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course phy 201
08/28 10:50 pm
Copy the questions below into a text editor, complete in the usual manner and submit using the Submit Work Form at http://vhcc2.vhcc.edu/dsmith/submit_work.htm . You may give the exercise any title you wish, but you might want to consider including the date in your title (0827, the date on which this was assigned, would be a good choice). This will help you keep track of documents.Questions `q001 - `q004 are for everybody.
Questions `q005 - `q007 require the use of calculus and are for University Physics students only.
`q001. This series of questions uses the basic analysis of a straight-line v vs. t graph for an object which starts from rest:
Sketch a v vs. t graph representing the motion of a ball that starts from rest and moves for 6 seconds, averaging a velocity of 15 cm / sec.
Describe your graph.
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The graph is exponential, increasing at an increased rate
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What are the initial and final velocities of the ball?
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Initial: 0 cm/s; Final: 30 cm/s
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What is its velocity at the 3-second mark?
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15 cm/s
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If the graph was exponential the midpoint velocity would not be halfway between the initial and final velocities.
The graph is assumed to be linear, which justifies the 15 cm/s result.
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By how much does its velocity change during the 6-second time interval?
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30 cm/s
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How quickly is its velocity changing during the 6-second interval? Note that the answer to this question is also the slope of your v vs. t graph.
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5 cm/s^2
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`q002. This question asks you to do something closely related to today's class, but somewhat different from anything we actually did.
How far does the ball in the preceding question travel during the 6 second interval?
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average velocity: 15 cm/s 15cm/s * 6s = 90 cm. 90 cm.
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How far does it travel during the first 3 seconds?
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average velocity: 7.5 cm/s *3 seconds = 22.5 cm. Soluton: 22.5 cm.
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Would a sketch of its position vs. clock time be a straight line, a rising curve with an increasing slope, a rising curve with a decreasing slope, or some other type of curve?
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rising curve with an increasing slope.
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`q003. Report your data from today's experiment. Your report should be clear and concise, telling the reader what was measured and how, and specifically what the results were.
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We measured the time it took for a marble to roll down a ramp from rest. Once from a “flat” perspective from each direction, and once from a sloped perspective from each direction. These times were measured in oscillations from a pendulum.
From front of class to back, flat ramp: -First trial: 2 ˝ oscillations. -Second trial: 2 ˝ oscillations.
From back of class to front, flat ramp: -First trial: 4 oscillations. -Second trial: 3 oscillations before coming to rest, then moving backwards. Third Trial: 4 oscillations, came to rest at roughly 17 cm and stopped.
Front of class to back of class, sloped: -First trial: 2 oscillations. -Second trial: 2 oscillations.
Back of class to front, sloped: -First trial: 2 ˝ oscillations. -Second trial: 2 oscillations. -Third trial: 2 ˝ oscillations.
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`q004. For one of your ramps, indicate the displacement of the ball and the number of cycles of your pendulum corresponding to motion to or from rest in one direction, and the displacement of the ball and the number of cycles to or from rest in the other direction.
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Sloped. Slope was changed to slope downwards for the direction the ball was travelling for each direction.
The displacement was a full 15 centimeters each way
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What is the average velocity of the ball as it travels in each direction, according to your data? Your time will be measured in cycles of the pendulum, rather than in seconds. A cycle is a perfectly valid unit of time, as long as you know the length of the pendulum. So for example the average velocity of the ball will be in centimeters / cycle. We can later convert the result to units involving seconds.
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front to back: total distance: 15cm. Time: 2 oscillations. Average velocity: 7.5 cm/oscillation.
Back to front: total distance: 15 cm. Time 2 ˝ oscillations. Average velocity: 6 oscillations.
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What are the initial and final velocity of the ball in each direction?
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Front to back: initial: 0 cm/oscillation. Final: (assuming constant acceleration) 15 cm/oscillation
Back to front: initial: 0 cm/oscillation. Final: (assuming constant acceleration) 12 cm/oscillation
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What is the change in velocity in each direction?
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Front to back: 15 cm/oscillation
Back to front: 12 cm/oscillation
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How quickly did velocity change in each direction? Note that an answer to this question is also the slope of an appropriate v vs. t graph.
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7.5 cm/oscillaton^2
6 cm/oscillation^2
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Good, but the second trial required 2.5 oscillations, so I believe the rate would be 4.8 cm/oscillation^2.
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&#This looks good. See my notes. Let me know if you have any questions. &#