# Energy loss without displacement

musicgold
Hi,

This is about a basic fact which has never been clear to me.

As per the equation Work = Force x Displacement, if there is no displacement there is no work.

On the other hand, one of the exercises I do involves pushing a wall. I stand in front of a wall and try to push the wall as if I am moving a big cupboard. The idea is to push as hard as possible until one feels exhausted. The excecise is supposed to be good for arm and calf muscles. Technically, however, no work is being done.

Now my question is: If there is no work being done, why do I fee exhausted (loss of energy) after doing that action?

Thanks,

MG.

Bob S
Muscles require glucose (caloric) energy (actually ATP*) to contract. Muscle contraction with force burns a lot of calories, even when the exercise is isometric (no displacement). When there is force without displacement, no physical (physics definition) work is done.

Bob_for_short
The work spent on displacement is a "useful" work. The work spent by a machine or by a human being is the "total" work. Their ratio is the efficiency of the machine or the man' efforts.

Bob.

musicgold
Thanks folks.

The issue however is still not clear to me. I thought my question was quite simple.
Could you please point me to a webpage where I can read more on this issue.

Also,

Bob_for_short said:
The work spent by a machine or by a human being is the "total" work.
Is there a equation defining 'total work', something similar to 'useful work' = force x displacement ?

Thanks,

MG.

Homework Helper
Gold Member
The simplest answer is that force-displacement work is only one type of work. The other types also consist of two variables (analogous to force and displacement) that give the units of energy when multiplied together. Examples are:

- Moment (torque) and angle
- Stress and strain
- Pressure and volume
- Surface tension and area
- Voltage and charge
- Chemical potential and quantity of reacting species (chemical work)

Beside force-displacement and moment-angle work, your muscles also perform chemical work, and this is how energy is still transferred (and you get tired) even when your muscles are immobilized.

EDIT: This is also discussed http://en.wikipedia.org/wiki/Conjugate_variables_(thermodynamics)" [Broken].

Last edited by a moderator:
Bob_for_short
Thanks folks.

The issue however is still not clear to me. I thought my question was quite simple.
Could you please point me to a webpage where I can read more on this issue.

Also,

Is there a equation defining 'total work', something similar to 'useful work' = force x displacement ?

Thanks,

MG.

Yes, for example, if your machine cannot move something but works, the total work is the energy of the fuel consumed. Also somewhere should happen slipping (otherwise the machine stalls). Slipping transforms the machine work into heat (overcoming friction). Its formula is the friction force x displacement.

Bob.

musicgold
Mapes and Bob_for_short,

Thanks.

Beside force-displacement and moment-angle work, your muscles also perform chemical work, and this is how energy is still transferred (and you get tired) even when your muscles are immobilized.

Let me see if I got this right. The energy loss that I feel is because of the contraction of my muscles. The contraction cause the muscles to transfer energy in the form of heat to the rest of the body.

Is this correct?

Thanks again,

MG.

Bob_for_short
Let me see if I got this right. The energy loss that I feel is because of the contraction of my muscles. The contraction cause the muscles to transfer energy in the form of heat to the rest of the body.

Is this correct?

Thanks again,

MG.

Yes, that's right. To create the muscle tension it is necessary to apply an electric voltage to it. This voltage is created by your organism with help of increased rate of chemical reactions. So the rate of oxidation increases. Your muscles get hotter. Your body spends the chemical energy stored in it (in cells). That is why you get tired. Another thing is if you manage to displace something with your muscles tension (useful work).

Bob.

cesiumfrog
Imagine playing tug-of-war, with a stretchy (bungee) rope, and only using one hand. So that once you have pulled your arm all the way to your body, you have to quickly let go, reach forward and quickly try to grab the rope further up. In the pulling phase you would clearly be doing work (even if the other end of the rope was tied to a wall that doesn't move) because it takes work just stretching the rope out more, and you don't get energy back from it in the phase when you reach with open grip (perhaps it dissipates in the twang of the rope). This is roughly how muscle cells work (on a molecular level): they burn energy just maintaining a force, even if that force doesn't create external motion.

Mentor
As per the equation Work = Force x Displacement, if there is no displacement there is no work.

On the other hand, one of the exercises I do involves pushing a wall. I stand in front of a wall and try to push the wall as if I am moving a big cupboard. The idea is to push as hard as possible until one feels exhausted. The excecise is supposed to be good for arm and calf muscles. Technically, however, no work is being done.

Now my question is: If there is no work being done, why do I fee exhausted (loss of energy) after doing that action?
Each of your muscle fibers has millions of actin and myosin filaments, and each one has a little head that physically exerts a force over a microscopic distance doing work (W=f.d) at the expense of the energy in ATP molecules. Although you are not doing any work on the wall, the reason that you feel exhausted is because you are doing a lot of work internally on a cellular level. As Bob_for_short mentioned this is a case of 0% efficiency. Whenever there is 0% efficiency you will find that there is some force and displacement internally.

mikelepore
Let me see if I got this right. The energy loss that I feel is because of the contraction of my muscles. The contraction cause the muscles to transfer energy in the form of heat to the rest of the body.

And not just once. As long as you continue pushing on something, the filaments of the muscles are repeating sliding back and forth past each other, chemically bonding and unbonding during each sliding cycle. The energy-dissipating chemical reactions occur during the moments when they are bonded, then they let go, slide, reattach, and do it again. They call this principle the "sliding filament theory" of muscle contraction. A Google search for "sliding filament theory" finds a lot of pages. There are some similarities there to asking where the energy went if you slide sandpaper back and forth on a block of wood a thousand times but ultimately having no displacement.

Mentor
Consider a boiler driving a steam engine...or not driving a steam engine. Fuel is burned and chemical energy released to keep the boiler hot and the steam pressurizing the system, but if the engine isn't spinning, then for all that input energy, there is no output work.

Or how about a car at idle or balancing the clutch and engine to hold still on a hill?

More cases of zero energy conversion efficiency.