# Calculating Calories burned from mass and acceleration

I know force is equal to mass times acceleration. What I'm trying to do is find a formula that will calculate how many calories are burned using mass, acceleration and time.

For example, if I have a two pound object in my hand and I am shaking the object at 3 mph for 30 minutes, how many calories have I burned?

If anyone can provide a formula for this, it would be appreciated!

-
You don't shake something with a constant speed. –  draks ... Apr 5 '12 at 23:10
Maybe you can model the movement with a sine wave. –  Pedro Tamaroff May 27 '12 at 23:55
This would be more appropriate for physics.stackexchange.com or physicsforums.com. Note that although you said "acceleration" in the first paragraph, in the second paragraph you gave a number with units of velocity. What you seem to be looking for is the equation for mechanical work: en.wikipedia.org/wiki/Work_%28physics%29 Even that is not going to provide an answer to your question, because the answer depends on the amount of friction in your arm. If the two-pound object oscillates frictionlessly, the net work done over every cycle is zero. –  Ben Crowell Oct 11 '12 at 1:08

## 2 Answers

As noted in the comments, you cannot calculate the calories burned from this information alone. Suppose you attach the $3$ kg weight to a spring (disregard friction) and let the weight oscillate. You are doing no work, but you are "shaking" the weight for arbitrarily long amounts of time. So, strictly speaking, you are not required to burn any calories from this. The calories you burn depend on biology: the friction of your arm movements, the efficiency of cellular respiration, etc. That is outside the scope of this site.

-

Decide if you are shaking the object in a vertical path ( from low position to high and viceversa ) or on a horizontal plane. The two "path" require different energy.

Calculate the energy for that kind of movement ( mass, length of movement ).

Then sum how many movements you can do in 30 minutes.

-
I don't think this answer works, for the reasons given in my comment above. E.g., in the horizontal case the work done by gravity is zero, and the net work done by the hand on the object over one cycle is also zero. You can't infer the heat dissipated in the muscles without knowing something about the frictional forces within the arm. You're also going to get the wrong answer in the case where the person simply lowers a weight; although gravitational PE is being extracted from the object, the body's supply of chemical PE is not increased, it's decreased. –  Ben Crowell Oct 11 '12 at 1:35