_ THE _5A 2007 V10 B

_ THE _5A 2007 V10 B - TAKE-HOME EXP # 5A The Location,...

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TAKE-HOME EXP # 5A The Location, Velocity, and Acceleration of a Bouncing Ball First, we’ll do some exercises that will give you a “feel for” the phenomena and representations of their relationships in graphs. Then we will examine the tricky motion of a bouncing ball. Actually it’s not the motion that’s tricky, it’s how you communicate it. The real “trick” is to connect what you see with graphic visualizations of the location, velocity, and acceleration of the ball as time passes. A racquetball or tennis ball can do this job, but a "super" elastic ball works best because it bounces higher for a longer time. Drop the ball from about 1.5 meters. What do you observe? I'm interested in looking at the time evolution of the vertical location of the ball, of its velocity (magnitude and direction), and of its acceleration. Three graphs can describe the motion of the bouncing ball: 1) location vs. time, 2) velocity vs. time, and 3) acceleration vs. time. The graphs themselves will be qualitative, and capture the general features of the motion. That means that only estimates of relative effects will be important. We will assume that air friction plays no significant role in changing the motion, and this is a very good assumption at these low speeds. I'll start you off with the first graph, and give some hints about the others.
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TAKE-HOME EXPERIMENT #5A T.H.E.# __________________________________________________ 5A-2 0 + table or countertop Part I. How can one get a good operational sense of the motion quantities? ( adapted from A. Arons, A Guide . . ., John Wiley and Sons, NY, 1990) It’s not easy to separate the concepts of location and displacement and the latter’s change as time passes, producing acceleration and velocity. The exercises below are easy to do, alone or with friends to check your movements. They can give you a body-sense experience to relate to these ideas. 1. First, let’s set up a straight-line track, a one-dimensional line along which you can freely move. Let the straight edge of the long side of a table or countertop be the straight-line track. Use a pen, book-edge, or anything to mark the center of this “track” as the zero reference. Assume locations to the right are positive, that is a displacement from zero to the right will be our choice for a “+” direction. Locations to the left will be negative (“—“). Your own hand will be the moving object. a) Interpret each diagram below by performing the indicated motion with your hand. Describe the motion in words as you execute it. Include all the descriptive details, such as speeding up. slowing down, reversing direction, standing still as time passes, moving with constant velocity, having your hand at the appropriate location at time t = 0 (the value assigned to whatever clock-reading with which you start), and so on. Note the labels on the axes of the following graphs. The graphs give histories
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_ THE _5A 2007 V10 B - TAKE-HOME EXP # 5A The Location,...

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