# Work done by weight training

1. Aug 3, 2013

I am very confused about weight training and running as I learn physics. When I run at 6 miles/hr (about 3 m/s) on treadmill for a minutes, I spend more than 10 calories. I believe these are food calories (KCal) so it is 10,000 cal or 10,000*4.18 Joules or approx 50,000 J ie 50KJ
Ok so far so good.
Now I lift 10Kg dumbbell 1 meter. Work Done = PE change = 10*9.8*1 = 98 Joules or say 100J

Does it mean I have to lift it 500 times to burn same amount of calories as running for 1 min? I can easily run for a min but it is nearly impossible to lift 10kg 500 times so I know you need significantly more energy to lift weight than running.

But the physics does not add up even after I account for all approximation, friction etc.

What am I doing wrong?

Last edited: Aug 3, 2013
2. Aug 3, 2013

### 1MileCrash

Why are you talking about the actual calories burned by the body when running, and then just talking about the energy required for a weight to move 3 meters (as in, nothing to do with a human body doing this task)? Obviously I could choose to move this weight that 3 meters by some extremely inefficient process (aka the human body) thus making your energy calculation almost meaningless.

3. Aug 4, 2013

### BruceW

this is true. the human body is very inefficient, so the energy used to lift a weight will typically be a lot more than just the potential energy gained by the weight. If you think about it, if you hold a weight out to the side, you will use up a lot of energy, even though the potential energy of the weight is not changing. One way to actually calculate how much energy your body is using is by indirect calorimetry.

4. Aug 4, 2013

### sophiecentaur

Your quoted food energy for running exercise will have bee measured by detecting the amount of CO2 produced by an athlete. There will exist similar measurements for other forms of exercise, too. You can them validly compare two figures. It is just not valid to compare apples with pears.

5. Aug 5, 2013

### Lsos

Also, when lifting a dumbbell, you are using mainly what...one or two small arm muscles? When running, you are using not only your entire, relatively much larger leg, but practically all the muscles, in both of them. AND all the other muscles involved in running.

You can also put out quite a bit of power when rowing, as you're using many more and larger muscles than just lifting a weight.

6. Aug 5, 2013

### sophiecentaur

This question appears regularly, in various guises. The point about living systems is that they cannot easily be analysed in simple 'mechanical' terms and the term 'Work' does not really apply. The definition of work done is Force times Distance moved in the direction of the Force. (the 'dot' product of the force and displacement vectors). But it tells you the work done on an object and not by your muscles. If you run for an hour and arrive back where you started (not gaining of losing height) then you have not really done any work on your body, in strict terms - you have not increased its Potential Energy. (Despite needing to have a lie down, afterwards.)
There is no paradox or contradiction. It's just a mis-application of the term 'work'.

7. Aug 5, 2013

### BruceW

maybe another way to look at it: is that the GPE change of the weight is a minimum bound on the actual energy used by the person. And since the human body is generally pretty inefficient, this minimum bound is generally not very close to the actual energy used.

8. Aug 5, 2013

This:

9. Aug 6, 2013

### sophiecentaur

Yes. It's all down to efficiency. Although, of course, the definition of "useful work" is all a matter of context. Animals (all living things, in fact) are pretty good at doing no more than is absolutely necessary and making the best use of their input. Best, in their terms, that is.

10. Aug 6, 2013

### Staff: Mentor

What you are doing wrong is comparing two different things. For running you are citing the energy used. For weightlifting you are calculating the work done. Unless your efficiency is 100% those two things are not equal.

Actually, neglecting air resistance, and assuming that the runner starts at rest and finishes at rest and assuming that the weightlifter returns the weight to the place he got it then both do 0 work.

11. Aug 6, 2013

### Staff: Mentor

Wow, that's an obvious miss! [Hangs head in shame.]