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course Phy 231
9/9 520I sent two emails yesterday with initial answers for the assigned hw and have not received a response. I am hoping to have your insights/corrections soon so I can submit my report in acceptable fashion.
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I've copied your questions from the email. Responses are inserted accordingly.
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Video-related question: can you discuss the significance of and applications for the dot product a little? I am well-acquainted with the methods of finding cross product and its application, but dot product seems to be a little fuzzy to me still.
Analysis and predictions for the ball on ramp activity:
For my graph of acceleration vs. ramp slope, I have plotted my slope along the x-axis, and it is measured in stacked dice/2' bracket. For my y-axis, I have tU plotted. My data coordinates are (1, 1.59), (2, 1.02), (3, .86), (4, .73), and (5, .66).
The acceleration for my slope of 1 die/2' bracket is 48.2 cm/tU^2. (Found from finding average velocity, then dividing that by half my time interval).
The acceleration necessary for a second ramp if a ball rolled down the second ramp is to cover 25 cm while the first ball covers 50 is 29.5 cm/tU^2.
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For this question and the preceding, I need to see how you proceeded from your data to your conclusions. At least one detailed calculation needs to be provided for each type of calculation.
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I'm a little unsure of what exactly you're looking for as to the next couple questions. They seem like lab problems, but I could be wrong.
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I'm not sure what the 'next couple questions' are. A copy of those questions would have been helpful.
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Chapter 1 - is there ever a scenario in which the LH coordinate system is used? I've been taught all about and used the RH system, but I'm having trouble thinking of a situation in which the RH system would be inadequate and the LH system would be necessary.
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There is a linear transformation that will transform a right-hand to a left-hand system, but I can't think of a case where a LH system would be an advantage. I'll give this some more thought. However all our conventions and intuitions are built on a RH system.
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Chapter 2 - in section 2.4, motion with constant acceleration is discussed and many helpful equations are given. However, I'm curious if I could use those equations even if the acceleration function were linear. For instance, could I calculate the average acceleration for the interval in question and insert that value into the equations from section 2.4?
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If acceleration is not uniform, none of the equations of uniform motion are applicable.
For a linear acceleration function you integrate to get a quadratic velocity function and a cubic position function.
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