# Simple problem for experts.... (work done lifting weights at the Gym)

• Juanmdq
In summary, the person writing this summary thinks that the calculation for the energy used when doing a particular exercise is easy, but that the calculation can vary wildly depending on the individual and the technique being used.
Juanmdq
Hi everyone! I know this is probably a really easy problem for you guys but I want to estimate how much energy a person uses when it goes to the gym. The joules or watts needed to move the weight.

Let's say for example when a person is doing overhead press and lifts 50kg 40cm up and then 40cm down ten. It takes 1 second going up and 2 seconds going down. How would you calculate that? Can you please detail the calculation so I can use it for other exercises.

I don't even train but I was thinking about how an amazing machine the human body is and I got curious.

Hopefully this is interesting for more people!

Thanks!

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Juanmdq said:
Hi everyone! I know this is probably a really easy problem for you guys but I want to estimate how much energy a person uses when it goes to the gym. The joules or watts needed to move the weight.

Let's say for example when a person is doing overhead press and lifts 50kg 40cm up and then 40cm down ten. It takes 1 second going up and 2 seconds going down. How would you calculate that? Can you please detail the calculation so I can use it for other exercises.
Work is force times distance. That's it. Assuming a person doesn't jerk the weight so hard that he needs an opposite force to stop it you can assume the force equals the weight. So 50x9.8x.4=196J per lift.

Note, that's not the energy used(input) it is the energy output.

Thanks Russ! two questions:
To calculate the force when the weight is going down?
When you consider the time that it takes to move the mass?

thanks!

Juanmdq said:
To calculate the force when the weight is going down?
The force is equal to the weight on the way up and the way down. But the work on the way down is negative; the body isn't outputting energy, it is absorbing energy.
When you consider the time that it takes to move the mass?
If you want power instead of work or energy, you divide by time.

...
We get questions about exercise energy use a lot, but I don't think they usually complete the thought or go far enough. What I think would be useful to know is just how efficient the human body is. Here's a method for figuring it out:

Energy burn rate is roughly proportional to heart rate for people. So if you baseline the resting heart rate and subtract it from the exercise heart rate and compare to the daily caloric intake you can find the exercise energy expenditure rate. Then you just divide that into the power output to find efficiency.

For example, say your average heart rate on a day you don't exercise is 60 bpm and you burn 2,400 "calories" per day. A "calorie" is actually a kilocalorie and is equal to 4,184 Joules. So that's 116 watts or 1.93 Joules per beat.

Then let's say you ride an exercise bike that accurately measures your power output at 150 Watts and you also measure your heart rate at an average of 170bpm. A difference of 170-60 = 110 bpm, or 212 Watts or 70% efficiency.

Please note: I'm not vouching for these numbers, I just pulled them out of thin air. This is just a method. Three of the four numbers are problematic to accurately measure.

Anand Sivaram and tnich
russ_watters said:
Energy burn rate is roughly proportional to heart rate for people.
That is a much more useful way to define workout energy/power. You can increase your heart rate by just sitting to watch certain videos (or by reading certain threads on PF :-). Even that burns nonzero quantity of calories.

russ_watters
@Juanmdq So far in this thread, I haven't read the enormous CAVEAT that's needed. Your thread title describes a "Simple problem for Experts". You really are being much too hopeful here. The work expended on Gym apparatus is easy to work out with some careful measurements. Force times distance moved or Force times speed will both give you reasonable repeatable answers - for different 'experts' BUT the work or power actually expended by a body will vary wildly with different bodies and different techniques. But the Physics has been dealt with very capably already, above.

If you are interested in gauging improvement in personal performance then the forces and work can be measured and you get a possibly useful answer and note that you can shift more weight - so called self-referenced assessment. As you get better at an exercise, your body can get more and more efficient but you are getting into very uncertain territory there. I imagine that many personal trainers could justify their fees by giving you a long chat about it.

Even following your weight measurements over a period of time will not tell you the whole story because exercise will cause you to put on more muscle and probably lose some of your existing fat. So the net weight change won't tell you how much fat you lost. (If it matters to you)
They hook up cyclists to gas analysers and make connections between the CO2 produced (food burned) and the measured work done on a stationary bike. But, as I already mentioned, the relationship varies a lot and the conclusions are open to 'discussion'. Remember - you can just lie down for a rest and you are metabolising food and, holding a barbell at a constant height still requires your muscles to be using food.

You ask about the work done when you lower a weight. I would say that it could be described as wasted. The only useful work you have really done is to raise the weight in the first place - because that rise in potential energy of the weight could be used to drive a machine (long case clock, for instance). On the way down, you are just dissipating energy in the same way that a brake will.

russ_watters

## 1. How is work calculated when lifting weights at the gym?

The work done when lifting weights at the gym is calculated by multiplying the weight being lifted by the distance it is lifted. This is known as the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

## 2. What units are used to measure work in weightlifting?

The standard unit of measurement for work in weightlifting is joules (J). However, some weightlifters may also use the unit of foot-pounds (ft-lb) or kilogram-meters (kg-m).

## 3. Does the speed at which the weight is lifted affect the amount of work done?

Yes, the speed at which the weight is lifted does affect the amount of work done. According to the work-energy principle, the faster the weight is lifted, the more work is done as there is a greater change in kinetic energy.

## 4. How does the angle of the lift affect the work done?

The angle of the lift can affect the amount of work done as it changes the distance over which the weight is lifted. For example, lifting a weight straight up requires less work than lifting it at an angle, as the distance over which the weight is lifted is shorter.

## 5. Is there a limit to the amount of work that can be done when lifting weights at the gym?

Yes, there is a limit to the amount of work that can be done when lifting weights at the gym. This is determined by the individual's physical abilities and the weight being lifted. Continuously pushing beyond this limit can lead to muscle fatigue and potential injury.

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