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Appendix 2. When the Past Leaves its Mark

Appendix 2. When the Past Leaves its Mark

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Laws for quantities at time t



83



OUTLINE OF CORRECT ANSWERS

Any kinematic data before time is not pertinent. Only the velocity of the ice cube, the

forces acting on it, and the subsequent motion of the plane matter here. These elements are the

same for questions 1 and 2. The answers to both questions are therefore identical.

The motion of the ice cube in the (Galilean) reference frame of the sky obeys the

following relationship:

F exerted on the ice cube = ma of the ice cube

The resulting force F exerted on the ice cube is zero everywhere, and, therefore, so is the

acceleration of the ice cube. The latter continues in its course, tangential to the initial

trajectory, at the same velocity. The plane does not. The diagrams below correspond to three

different moments

and show that the ice cube moves relative to the table.



The initial directions of the motion of the ice cube can therefore be represented as follows:



Chapter 4



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FREQUENT ANSWERS

The answers are very mixed. But when the ideas that informed the design of the question

are considered, the picture becomes clearer.

The two things to be assessed were:

- whether the students realise that the answer in no way depends on the past history of the

motion, but only on the velocity of the ice cube at the moment it is released, and on what

happens after that;

- whether, for each question, the students propose different trajectories according to the

frame of reference.

The student who gave the answer below has formed an opinion on each point. According

to him,

- the past history of the motion does count;

- the directions of the motions are transposed from one frame of reference to the next: the

ice cube starts “radially” (question 1) or else “tangentially” or “forwards” (question 2), in

both frames.



These examples illustrate the same aspects of answers, but with more complex trajectories.



Laws for quantities at time t



85



These aspects account for a large proportion of answers, as the following table shows:



The answers combine two previously identified elements of common thought:

- The tendency to “rigidify” trajectories and directions results in their being understood as

independent of a frame of reference.

- Although a moving object has no recollection of the past beyond its present velocity, it is

seen as keeping a more “informed” trace of it stored inside itself: a “supply of cause,” so to

speak. Here, this trace is the type of motion just depicted (rectilinear or circular).



86



Chapter 4



APPENDIX 3



ANALYSING INTERACTIONS: TWO SITUATIONS



Laws for quantities at time t



87



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Appendix 2. When the Past Leaves its Mark

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