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Uncertainties

Vixus

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.

broughy

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!

Vixus

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

Pringles

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

broughy

Posted 14 May 2006 - 06:08 PM

i'd say, on first glance, that that looks right to be

skint_student

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.

Vixus

Posted 14 May 2006 - 09:52 PM

Yep, those're the answers. Thanks!

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