| Basic Thermodynamics ~ J. Pohl © | www.THERMOspokenhere.com (40-A421) |
It is common that problem statements of high school physics texts are misleadingly incomplete. Precise solutions are not possible, the matter of all physical events is modeled as a simpler existence, yet texts do not ask students to determine an answer that is "approximate," or "the least or greatest," as the author's answer always is." Authors assume students know all answers are wrong. Consider the following physics text problem:
Statement: "A dog runs back and forth between its two owners, who are walking toward one another. The dog starts running when the owners are 10 meters apart. If the dog runs with a speed of 3 m/s and the owners each walk with a speed of 1.3 m/s how far will the dog have traveled when the owners meet?"
The author of this statement did not include the conditions he/she intended to be applied in its solution.
i) "A dog runs back and forth between its two owners..." means the system/event shall consists of three entities: a dog and two persons.
ii) Author assumes students realize the system Model as being the dog and persons taken as a BODY (mass that exists "at a point"). Or that they will solve the problem not knowing that BODY was the system model.
iii) "The dog starts running when the owners are 10 meters apart..." Students will know this initiates the event.
iv) "If the dog runs with a speed of 3 m/s and the owners each walk with a speed of 1.3 m/s..." The problem authors know it is possible for the dog to move at 1.3 m/s for the duration of the event. What the author means is, "Assume the dog and persons move at constant speed. Thus the authors ask for an approximate solution.
v) "... how far will the dog have traveled when the owners meet?" The author means, "subject to unspecified approximations, and assuming the turning of the dog requires no time and is at the speed of 3 m/s..."
This Solution: Let the persons be designated as "p1," "p2" and the dog as "d." The event is described in terms of the relative positions of the dog owners. We write that vector equation.
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(1)The position of person "1" plus the position of "2 relative to 1" equals the position of person "2." |
Equation (1) specifies that the persons are ten meters apart at time equal to zero. That distance diminishes with time but it never becomes less than zero. Consequently the time the persons walk until they stand in the same space is:
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(2)To start the persons are 10 meters apart. That distance diminishes 2.6 meters each second. |
So now we understand that the duration of the approximated event is 3.85 seconds. So what does the dog do during this time period. Knowing dogs, as we all do, we envision craziness... running, dancing, turning. It is difficult to proceed to solve this problem knowing dogs as we do.
The dog of the physics text author is sedated, turns on a dime an always has constant speed: 3 m/s. The time that the author's dog can run is 3.85 seconds. Obviously the distance the author's (imaginary) dog can travel is:
| (3)(3) |
The message of this problem was the relevance of physics to dogs and owners. The premise is reasonable. The event, numbers and how it unfolds are believable. The physics text author knew how to "find" (the word usually used) the missing fact, the distance recorded by the "distance-meter" worn by the dog.