# What is the relationship between muscle energy consumption, the period over which the contraction occurs and the mechanical work performed?

I'm asking this question with some basic knowledge of physics and general fitness.

Suppose you are lifting a still object with mass $$m$$ from height $$h_1$$ to height $$h_2$$ with an arbitrary (straight or curved) path. Let's ignore the movement of the body parts during the lift. Suppose you keep the object still at the final height $$h_2$$.

From physics, the object gains a mechanical energy equal to the variation of the gravitational potential energy during the movement:

$$\Delta E = mg(h_2-h_1)$$ [Joule]

Now, from what I can gather, such a quantity is absolutely not equal to the energy consumption of the muscles performing the lift, as:

1. Muscles fatigue more if they are shortened for a longer amount of time. That's the reason why lifting an object slowly is harder than lifting it fast. The previous equation does not consider the duration of the lift.

2. The previous equation ignores the object path because the mechanical energy gained by the object depends only on the vertical distance. But a curved and longer path may mean a longer duration of the lift. Hence it may mean more energy consumption, because of point 1.

3. Not sure of this, but I suppose muscles aren't 100% efficient. Hence, for each Joule (or Kcal) of input energy (in terms of ATP), they won't provide one Joule (or Kcal) of mechanical energy. I suppose some of that becomes heat.

So, I'd say that the previous equation provides the minimum amount of energy expended by muscles. It ignores the muscles inefficiency and the duration of the movement. But at the same time, the mechanical work does contribute to the energy consumption, since lifting an object is much harder that just keeping the muscles squeezed for the same amount of time.

Do you know some equations which take into account of these factors, and hence relate the mechanical work to these last two variables? Also some papers dealing with t

• I suggest also posting this question in physics community Sep 23, 2021 at 4:49
• @RogerVadim Cross-posting is typically frowned upon. That said, similar questions have been asked at Physics so I'd strongly suggest OP to look for them there. Sep 23, 2021 at 18:44
• Welcome to Biology.SE. I've made some changes that I think make your question clearer, but please check to make sure I've not changed your meaning. In addition, note that your post stops mid-sentence. Also note that this may be too unfocused to be answered here — I would guess that there is a large literature on this subject. Some key words you can try to add to your searches: biophysics, kinematics. Sep 23, 2021 at 18:49
• Likewise I have edited your title so it employs standard scientific English. Check whether I have not inadvertently changed your meaning. Sep 23, 2021 at 21:53
• Does this answer your question? Why a continuous supply of energy is needed to support a weight? Nov 8, 2021 at 18:00