If you walk four metres east, two metres south, four metres west, and two metres north, displacement is zero?

Question

I understand the concept of distance and displacement, but if you walk this rectangle, the position of your body is ultimately changed from its original position when standing at the starting point. This change in position would amount in even the tiniest amount of displacement no matter how much you try to stand in the exact same place. I think it would be physically impossible to stand in exactly the same place as one stood after walking a rectangle? Could someone explain this to me?
-From someone who has no formal education in physics.

Answer 1

You're correct; in the real world, it's just about impossible to return to *exactly* the same position you were in, for a number of very good reasons.

However, that's largely irrelevent in examples used to demonstrate physical concepts. Examples in textbooks and on websites will always idealize the situation so that they can easily and clearly demonstrate a concept (in this case, displacement) to the reader.

If a text started talking about the practical limits of measurement and about quantum uncertainty, and whatnot, a person who is new to physics would get very confused, without learning anything. Instead, it's easier to build up one's understanding of concepts by using simple, and ideal, thought experiments.

Answer 2

The best chance one has for ending up at EXACTLY the same place as one started would be if one started at the Equator. And even then, there will still probably be error involved because as humans, no matter hard hard we try, there will always be error involved.

Now if we were to try and do this at some starting point NOT at the Equator, particularly at some starting point quite far from the Equator in the Northern or Southern Hemisphere of the planet, then the curvature (and thus arc of travel when traveling East [then South] then West) of the planet would begin to significantly alter the accuracy and hence increase the error of the final location we would end up. The farther into the Northern or Southern Hemisphere, then the greater the Error due to planet curvature/arc.

The only way to wind up EXACTLY where you started at is by doing 2 thiongs:
1) Start EXACTLY at +1m North from the Equator, and ...
2) have a precisely controlled machine perform the EAST-SOUTH-WEST-NORTH maneuver (preferably controlled through some positioning scheme such as GPS).
These two steps would ensure a very precise ending point equal to the starting point.

Sincerely,
Ruben
Yahoo! ID: ruben_pena_pro

Answer 3

Well, just from a practical standpoint, even if you started out facing north with your feet on two painted footprints on the ground, then did a right-face and walked your rectangle, you'd still end up slightly off from where you started, just because we can't possibly measure our steps perfectly, and on an atomic scale, you'll always be a little off. From the standpoint of a physics/mathematics problem, however, you treat your position as a point on (in this instance) a two-dimensional grid. It doesn't matter how you stand on this point in space, or even which direction you're facing when you start -- it's a point. This illustrates the difference between problems you get in school and ones that present themselves in real life: you can assume a horse is shaped like a sphere for mathematical simplicity, but in real life it simply doesn't work that way. Same here -- you can treat your position as a point to determine your general position, but you have to realize that if you're using this as a real-life orienteering problem, you have to take the length of your stride, the size of your shoes, and even the terrain into consideration.

Answer 4

Of course, if just stand still the earth is moving and no matter what you do you won't end up back in the same place. It depends on what you're moving relative to.

Another question is are you still you after the steps? In the time it takes to go a couple steps, some of your particles will be different. Your foot may be slightly bigger if you're growing, etc.

So technically, no, but in an greatly simplified sense yes.

Technically, we can never tell where you really were in the first place due to Heisenberg's uncertainty principle.

Answer 5

Forget the details of precision -- we can do the thought experiment perfectly well if we assume infinite precision.

You get back exactly to your starting point only if it is exactly one meter north of the equator. From any other place, you get bitten by the earth's curvature. Suppose that your starting point is one meter south of the North Pole. The easterly motion will make a certain change in longitude. Go two meters south, and the longitude lines are considerably farther apart, so four meters west will make a smaller change. Then, going back north will put you nowhere near the original starting point.

Answer 6

When you draw a rectangle you do not rotate the pencil 90 degrees at every corner. You are confusing placement with direction. When you finish walking the rectangle you will be at the same place where you started. The fact that you are facing north when you finish doesn't matter.

Answer 7

take E/W as X and N/S as Y on a graph and commence at (0,0) then ?X = -4 + 4 = 0 and ?Y = -2 + 2 = 0 so very last position (0,0) and also you're proper back the position you began - no displacement

Answer 8

Scientifically, we are not considering a person, a boat or a car at motion, but a POINT. So if you can imagine a point moving exactly 400.00cm to east, 200.00cm south etc., the point will end up at the origin.

Answer 9

You're being too literal in reading the question. Instead of reading it as "you walk...", read it as "a mathematical point is moved...". The point of the question is to get the idea of displacement across. Personalizing the question is one way of engaging a student's imagination, which is key in learning physics.

Answer 10

I believe displacement is zero if meters were measured exactly.