If work is Force x Distance, what is Force x Time?

 

Example: you're holding a large book mid-air, eventually you get tired from it -- yet no distance was covered. But since a force exerted over a measure of time doesn't fit as "work", how's it result in spent energy?

 

What's the term if no distance was covered? --Power? Effort?

impulse.

 

but holding a book sstationary does not actually take any energy so again impulse is zero too in this case.

 

you get tired holding a book up because your muscles have to keep tensed. this requires a reaction going on in the cells that produces an abundance of chemicals that give the tired and achey feeling. the energy expended does not go into the book, only to keepin your muscles tensed due to certain mechanical disadvantages of our body.

 

when thinking about this it would be best to consider a nonbiological system. such as a book sitting on a table.

when thinking about this it would be best to consider a nonbiological system. such as a book sitting on a table.

Ahh, makes sense.

 

But in a way, it's still problematic in one non-biological area.

 

Let's say a tiny machine anchored in the ground is pushing against a large building. Nothing moves. Yet in a few hours, the machine's batteries are dead.

again, all the energy is lost in the non ideality of the motor.

In both cases, is work being done to the muscles system and motor themselves -- even if neither moves?

no.

 

in the biological case energy is lost through chemical reactions so the energy goes to heat and in the case of the electric motor the energy is lost to resistance (and hence turned into heat) as there must be current.

 

if you used a clockwork mechanism that used a spring to deliver the energy then the spring would not come unwound over time(ignoring the fact that you can never get a perfect spring).

The engine has merely become an entropy generator. All waste heat, no work.

The engine has merely become an entropy generator. All waste heat, no work.

 

Yep, 0 % efficiency, or like the claims (correctly in context) on those electric heaters it's a 100% efficient heater.

Another way to view impulse is as change in momentum. So, infinitesimally we have

 

[math]\delta I = F \delta t = \frac{\delta p}{\delta t} \delta t = \delta p[/math]

 

(being very slack here with any rigour).