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Uncertainties - HSN forum

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Uncertainties


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#1 Vixus

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Posted 13 May 2006 - 03:42 PM

How are the various uncertainties calculated?
I know how to calculate range/n, I think that's random error.

But what about percentage and absolute error? Maybe it would be easier if someone solved Q1 from 2003.

#2 broughy

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Posted 14 May 2006 - 12:03 AM

er, you'd need to show me that question.....i'd have a go at it, not making any promises though! don't remember much about errors from the days of school!
when i'm dancin' with you,
tomorrow doesn't matter,
turn that music up,
till the windows start to shatter,
cos you're the only one who can get me on my feet,
& i can't even dance

No Tomorrow - Orson

#3 Vixus

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Posted 14 May 2006 - 11:33 AM

Acceleration of a car is measured. Following data gathered:

s = 3.54 +- 0.01m
t = 2.53, 2.29, 2.34, 2.36, 2.65, 2.53 s

a = 2s/t2

Calculate random uncertainty in time measurement.
Calculate % uncertainty in average acceleration.
Express numerical result in form

final value +- absolute uncertainty

#4 Pringles

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Posted 14 May 2006 - 03:18 PM

Here is how I done this.

Average time firstly is = 2.45 seconds

Average acceleration =  \frac {2*3.54}{2.45^2} = 1.17m/{s^2}

Random uncertainty =  \frac {max recording - min recording}{number of readings}
                                         = \frac {2.65 - 2.29}{6} 
                                         = +/- 0.06s

 percentage\ uncertainty\ in\ time = \frac {random\ uncertainty}{average\ recorded\ time} *100
 = +/- 2.45%
 Uncertainty\ in\ {t^2} = +/- 4.9%

Percentage uncertainty in distance =  \frac {0.01}{3.54}
= +/- 0.28%

Since this value is less than a third of the percentage uncertainty in time then it can be ignored.

Therefore uncertainty in  a = +/- 4.9%

 a = \frac {2\*\3.54}{2.45^2} = 1.18m/s/s
 uncertainty\ in\ a = 1.18 * \frac{4.9}{100} = +/-0.06m/s/s

so in numerical form = 1.18 +/- 0.06m/s/s

#5 broughy

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Posted 14 May 2006 - 06:08 PM

i'd say, on first glance, that that looks right to be
when i'm dancin' with you,
tomorrow doesn't matter,
turn that music up,
till the windows start to shatter,
cos you're the only one who can get me on my feet,
& i can't even dance

No Tomorrow - Orson

#6 skint_student

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Posted 14 May 2006 - 09:14 PM

yeah that looks about right.
you could work out the standard deviation for the random error but I dunno if that is required in advanced higher. Max - min divided by number of readings is probably fine.

#7 Vixus

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Posted 14 May 2006 - 09:52 PM

Yep, those're the answers. Thanks!





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