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PHY 201
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: ->->->->->->->->->->->-> :
'ds = 20 cm, v0 = 0 m/s, 'dt = 2 s
vAve = 'ds / 'dt = 20 cm / 2 s =10 cm/s
vAve = (vf + v0) / 2
vf = 2(vAve) - v0 = 2(10 cm/s) - 0 m/s = 20 cm/s
vf = v0 + a'dtt => (vf - v0) / t = a
a = (vf) / 'dt = 20 cm/s / 2 s = 10 cm/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: ->->->->->->->->->->->-> :
'dt = 2 s / 1.03 = 1.94 s
vAve = 'ds / 'dt = 20 cm / 1.94 s = 10.3 cm/s
vf = 2(vAve) - v0 = 2(10.3 cm/s) = 20.6 cm/s
a = vf / 'dt = 20.6 cm/s / 1.94 s = 10.6 cm/s^2
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• What is the percent error in each?
answer/question/discussion: ->->->->->->->->->->->-> :
vf percent error = (1 - (20.0 / 20.6)) * 100 = 2.91%
a percent error = (1 - (10 / 10.6)) * 100 = 5.66%
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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: ->->->->->->->->->->->-> :
They are not the same.
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• If the percent errors are different explain why it must be so.
answer/question/discussion: ->->->->->->->->->->->-> :
I am not 100% sure on how to explain this. But the smaller the number, for example 10 and 10.6, the percent error is higher, however, as the numbers become larger the percent difference is smaller.
I am hoping you will explain this in better mathematical way.
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The uncertainty in the time interval gives you an approximate 3% error in the final velocity. You use the time interval, which has a 3% error, along with the final velocity, which now has a 3% error, to calculate the acceleration. The two 3% errors compound, giving you a 6% error.
More rigorous mathematical arguments are possible, but this is sufficient for the present.
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10 mins
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