Physics of weight lifting

  1. Hello to the Forum.

    I just started doing some very light weight lifting and decided to do a rough calculation of how many calories I might be burning during each of my workouts, however the figure I arrive at seems too high by comparison with the numbers one regularly see bandied about. What am I doing wrong?

    My calculation goes as follows:

    I'll use conservation of energy and only account for the upward movement (when you're letting the weights down again in the second half of each repetition you're also exerting force in the direction opposite to movement so as not to let them fall at the full acceleration due to gravity).

    I just started so I'm using a pair of 9 lbs dumbbells. This gives us ~4Kg for each dumbbell, 8Kg for the two, and 78.4N. Let's say the average length that you extend each dumbbell upwards during a single repetition is 0.3m. This gives us 23.52J spent in each repetition according to conservation of energy principles, mgh=W.

    Now, I do 12 repetitions of each of 8 different exercises, and repeat the whole cycle 3 times. This gives us 23.52(12)(8)(3) = 6774J, which converted to calories result in ~1600 calories, not taking into account the work done during the downward movement of the weights nor leg work, which is perhaps more strenuous.

    By all accounts though, 1600 cal burned during a single workout session seems a lot, even more so for such light weights. Is my physics wrong?
  2. jcsd
  3. With this type of calculation it is usually a cal/kcal confusion. You should check for that, then you are probably off by a factor of 1000.
  4. Thank you for your reply. In that case we would be talking about 1.6 calories, which again is much too little.
  5. sophiecentaur

    sophiecentaur 13,771
    Science Advisor
    Gold Member

    Your calculation tells you that you are doing 1.6kcal of equivalent useful work. Meanwhile, your body is consuming loads more energy in just performing that exercise - around four times as much.
    Look at this link for some representative values of work done and food consumed. It requires an awful lot of mechanical work to burn off a few pies!
  6. I've often wondered about this myself. Weightlifting is usually not considered a good way to burn calories, but I've never done the math. One suggestion: 9Lbs is far to light, even for a beginner. Unless you have some physical disability.

    "There are no gains without pains." ~ Benjamin Franklin: the man who "discovered" electricity.
  7. Still, the range I usually see mentioned is around 220-250 "calories", so we're still off by a factor of ~40.
  8. I've never done exercise and these dumbbells is what I had available, so while I learn good form and put together a set of exercises it'll have do.
  9. sophiecentaur

    sophiecentaur 13,771
    Science Advisor
    Gold Member

    That's 'per hour', I believe. This mild bit of exercise doesn't take an hour, surely. I would certainly die of boredom, doing that for a whole hour.
  10. I highly recommend this site:

    They have a section with some calculators that will give you some better estimates than what you can get by the procedure you are attempting. The problem is that the human body is extremely inefficient and the inefficiency is highly variable. So the relationship between work done and energy expended is non trivial. Running a marathon on a level track does approximately 0 work, but burns lots of calories.

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