Why is work considered a conservative force?

[Calpalned]

My textbook says that work done by a conservative force is independent of the path taken. This tells me that $\int_{a}^{b} \vec{f} \vec{dl}$ only needs displacement (not distance) between points a and b. Conservative, according to my book, means that there is no friction. I have difficulty conceptually understanding this. Of course I'll feel more tired if I move a block of ice in a complicated path than if I did a straight line. Thank you.

 

[Orodruin]

The physical concept of work is not related to how tired you become. If you hold a 40 kg weight above your head you are likely to get tired after a while, but you are not doing any work.

 

[Chandra Prayaga]

The physical concept of work is not related to how tired you become. If you hold a 40 kg weight above your head you are likely to get tired after a while, but you are not doing any work.

Absolutely. Most of the feeling of unease comes from somehow relating work to our "common sense" or intuition. A force can do zero work, as Orodruin points out, or even negative work. The concept of work should be always related to the basic definition, and not to any ideas arising from literal meanings.

 

[DrewD]

The physical concept of work is not related to how tired you become. If you hold a 40 kg weight above your head you are likely to get tired after a while, but you are not doing any work.

This was something that bothered me when I started learning physics, so I want to make a somewhat tangential note. You are not doing work ON THE 40kg WEIGHT, but your muscles certainly require energy. Your body is built to be dynamic. Your muscles are not best suited for holding something stationary. They require continuous exchange of chemically energy to stay contracted. This often confuses people because you are "working" in the sense that there is $\Delta E$, but that energy is being exchanged in your muscles and not transferred to the object that you are holding.

Since this is a complicated system to deal with the physics you are learning first deals with rigid objects that are being moved around without waste in the subsystems (like your muscles). So, your body is not doing work on the object and your physics class is interested in the interactions between your body and the object or gravity and the object or something else and the object. For most (if not all) of your physics career the interactions in your muscles will be left to the biologists.