Kinetic friction while walking

[HamsterPower]

So i just had a physics exam the other day, and we were learning about forces and frictions

While i was walking back home from school , I wondered how much more energy am i using because of walking in snow than just walking on normal dry ground (pavement)

But i don't know where to get all the Mew K for friction between by shoes and snow/pavement and energy i spend for every step i take

Can somebody give me ideas on how to calculate this?

[Mr Skeptic]

It would be a horribly complicated calculation. You are doing work to compress snow, your body uses energy even at rest, your body is very inefficient at doing some kinds of work, snow is lumpy and some parts slipperier than others, and other problems. I suppose you could model that as an increase in the coefficient of friction between humans and snowy/clear sidewalk, but I doubt that would be a good model because it wouldn't really follow the formula for friction (for example on slopes or when carrying extra weight).

 

In theory, no work is done moving an object any horizontal distance (without friction), and if you do have friction on the ground it wouldn't matter much if you have a wheel.

[Schrödinger's hat]

Also, when you are walking, the contact friction with the ground points towards the direction of travel (which is rather counter-intuitive).

As you push your foot back, the reaction (friction) propels you forward. Losses are mostly from other sources, the energy lost in converting from chemical to work. You put a little bit of energy into lifting yourself up each step, this is mostly lost as your tendons do not absorb very much. The kinetic energy of your foot is also lost as you put it down. Your muscles, impact with the ground, and some friction (this time pointing backwards) absorb that energy.

Another inefficiency of human motion is our muscles do not work like, for example, an electric motor. To resist or slow a motion we have to put more energy in (rather than storing some of it) so we get a net loss both ways.

As Mr Skeptic said, walking in the snow is more difficult because you spend energy compressing it, or you can think of this as the energy required to lift yourself back up to a comfortable height after sinking a little bit each step. You also walk less efficiently, your legs will not be in their optimal configuration, so less energy will be stored in tendons and muscles will not be working at optimum efficiency. You may also have to hold yourself in a position where muscles are taking your weight. This takes energy too.

 

All in all, it's an extremely complex calculation. It could potentially be modelled in full, but usually the best way for a problem such as this is to study it empirically. You simply take measurements of someone's energy use (measured by heart rate, or CO2 exhaled or similar) in different situations and make some graphs.