A Question for You Physics Experts

It would be the exact same energy…….. However I suspect that you would increase the energy in the faster mode because the mechanics of your motion may become less efficient.

short answer : in an ideal world where nothing but the time to perform the task changes, the same energy, but more energy per unit of time. It takes more power to due the same work faster. But, the body is not an ideal world, and the energy required increases as it uses less efficient pathways to keep the muscles going at a higher intensity.

Been awhile since I taught integrated physics and chemistry but I'll take a stab. It takes the same amount of energy to move your mass but (1) there's a time component in the power equation – delta t – and (2) your muscles will burn more Calories per hour moving faster everything else staying relatively the same (last I saw this were treadmill studies from University of Texas measuring respiration, calories, etc.. written up in a professional journal iirc). Add that I need to apply any of the above after Xmas Caloric Intake.

The best way that it was explained to me was this – Imagine you are crushing a Pepsi can in one of those old school crushers with the long lever. You can crush it very slowly and it takes minimal effort. Crush it as fast as you can and it takes as much force as you can generate. The added speed increases the effort you have to put into it, thus increasing the energy output.

I've also seen this measured on a chassis dyno. The higher the engine RPM and wheel speed, the higher the parasitic losses on horsepower all things being equal. Takes more horsepower to turn everything at 7k rpm as opposed to 2k rpm.

Ryan

It is generally the same amount of energy being expended when you view your body as an isolated system(except you have more kinetic energy at the very tail end of your trip because you are going faster, presumably). I suspect your body is less efficient at the higher speeds too, which involves more energy burned by your body but being converted to heat instead of energy needed to move your body.

If you look at it from a more pure standpoint, there has been no net change in energy states if you go up and come back down to the same place and stop. Really, all the energy your body has burned has been blown on friction and heat and you energy state is the same since you are back in the same place.

"… am I expending more, less, or the same amount of energy each time …"

First of all, reading a little more into your question –

If you are asking about Work-

it's Mass over Distance – and Work stays the same. Same mass, same distance.

If you really are asking about Energy it gets a lot more complex. Your physiology comes into play, and the answer is "More".

People aren't efficient and straightforward about converting energy into work. A large amount of calories expended go into heat (just like an incandescent light bulb). As effort goes up utilization, and efficiency, may go down.

Depending on output level, our energy source may change from one metabolic source to another, which may affect your overall efficiency. Some people (elite athletes) maintain their efficiency during very high levels of output. Others, not so much.

And as Greg G. mentions, we may become less efficient mechanically just due to the difference in the mechanics of our stride, arm swing, posture, etc., which means more energy is needed.

YMMV

p.s. Not an expert in Any field.

Work is force x distance. Mass may have a role in that.

so I'm not really sure now if I'm asking about work or energy.
are these 2 the same in a perfect world with no inefficiencies ?

thus with no inefficiencies time is not relevant to my question because I am simply moving the same mass from A to B each time ?

and it is only the fact that inefficincies develop as I speed up that causes the shorter time hike to use more energy ?

"are these 2 the same in a perfect world with no inefficiencies ?"

yep.

"and it is only the fact that inefficincies develop as I speed up that causes the shorter time hike to use more energy ?"

Yep, for you, in this scenario.

It does take the same amount of work to go from point A to point B assuming no lost energy to heat,friction, etc. Its just being done in a shorter amount of time.

Truly, though, if you wind up in the same spot and there is nothing lost to friction or heat, it would take no energy. Walking is virtually all friction/heat/ lost energy unless you are going up hill. At least if you consider the body as a whole system. If we were truly efficient, we would glide like an air hockey puck (even a little better)and it wouldn't take any energy to travel, except when going uphill. When we come back downhill, we would gain that work back.

"Truly, though, if you wind up in the same spot and there is nothing lost to friction or heat, it would take no energy."

If only this Were true…

I think you meant Work. But that is only for the specialized cases involving conservative force fields. Otherwise it is the "force along the path", and is certainly not zero.

If we were truly efficient, we would glide like an air hockey puck (even a little better)and it wouldn't take any energy to travel, except when going uphill.

Here's where I'll toss in Newtons 1st and 2nd laws. Assuming you are starting the hike from a standstill, and want to stop at the destination (rather than glide right past), you'll need to exert a force to both start and stop. (F=ma) Note that in this case, since acceleration has a time component, more force will be needed to achieve faster transit times.

Good point Jeremy, except for one thing. In deceleration, the force and distance are in opposite directions. This means that you actually could capture energy by stopping a moving object(the hiker in this case) in the exact same amount that was spent accelerating the object(the hiker)and the work involved is still the same(under the big assumptions of no energy lost to friction, heat, drag, etc.). Its zero.

You can actually have a braking system that captures energy.

This has gone off in ways that are useless and interesting. :) Here's my contribution to both:

It takes the same amount of work to haul your carcass up and down the mountain no matter how fast you move.

The energy you burn to do that work differs because of differences in efficiency between the slow and fast trips:

* Friction between your feet and the ground is different. I'd guess running results in more slippage, hence lower efficiency.

* Your body's mechanical efficiency is probably lower when walking. We're smoother runners than walkers, at least when we're working hard at both.

* Your body's metabolic (right word?) efficiency is probably lower when running. I'm guessing at this one too, but the necessity of sweating and such probably lowers efficiency.

This came up at the Olympics. They were saying Usain Bolt was doing less work because in the 50 he takes like 43 steps while others avg 49 steps. (numbers are estimates, but they are close IIRC)

"They were saying Usain Bolt was doing less work because in the 50 he takes like 43 steps while others avg 49 steps."

41 strides may require less Energy than 45 strides. (He is more efficient.)

But if both athletes weighed the same the Work would be the same.

There is a rule of thumb (ie an approximation) for energy expenditure that some runners may be familiar with:

Energy expended (kCal) in running from A to B = body mass (kg) x Distance (km)

To a first approximation, there is no dependency on speed.
The implication is that the maximum speed that you can run any particular distance (ignoring sprint distances) will depend on your maximum oxygen consumption (VO2max) (a measure of sustained power capability), weight and running efficiency.

I suspect the equation will hold true for walking on level ground too, but obviously not for hiking/running up and down, where potential energy would have to be taken into account.

If we were speaking of a mechanical machine, you could perform all these fabulous calculations and whatnot to arrive to a conclusion. The human body, however, has many, many more variables than mass, energy, work, etc.

There are so many other systems going at the same time in your body and they will all have an effect…under some conditions the 4 hour ascent will take more energy, under others the faster ascent will. What is your immune system doing? How efficient was your digestion before you started your ascent? Did you expend energy yesterday and have a depleted supply? This would mean drawing on more reserves, which consumes more energy to perform the same task (think the cumulative challenge of the Tour de France)
Anyway, as much as I truly love a good physics discussion, there is a great deal more to your question….

In my very unscientific/untrained mind what comes up is that it would depend a lot on how close the shorter time is to your best possible time.
To explain if, say ,I take 20 sec to run 100m (at my very best) I am pretty sure that taking 26 sec (about 30% longer) I would spend less energy as well as feeling less tired .
Now if I walked the 100m in 60 second or 90 it would hardly matter.
( no I have not tested that, it"s just the way I think )

Franco – in terms of energy used, it does not make a lot of difference whether you run or walk 100m. How tired you feel afterwards is a totally different question. That will depend on how much of the energy source is used (ATP, glucose, glycogen, or fatty acids), how well trained you are at a particular speed and a host of other factors.

There is an actual calculation that we can do in the lab that calculates something called running efficiency. Much of it is genetic, but it can be improved with training. Certain gait styles, shoes, ambient temps, etc can all alter running efficiency and this may be more to the point of your original question….

Short story – it's roughly the same if the only variable is speed. You can get as technical as you want, but the outcome won't change.

You use more fuel if you drive at 100mph than if you drive at 60mph. :-)

Depends on what the vehicle is geared for. You can gear for max efficiency at 60 or 100.