Force, acceleration problems

Welcome!
1) pressure = weight/area , not force.
2) If the speed is constant then there's no acceleration. But when a person is walking he stops and starts all the time so he's really accelerating.

 

Hi Emily,

I'm afraid that's not quite correct. Weight is a type of force. It's pressure that is equal to force/area.

As for the force exerted on the foot while walking, here are my two cents. I don't think that the walking speed is necessarily the most useful information, because it is determined by the length of a stride and the frequency of those strides (how often they occur), but not by how hard the foot comes down on the ground. Furthermore, if the initial velocity of the foot is known and we can assume that the accelaration is constant (it is slowed to a stop by the ground at a constant rate), then the force exerted on the foot by the ground is constant and we can in principle use Newton's 2nd law with this constant acceleration to solve for it.

However, this assumption is unlikely to be valid. Taking a step is a very dynamic process, especially since the foot deforms upon impact, so that it seems more likely that the contact force goes from zero, increases rapidly (and not necessarily linearly) to some maximum value, and then falls off as the foot begins to rise again but is still in contact with the ground. In this case, the rate of change of velocity (i.e. acceleration) is not constant and therefore you need calculus just to do your calculation (assuming you had some way of measuring or modelling this acceleration as a function of time). Speaking of deforming, that brings me to another point: most of the physics you are learning at the introductory level is the mechanics of single particles (that we can consider to have fairly localized mass at a single point in space e.g. a projectile) or rigid bodies (they do have some finite extent in space, but they don't deform). The human body is neither of these idealizations, and the foot is connected to all kinds of other things that exert forces on it. How do we take into account the fact that the leg initially pushes down and then later starts to pull up, and this change occurs not abruptly but all in a fluid and continous way. What mass do we use in Newton's 2nd law? The foot? The entire leg? A larger portion of the body?

I don't mean to be discouraging, I just meant to point out that you have chosen to tackle a very tough problem!

Is this a homework assignment?

 

Hi. welcome to the forums.

This is a difficult question and it's not easy to calculate. In practice, one would have to attach so measuring device under the feet of the person to measure that, there are probably sites where this type of measurement is done.

Notice that what you need is how the vertical velocity of the foot changes with time. What you providedis the horizontal velocity of the person, which is roughly constant. But this is unrelated to the force on the feet. You would need to know the vertical velocity as a function of time of the foot and take the derivative of that. Or, if one coudl approcimate the acceleration as constant, what you would need is the vertical speed of the foot just before it reaches the ground and then you would need to knwo the time it takes for the foot to come to rest. Then the acceleration (the average) would be the speed before it reaches the ground divided by the time interval.

 

Well, how important is this t your thesis? Yes, it is clear that the force is greater than while standing. But to be more quantitative would require quite abit of work. It would depend on the type of shoe worn by the person and also on the way the person walks (you know how some people make much more noise while walking barefeet on a hardwood floor than others because they hit hard the surface). So it's very complex. But I am sure there are some sites with relevant data somewhere. Have you tried a google search?

 

Do you have access to American Journal of Physics? Here's an article that could provide some data (I could look it up when I go back to my office)

link.aip.org/link/?AJPIAS/67/304/1

 

I am not surprised that the pressure would go so high while walking. There is a fairly large acceleration when the foot is in contact with the floor (the change of speedis not large but it occurs in a very small time interval, which leads to a large impact force). So those numbers seem very reasonable to me !

When you calculated 11.36 PSI, did you divide by two to take into account the fact that the force is spread over both feet? I am assuming that the 11 square inches is for one foot alone...)

Of course you may ask as many questions as you want!!! There are people very very knowledgeable in all fields of physics here so some of them may be much more helpful than I am.

And you may want to post your next questions in the "General Physics" forum because the present forum is usually reserved to assignment problems.

Patrick