Question
Name the object motion assumptions, and explain their rationale.
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The primary assumptions in object motion typically include: Show more…
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Describe one key assumption that is required for the Kinematic Equations to apply to an object. When might this assumption break down, and how would that change the motion of the object through its trajectory?
Three digital movies depicting the motions of four single objects have been selected for you to examine using a video-analysis program. They are as follows: PASCO004: A cart moves on an upper track while another moves on a track just below. PASCO153: A metal ball attached to a string swings gently. HRSY003: A boat with people moves in a water trough at Hershey Amusement Park. Please examine the horizontal motion of each object carefully by viewing the digital movies. In other words, just examine the motion in the $x$ direction (and ignore any slight motions in the $y$ direction). You may use LoggerPro 3, VideoPoint, VideoGraph, or World-inMotion digital analysis software and a spreadsheet to analyze the motion in more detail if needed. Based on what you have learned so far, there is more than one analysis method that can be used to answer the questions that follow. Note: Since we are interested only in the nature of these motions (not exact values) you do not need to scale any of the movies. Working in pixel units is fine. (a) Which of these four objects (upper cart, lower cart, metal ball, or boat), if any, move at a constant horizontal velocity? Cite the evidence for your conclusions. (b) Which of these four objects, if any, move at a constant horizontal acceleration? Cite the evidence for your conclusions. (c) Which of these four objects, if any, move at neither a constant horizontal velocity nor acceleration? Cite the evidence for your conclusions. (d) The kinematic equations are very useful for describing motions. Which of the four motions, if any, cannot be described using the kinematic equations? Explain the reasons for your answer.
Translational motion of the rigid body is defined as one in which any line, say PQ, remains parallel to a fixed direction. Let $\overline{\mathrm{R}}_{\mathrm{A}}, \overline{\mathrm{R}}_{\mathrm{B}}, \overline{\mathrm{R}}_{\mathrm{p}}, \ldots \overline{\mathrm{v}}_{\mathrm{A}}, \overline{\mathrm{v}}_{\mathrm{B}}, \overline{\mathrm{v}}_{\mathrm{p}} \ldots$ and $\overline{\mathrm{a}}_{\mathrm{A}}, \overline{\mathrm{a}}_{\mathrm{B}}, \overline{\mathrm{a}}_{\mathrm{p}}, .$ denote the position vectors, velocity vectors and acceleration vectors of $\mathrm{A}, \mathrm{B}, \mathrm{P} . . .$ with respect to $\mathrm{O}$. Then, for translational motion. (a) $\overline{\mathrm{R}}_{\mathrm{p}}-\overline{\mathrm{R}}_{\mathrm{A}}$ must be a constant vector (b) $\overline{\mathrm{v}}_{\mathrm{A}}=\overline{\mathrm{v}}_{\mathrm{B}}=\overline{\mathrm{v}}_{\mathrm{p}}=\ldots$ and $\overline{\mathrm{a}}_{\mathrm{A}}=\overline{\mathrm{a}}_{\mathrm{B}}=\overline{\mathrm{a}}_{\mathrm{p}}=\ldots$ at any instant $\mathrm{t}$. (c) $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{P}, \ldots$ must move in straight lines that are parallel. (d) All of the above.
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