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Phy 231
Your 'cq_1_09.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** CQ_1_09.1_labelMessages **
A ball accelerates uniformly as it rolls 20 cm down a ramp, starting from rest, in 2 seconds.
What are its average velocity, final velocity and acceleration?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
v0=0
`dt=2s
`ds=20cm
vAve=20cm/2s=10cm/s
10cm/s=(vf-v0)/2
20cm/s=vf-0
vf=20cm/s
aAve=`dv/`dt
=(20cm/s-0)/2c
aAve=10cm/s^2
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If the time interval is in error so that it is 3% longer than the actual time interval, then what are the actual values of the final velocity and acceleration?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
recorded interval=1.03(actual interval)
2s=1.03(actual interval)
1.94s=actual interval
actual vAve=20cm/1.94s=10.31cm/s
10.31cm/s=(actual vf-0)/2
20.62cm/s=actual vf
actual aAve=(20.62cm/s-0)/(1.94s)
actual aAve=10.63cm/s^2
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What is the percent error in each?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
difference between recorded vF and actual vf = 20.62cm/s-20cm/s = .62cm/s
.62 is what percent of actual vF?
.62=x*20.62
x=.0301
Error is 3.01%, or 3%
Recorded vF is 3% lower than actual vF.
difference between recorded aAve and actual aAve = 10.63cm/s^2-10cm/s^2=.63cm/s^2
.63 is what percent of actual aAve?
.63=x*10.63
x=.0593
Error is 5.93%, or 6%
Recorded aAve is 6% lower than actual aAve
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If the percent error is the same for both velocity and acceleration, explain why this must be so.
answer/question/discussion: ->->->->->->->->->->->-> scussion:
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If the percent errors are different explain why it must be so.
answer/question/discussion: ->->->->->->->->->->->-> scussion:
Assuming that when this set of questions referred to acceleration (which implies aAve) as opposed to final acceleration-- going back and looking at the wording, it is maybe ambiguous-- I believe the difference has to do with the fact that we measure acceleration here in cm per second per second. The time interval, in seconds, get squared in all calculations involving acceleration. Since we know that the source of the error was a time interval, that error gets magnified.
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Very good attention to detail. However the ball is said to accelerate uniformly, so the acceleration is always equal to the average acceleration. In this case it is unnecessary to use the word 'average' and we can just speak of 'the acceleration'.
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&#Good responses. See my notes and let me know if you have questions. &#