel you. A Quarter Pounder (according to the box) gives you roughly 2000 kilojoules, and my mass is about 80kg. so...

E = 1/2 m v^2
2000kj=.5*80*v^2
sqrt(50) = v = 7ish ms^1 = 25ishkph

Which is fast, but is not THAT fast. Certainly well slower than the records.

So I tried to look at things another way.

If the average person can run 100m in about 20seconds then they're running at 5ms^1.
So, 1/2 mv^2 = .5*80*25=1000kj.

When one is running, chemical energy is being turned into kinetic energy to propell me up to that speed. When I slow down, I can't see how the kinetic energy could be transferred into chemical potential energy in my body...

so this math would say that to burn off a burger, I only need to do two short sprints, reaching 5ms^-1. This seems far far far too easy in my mind.

Where is the mistake in my thinking?

Cheers,

 

[xts]

You messed units (kiloJoules), missing factor 1000.
And, of course, the nutrition energy may be converted to mechanical one in your muscles with pretty limited efficiency.

 

[Hootenanny]

Welcome to Physics Forums, oneiron.

You have made several simplifications here and a number of errors. Firstly, your initial calculation is off by some way. It should be

$$2\times10^6 = \frac{1}{2}80v^2 \Rightarrow v \approx 224 \text{m}.\text{s}^{-1}$$

Secondly, you assume that the body has unit efficiency, i.e. it absorbs everything it takes in. Obviously this isn't true. Thirdly, you assume that the runner runs at constant speed for the entire distance, which isn't true - there will be a period of acceleration followed by a short period of constant speed, followed by another period of acceleration. Fourthly, you assume again, the the body is 100% efficient, in that any energy it uses is converted entirely to speed, which isn't the case - what about the wasted energy breathing, thinking, blinking, repairing damage, heartbeat etc.

Regarding your final point:

When one is running, chemical energy is being turned into kinetic energy to propell me up to that speed. When I slow down, I can't see how the kinetic energy could be transferred into chemical potential energy in my body...

This is very worrying if you are indeed teaching a physics class and had to ask this question. In actuality, this entire thread is worrying if you are teaching physics. After the sprint, your body does not "reabsorb" the energy you expelled during the race. In fact, your body uses energy in slowing you down. The energy you expelled during the race (and slowing down afterward) is "lost" to the environment so to speak.