# How much work will a human do to lift a weight?

I saw a pretty simple homework question here that asked how much work it takes to lift a 200 kg weight, and while the math for a basic answer is simple the weightlifter in me instead wanted to actually approach this question with a critical and pragmatic eye. There are many factors that one could consider to easily get a value different from the answer in a conservative field (for example: 1960 N for 1 meter).

I figure exact answers are obviously impossible. I want to instead see what methodologies can be used to start formalizing my upcoming reasoning (and also take this opportunity to correct any misconceptions I have) in hopes of closing in on a reasonable method to create an answer with more data. I also would love to see similar bio-mechanical studies and related material.

I mainly broke this problem up into two levels:

Mechanical:

The human body is a collection of support structures (basically curved trusses), complex muscular tissue (non-linear springs with various attachment points), and connective tissue (constraints). Something I really could use clarification about here is the effect duration of the lift could have on the work exerted.

Thermodynamic:

Our body metabolizes chemicals to generate store energy in tissue, then later break down that tissue into work and heat. Let's ignore the energy lost due to digestion and other secondary factors, and instead rate the efficiency of the human "engine" as a function of how much work he creates from the energy he expends doing the exercise.

The Problem:

Let's say we have a (large) man who lifts a bar 1 meter up from the earth when he does a deadlift, squat, or bench press.

How much energy does this body use to move 200kg doing each motion?

How much energy does this body expend to move 200kg doing each motion?

Well, I suppose that you are well aware that neglecting air friction the work done on the bar will be $MgL$. This much energy is spent by the person on lifting the bar.

This question might be helpful. It says the efficiency for a human body on average for cycling is 20%. So it is a safe bet to say that the man used $5MgL$ energy, spent $MgL$ on lifting the bar and $4MgL$ is wasted away.

Keep in mind that people spend energy just to live unlike machines, it is a much harder process to separate the amount of energy used for particular tasks from the total amount of energy used in a given amount of time.

I would think that the energy spent to make a deadlift is related ( maybe in a non-linear way ) to the work done to move the bar. If you define work as always: $$W = F\Delta h = mg \Delta h$$ then you can define the energy spent by a machine as $$E = \frac{L}{\eta}$$ where $\eta$ is the efficiency of the machine.

Now, no one can tell exactly what is the efficiency of the "human machine". Indeed, when you lift weights the same way for long time you body improve their efficiency. That's why if you want to burn calories, you should change periodicaly exercises.

Another fact: the energy used for work is a little part of the daily intake. More or less 70% is used for metabolism.

• what was L suppose to signify? Aug 8 '14 at 20:35