Graphs of Position and Velocity, Grade 10 Physics

Physics 10.IV Transverse Pulses T.Trường 9/6/17 943 0
  1. Graphs of Position and Velocity, Grade 10 Physics
    1/ Graphs of Position and Velocity

    When a pulse moves through a medium, there are two different motions: the motion of the particles of the medium and the motion of the pulse. These two motions are at right angles to each other when the pulse is transverse. Each motion will be discussed.
    Consider the situation shown in Figure ??. The dot represents one particle of the medium. We see that as the pulse moves to the right the particle only moves up and down.

    2/ Motion of a Particle of the Medium
    First we consider the motion of a particle of the medium when a pulse moves through the medium. For the explanation we will zoom into the medium so that we are looking at the atoms of the medium. These atoms are connected to each other as shown in Figure 5.2.
    [​IMG]
    When a pulse moves through the medium, the particles in the medium only move up and down. We can see this in the figure below which shows the motion of a single particle as a pulse moves through the medium.
    [​IMG]
    Important: A particle in the medium only moves up and down when a transverse pulse moves through the medium. The pulse moves from left to right (or right to left). The motion of the particle is perpendicular to the motion of a transverse pulse.
    If you consider the motion of the particle as a function of time, you can draw a graph of position vs. time and velocity vs. time.
    Activity :: Investigation : Drawing a position-time graph
    1. Study Figure ?? and complete the following table:
    [​IMG]
    1. Use your table to draw a graph of position vs. time for a particle in a medium.
    The position vs. time graph for a particle in a medium when a pulse passes through the medium is shown in Figure 5.3
    Activity :: Investigation : Drawing a velocity-time graph
    1. Study Figure 5.3 and Figure 5.4 and complete the following table:
    [​IMG]
    1. Use your table to draw a graph of velocity vs time for a particle in a medium.
    The velocity vs. time graph far a particle in a medium when a pulse passes through the medium is shown in Figure 5.4.
    [​IMG]
    Figure 5.4: Velocity against Time graph of a particle in the medium through which a transverse
    pulse is travelling.

    3/Motion of the Pulse
    The motion of the pulse is much simpler than the motion of a particle in the medium.
    Important: A point on a transverse pulse, eg. the peak, only moves in the direction of the
    motion of the pulse.

    Worked Example 1: Transverse pulse through a medium
    Question:

    [​IMG]
    Figure 5.5: Position of the peak of a pulse at different times (since we know the shape of the pulse does not change we can look at only one point on the pulse to keep track of its position, the peak for example). The pulse moves to the right as shown by the arrow.

    Given the series of snapshots of a transverse pulse moving through a medium, depicted in Figure 5.5, do the following:
    • draw up a table of time, position and velocity,
    • plot a position vs. time graph,
    • plot a velocity vs. time graph.
    Answer
    Step 1 : Interpreting the figure

    Figure 5.5 shows the motion of a pulse through a medium and a dot to indicate the same position on the pulse. If we follow the dot, we can draw a graph of position vs time for a pulse. At t = 0 s the dot is at 0cm. At t = 1 s the dot is 1 cm away from its original postion. At t = 2 s the dot is 2 cm away from its original postion, and so on.
    Step 2 : We can draw the following table:
    [​IMG]
    Step 3 : A graph of position vs time is drawn as is shown in the figure.
    [​IMG]
    Step 4 : Similarly, a graph of velocity vs time is drawn and is shown in the figure below.
    [​IMG]

    Exercise: Travelling Pulse
    E - 1.
    A pulse is passed through a rope and the following pictures were obtained for each time interval:
    [​IMG]
    (a) Complete the following table for a particle in the medium:
    [​IMG]
    (b) Draw a position vs. time graph for the motion of a particle in the medium.
    (c) Draw a velocity vs. time graph for the motion of a particle in the medium.
    (d) Draw a position vs. time graph for the motion of the pulse through the rope.
    (e) Draw a velocity vs. time graph for the motion of the pulse through the rope.

    High School Students Studying the Sciences Physics
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