Students also create a third model to represent motion in the form of graphs: position vs. time graphs, velocity vs. time graphs, and acceleration graphs. Finally students create a model as an equation to describe the observed pattern for motion.  Each model requires cognition, a process where new stimuli are compared, contrasted and sorted with prior experience or understanding. Each of the models that describe the observed pattern involve creative options The variety of representations provide students with individualized opportunities to model understanding of motion. Some students will be most comfortable with verbal descriptions of motion. Others will prefer graphs as models for motion. Still others will be drawn first to seeing motion in terms of an equation. All representations are valid, and all may be attained with practice.

     Poetry and music present many forms and patterns of motion. Sometimes poetry includes rhyme and rhythm, one or the other, or neither. All poems exhibit some shape or pattern or motion. In the lessons that I prepare for this course, patterns of motion in poetry and music will be tied to the study of kinematics. Students will be asked to develop models for motion in my classroom. These models describe patterns that exist due to forces that result in motion. Students will learn how to describe forces in diagrams and equations that describe how motion is either constant or accelerated. Students will choose a frame of reference to properly describe the motion as positive or negative, accelerating or moving with a constant velocity.  Poems and musical selections will be added specifically as content that evokes a sense of motion in patterns of words or musical notation.

   The use of poetry and music and the motion described within the words, rhythm or shape of a musical line will be  familiar to many students and may enhance and support the understanding of kinematics. Students may not immediately notice that physical motion is poetic and varied and includes patterns like those found in a musical line or a poetic device.  

     Robert Frost’s Hyla Brook, was chosen for this lesson as an initial example of a poem whose form and pattern suggest motion. The design extends and broadens the conceptual experience from the traditional Physics classroom plan to include patterns in poetic and musical forms. The form that Frost employs for the poem is reminiscent of a sonnet. The use use of a rhyme pattern enhances a sense of motion coupled with the cyclic nature of time. A final line is outside of the traditional form but may serve as an opportunity to expand a students thoughts about what is loved about motion. A second activity includes piano music and opportunities to describe and graph patterns in music that evoke a feeling of motion.

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     To begin, students will be asked to consider why the water is moving, and if the brook has a direction. Students should remember that water will flow downward, so some slope must be present and the movement down the slope will include a component of gravity that acts on the particles of water in the direction of motion. Students will also consider what might have slowed the stream on its course, and what will happen to the water when the particles eventually are absorbed into the underground and what aspect of gravity or other force might make this absorption possible. Direction of force and frame of reference are particularly important to the image of the jewel-weed and the force associated to blow and bend the plants in a direction that opposes the fromer motion of the brook. Students will employ this format to assess the potential for acceleration or constant velocity of the particles that comprise both the flowing water, the slowing water, the potentially stagnant water and also the velocity or acceleration of the weak foliage as it is blown by the wind in a direction opposite to the flow of the stream.  The poem suggests that time cycles have determined the motion of the stream, a theme that could link the study of cyclical motion of and forces acting in a non-linear setting.

 

     Immediately, Frost evokes the the image of speed. To Physics students, speed is a scalar measure that does not include a direction. One supposes that that the motion of the brook does include a direction and that as the particles of water are displaced due to an interaction of forces, displacement, (a vector quantity,) will result.  To evaluate the patterns of motion in the poem, students will first describe the motion in words. This is the first step in creating multiple models that explain the interactive patterns which ultimately result in the patterns of motion in the poem. Students next will create qualitative graphs to describe the motion of the water as it slows and ultimately stops or is drawn into the underground by unbalanced forces. Students will also create force diagrams to explain how patterns of interaction forces cause the water to accelerates or come to a halt and ultimately changes direction (groping underground).

 

     Example of a Written Description:  The brook moves from a source in a positive direction away from the source. At first the water accelerates due to unbalanced forces acting on the particles of the water. The acceleration is positive as the direction and increasing velocity are both positive. As time passes, the frictional forces equal the force of gravity in the direction of motion for the book, and the water comes briefly to a halt.  The downward component of gravity acting on the water particles pulls downward into the underground.

 

Examples of motion models for the brook:

 

1) Changing velocity of the brook in the direction of motion:  

     --> --> ----->   ----------> ------------------->

    Positive constant acceleration:  → → → →

2) The brook at rest: (no velocity and no acceleration.  

    . . .  . . . .  . . .

   Acceleration

   . .  . . .  . . . .  .

                                         Examples of Graphs for the motion of the brook

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     Students may use the following generic force diagram to support any conclusions concerning the forces that result in a) constant velocity of particles b) acceleration of particles c) particles at rest.  The angle for the bed of the stream would be much less than the 30 degrees in the figure below. Note: This discussion does not include reference to turbulent flow.

 

 

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Examples of potential kinematic equations that could be applied to the motion of water if data were to be available:

 

 

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     To conclude this lesson of poetry of motion, students will view a piano score for” Le Courante Limpide” or “The Limpid Stream” by Friedrich Burgmuller. Students will both listen to a recording and view the piano score for the selection. Students will discuss how constant velocity is indicated by the patterns of the the notes selected by the composer as well as the interpretation of the artist who generates the sound using force on the keys to place hammers on strings that vibrate and produce varied pitches when struck. The tempo for the performance is unchanging, as thought the artist was following an internal metronome. The students are asked to interpret the constant velocity of the stream as presented by the composer and performer. Then the students will create graphs of constant velocity and acceleration based on the patterns observed in the score and performance.