User:
Position in one dimension
Storyboard
To define the position of an object, a coordinate system is introduced that allows establishing an origin point and defining the position by measuring the distance along a straight line or a curve. As a result, the unit of position corresponds to a length measurement, such as kilometers, meters, centimeters, and so on.
The choice of the coordinate system is flexible and is made to simplify the modeling and associated calculations as much as possible. For instance, if the object moves along a track, which may not necessarily be straight, it is advantageous to define the coordinate system along that track. In this specific case, the position is defined as the distance from the origin or the starting point of the track.
ID:(607, 'ky')
Position, a dimension
Storyboard
One of the fundamental aspects of physics is determining the position of the objects we analyze. This simulator allows you to explore that concept: by generating a red bar and moving the mouse, you can determine its length. This length corresponds to the position of its right edge relative to an origin located at the left edge.
Consider the simulator panel:
Create a red box by pressing the button located below the ruler.
Then, drag it while holding down the left mouse button.
Make sure it is correctly aligned with the zero on the ruler at the left edge of the box.
Read the value shown at the right edge.
Enter the estimated value in the input field below (fractional values are allowed).
If the value is correct, a confirmation will be shown. If it is incorrect, the correct value will be displayed.
You can experiment by shifting the origin to the left and observe how a small misalignment leads to an error in the final result. You can also adjust the entered value it will be considered correct as long as it is within a one-millimeter margin.
If someone tells us their location is 45 km, we are immediately compelled to ask: from where? In other words, we need to know the origin that gives meaning to that information.
In the simulator, this means we must place the zero of the ruler at the left edge of the red box to correctly determine the position of the right edge.
If it is not positioned carefully, the value we read on the ruler at the right edge will be incorrect, and the simulation will show us that we have measured incorrectly:
When we place the ruler at the origin, we immediately realize how difficult it is to align the zero precisely with the left edge. A similar issue arises on the right edge, where it falls between two marks on the ruler, and we are forced to estimate its corresponding value:
In the end, we estimate the fraction of space covered and assign a value in tenths of a millimeter. However, we come to realize that we are operating at a scale of tenths of millimeters without even considering hundredths.
Therefore, we conclude that every measuring instrument (not just those for length) has an inherent limitation. For this reason, the values obtained from a measurement should always be expressed along with their uncertainty. This can be indicated by associating the number with a range, for example: [27.1, 27.7], or by using the average value (27.4) and specifying how much to add or subtract to obtain the range:
27.4±0.3
This principle applies not only to individual measurements but also to the calculation of distances, as demonstrated in the model with an example.
ID:(3, 0)
Position in one dimension
Description
To define the position of an object, a coordinate system is introduced that allows establishing an origin point and defining the position by measuring the distance along a straight line or a curve. As a result, the unit of position corresponds to a length measurement, such as kilometers, meters, centimeters, and so on. The choice of the coordinate system is flexible and is made to simplify the modeling and associated calculations as much as possible. For instance, if the object moves along a track, which may not necessarily be straight, it is advantageous to define the coordinate system along that track. In this specific case, the position is defined as the distance from the origin or the starting point of the track.
ID:(607, 0)