NO ME SALEN
THEORETICAL NOTES AND EXCERCISES OF PHYSICS AND BIOPHYSICS
(vectorial kinematics) |
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NMS 1.7 - An ant moves across the upper side of a blackboard. AT 11:40h the ant is at point A, 50 cm at the right of the center of the blackboard "C". At 11:41 h it is at B, 80 cm to the right of C. At 11:43h it is seen at A again, and at 11:46h it gets inside a crack, in D, 40 cm to the left of C. Pick a reference system, origin and posiive sense, and:
a - Assemble a value sheet with the position and time of the ant, with the available information.
b - Draw a position-time graph. (Can you complete it? Is anyone able to tell where the ant was at 11:42h?; Can you tell when it was at C? )
c - Calaculate the ant´s average speed in the next time-periods: 11:40h and 11:41h; 11:40h and 11:43h; 11:43 and 11:46h. Analyze. |
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Little traveling ant... let´s see what can we do about this excercise.
The first thing you should do in this or any other kinematics excercise is an scheme. If you do not know what a scheme is, you can at least begin with a drawing that reenacts the statement. What do you think about this one: |
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It is not exactly a scheme... but it is a nice start. A scheme contains the chosen reference system, names for the positions, instants, etc. |
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Details and clarifications. As you´ve seen, the statement does not indicate wich reference system must be taken. Well, I chose (you could choose other one) one that has de position zero in C, horizontal with positive sense to the right, measured in centimeters. For the timing, I chose the zero at 11 o´clock the day of the ant.
Watch as the ant retraces it´s path (did you know? Ants have 6 feet), the events of going cannot have the same name as the events of the coming, this way, I called A' the event where the ant walks again over A |
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| The value sheet is an atomical silliness. It consists in translating the data in an organized manner. Watch out, it must be the same information that is seen on the scheme. Don´t you ever forget to write the units in a value sheet. If you want to name every event you can add another column. In our case, it should be: A, B, A' and D. |
| x (cm) |
t (min) |
| 50 |
40 |
| 80 |
41 |
| 50 |
43 |
| -40 |
46 |
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This is the graph that shows the same information as the value sheet (and just that, if we write more, we are inventing). Each red dot shows the same amount of information than a row of the value sheet.
You can´t really add anything else and you can´t join the dots. Also, you can´t know when the ant went through C. We only know what the statement says, and that ants are loony. |
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You can calculate the average speeds. And we are asked to calculate a lot of them.
Between A and B. |
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| vAB = |
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ΔxAB |
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xB — xA |
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80 cm — 50 cm |
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30 cm |
= 30 cm/min |
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| ΔtAB |
tB — tA |
41 min — 40 min |
1 min |
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| Between A and A'. |
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| vAA' = |
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ΔxAA' |
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xA' — xA |
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50 cm — 50 cm |
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0 cm |
= 0 cm/min |
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| ΔtAA' |
tA' — tA |
43 min — 40 min |
3 min |
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| Between A' and D. |
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| vA'D = |
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ΔxA'D |
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xD — xA' |
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- 40 cm — 50 cm |
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- 90 cm |
= - 30 cm/min |
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| ΔtA'D |
tD — tA' |
46 min — 43 min |
3 min |
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| about the graph they ask you... it´s very hard and it doesn´t add anything to the interpretation of the information. There are other more usefull graphs out there. So I won´t show you this one. |
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| CHALLENGE: make a position-time graph (one of the infinite amount of possibilities there are) that completes the information on the ant´s movement. If the one you make is nothing else but joining dots with straigt lines... you are no longer my friend... c´mon a little more creativity please! |
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| Some rights reserved. Reproduction allowe by quoting the source. Translated by Santi Pisci. Last Updated jul-15. Buenos Aires, Argentina. |
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