This seems like a fair question: “How much energy does it take to jump one inch”.  And, remember this just an estimate, so grant me a little latitude in the solution.   A little background information might be helpful.  Here a few (ok, many) citations, of background material.  I think this will help lend some credibility to my estimations.

 

First of all, there are a few MadSci responses on ATP and energy. Some deal with fermentation and photosynthesis, while others are directly related to the question and discuss cellular respiration and oxygen’s role.

 

General MadSci:

how energy is released from ATP&what is the role of (P) ?

Re: how energy is released from ATP&what is the role of (P) ?

Re: What are ATP and NADPH? (7.2 Calories released when breaking phosphate bond)

Re: Where does fat actually go when people lose weight?

Re: What is the importance of oxygen in respiration?

Metabolic Pathways of Biochemistry

Re: How much actual iron is in the human body?

 

Specific to muscle reaction/execution:

Re: What determins the speed of a muscle reaction and execution? (38 molecules of ATP in glucose)

Re: Skeletal muscle may produce large amount of of lactic acid - why?

 

Of course there are many other sites that discuss ATP and energy (very good):

Cellular Respiration

Oxidative Phosphorylation(Washington University Site –great overview)

 

From the above link site I found this excellent site

ATP and Biological Energy

  ;

And finally, I recently read Atom: An Odyssey from Big Bang to Life on Earth and Beyond by Lawrence M. Krauss (physicist from CWRU).  His describes the “life” of an oxygen atom.  Oxygen is important because it helps power production of ATP by removing “used” electrons.  In his book, he cited that the average adult male use about 420 pounds of ATP each day.  And, since there is about 50 grams of ATP in the body that means each molecule of ATP is re-energized 4000 times per day!  I do not know where he got his numbers, but I suppose they seem reasonable.

 

A quick summary of useful numbers and facts:

• ATP -> ADP + inorganic P + Energy
• ADP + Energy + inorganic P  -> ATP
• 38 molecules of ATP are created from the breakdown of glucose. 7.2 Calories  (kcal) are released when the bond to the phosphate is broken (MadSci answer)
• The average adult generates about 100 Watts of power released as heat just sitting still (Krauss).
• A human is an inefficient jumper (only about of kinetic energy goes into jumping) (Physics of Sports Edited by Armenti – article Effects of wind and altitude on record performance in fast races, pole vault, and long jump –by Cloff Frohlich in Am. J. Phys. 53, 726-730 (1985) – original citation P. Kirkpatrick Am. J. Phys. 25 614, (1957).
• The website ATP and Biological Energy cites 7 kcal/mole when the most energetic of the phosphate covalent bonds is broken.
• The website Oxidative Phosphorylation expresses everything in terms of the thermodynamic variable free energy and states 30.5 kJ/mole when (1 cal = 4.18 J)
• I assume that Calories means the usual kilo-calories (kcals).  This is standard practice.
• My search and calculation yield a weight of 573.1 grams / mole (ATP C₁₀H₁₃N₅O₁₃P₃Na ₃)

 

So let’s work through the estimation.  First let’s verify that our information from Dr. Krauss and other source is consistent with what we know.

 

The daily human consumption of ATP is about 50 g * 4000 recyclings = 200,000 grams.  This is about (200,000 grams / 573.1 grams /mole) 349 moles of ATP per day.

 

Which means the average man uses about 2443 kcal/day.  Remembering that food Calories (capital C) equals kcal, this around 2400 Calories a day.  This seems to be a very reasonable estimate based on recommended daily allowance of calories and such.   In fact, I suspect Dr. Krauss worked from this number to get to ATP usage. 

 

Okay so everything seems reasonable up to this point.  Let’s move on to your question,

“How much ATP is used when a 140 pound person jumps 1 inch off the ground?”

 

140 pounds /2.2 kg / pound = 63.6 kg.

1 inch / 2.54 cm /inch = 0.39 cm = 0.0039 m

 

The amount of energy necessary to raise this person 1 inch into the air is given by the change in potential energy:

 

Potential Energy Change Required= mass * gravity * (change in height)

 

where mass is the person mass and gravity is acceleration of gravity.

 

Potential Energy Change Required = 63.3 kg * 9.8 m/s² * 0.0039 m = 2.4 Joules.

 

Now remember from our above point: Humans are lousy jumpers!  About 50% of the kinetic energy in jumping is wasted, (in other words efficiency = 0.5)

So:

 

Efficiency * Kinetic Energy Required = Potential Energy Change Required

 

or

 

Kinetic Energy Required = Potential Energy Change Required / Efficiency

 

Kinetic Energy Required = mass * gravity * change in height / Efficiency

 

 

 

How much ATP is used to generate the Kinetic Energy Required?

 

 

Kinetic Energy Required = 30.5 kJ/mole * Moles of ATP used.

 

or

 

Kinetic Energy Required / (30.5 kJ /mole) = Moles of ATP used

 

Therefore if Kinetic Energy Required = 4.8 J, plugging in the numbers to solve for moles of ATP we have the following:

 

4.8 J / (30500 J / mole) = 0.00015 moles of ATP.

 

Not too much in one jump.

 

 

Sincerely,

 

Tom “No Jump” Cull