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While we were studying pure rolling of bodies in the chapter rotation we were told that energy conservation holds if a body is purely rolling ( The point of contact between the rolling body and ground is stationary w.r.t. ground ). Considering a person to be system. Whenever the person walks his point of contact with the ground does not move. So apparently the only force(s) which acts on him are $(m_{man} + m_{clothes}) \cdot g,$ static friction and normal due to ground. Now energy can be conserved because normal and $mg$ while cancelling out each other are also perpendicular to the direction of walking. And since the force acting is static friction energy can be conserved. However if this is the case a person should not tire while walking becuase his energy is conserved. But practical experiences deny this. So what part of the work am I missing.

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marked as duplicate by knzhou, stafusa, John Rennie newtonian-mechanics Sep 25 '18 at 7:22

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  • $\begingroup$ What about the time between your steps? I mean, your analysis could be correct while your feet are in contact with the ground, but it's pretty clear that you need to move one of them to take a step and advance... which means you waste energy to bend your knee, move the foot against the gravitational force, and all the rest of movements that are involved in your walking. $\endgroup$ – Alex V. Jan 5 '17 at 14:47
  • $\begingroup$ thats nothing, i even get tired before going to the gym $\endgroup$ – user98038 Jan 10 '17 at 17:00
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You are, unfortunately, missing out on two crucial mechanisms of energy dissipation: kinetic friction in our joints (and other internal and external parts, like clothes) and the inefficiency of converting chemical energy into motion. As we walk, our muscles exert forces constantly in various directions; in order to do this, they have to do work against the kinetic friction that inevitably occurs at various points in the body. This work is dissipated as heat.

In addition, in a simplified sense, muscles receive chemical fuel in order to do work; however, the conversion from chemical bond energy to mechanical work is nowhere near 100% efficient. Once again, we lose this energy, as heat. So, as a person keeps walking, he or she gradually exhausts this finite chemical reserve, waste products build up in the muscles, and they feel tired.

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  • $\begingroup$ Of course there are such multiple argumenst. However, even a system with "lossless" joints and perfect chemistry would require energy to move forward since this is the work done by the forward force (force times the distance it acts). So if no force, no motion (except for "walking" in outer space at constant speed). $\endgroup$ – Jens Jan 5 '17 at 15:36
  • $\begingroup$ If you had frictionless joints and your muscles had perfect chemistry, then OP is right, energy would be conserved and you'd never get tired. The energy you'd spend to do work against gravity would be exactly balanced by the energy you'd gain as your foot dropped. $\endgroup$ – probably_someone Jan 5 '17 at 15:38
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In terms of energy conservation a human being is more similar to a car with lots of internal frictions than an ideal rolling body. As the wheels and gears grind along eachother energy is inevitably converted into heat and the combustion engine itself will keep running even if it is disconnected from wheels burning fuel even when standing still. The frictions of your joints and inside your muscles are just as real although not really the most signifi

When it comes to walking there still is some gravitational work involved as the knee moved up and down and whatever kinetic energy in the leg is gained as it "falls back to the ground" will be turned into heat upon impact with the ground. That said walking on a flat plane involves less of this kind of work than going up some stairs or running where you bob up and down more and all things considered walking is still not very tireing.

Howevert he sensation of becoming tired due to physical stress (muscular fatigue) has more to do with the chemistry of how our muscles produce work than the total amount. After all if running out of energy was what made you tired chugging sugar water while running should help you a lot more than it demonstrably does. Rather the issue is waste products of the chemical reactions (the "exhausts") build up faster than the body can move them out of the tissues, causing damage or inhibiting the reactions. Along with simple friction damage at the joints the body eventually reacts by producing tiredness or a pain response to stop you from continuing. The more work produced the faster this happens but it takes longer if your body is more capable of moving compounds in and out of the tissues or if you have become desensitized to the pain response.

Muscles are also mechanically peculiar in that they can require a lot of energy to maintain static poses. Holding up your arms out to your side and completely still requires no mechanical work and a locked metal beam could do this forever but we quickly get tired. As you walk your muscles also transitions through states which might be statically draining but this is less of an issue than in some other situations.

Generally the human body is not very instructive when trying to understand physics even though it obeys the same principles.

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