SIS & Error In Physics

The Basics

• Accuracy is how close our measurement is to the actual/real value
  • When describing, things are not 'reasonably accurate' - they are either accurate or not accurate
  • $\pm 5%$
• Precision in terms of a measuring instrument, is the fineness of the scale on the instrument
  • A property of the instrument itself
  • We use experimental precision - how far apart from average experimental value
• Reliable - when additional trials give a consistent result
• Validity occurs when every variable is controlled as you intend it - no other variable is having an impact on our experiment other than the deliberate experimentation of the independant bariable and the resulting response of the dependant variable.

Uncertainty & Error

• 3 Classes
  • Measurement error - unavoidable, property of the measuring instrument
    • Absolute Error - of the instrument, $= \frac{1}{2}$ of the smallest unit of scale on the instrument - e.g. 30cm ruler with millimeter increments = 0.5mm. So whatever value you get would be $n\pm 0.5mm$
    • Percentage Error - this is $$=(\dfrac{absolute \space error}{measurement}*100)%$$
    • However, what if we had multiple measurements stacked together?
      • If adding/subtracting measurements
        • Add absolute errors (don't subtract, just add - more measurements $\implies$ more error)
      • If multiplying/dividing measurements
        • Add the percentage errors
  • Systematic error - affect the results such that all measurements are skewed away from some ideal value sought
  • Random - affect the results in a way which, if truly random, tend to cancel each other out

Examples

1. $10cm - 0.5%$
2. $15cm - 0.\overline{3}%$
3. $21cm - 0.24%$

Desk Example

1. Width is 61 with 3 measurements
2. Length is 296 with 8 measurements
3. Depth is 2.5 with 1 measurements

Absolute error of width is 1.5mm
Absolue error of length is 4mm
Absolute error of depth is 0.5mm

Percentage error of width is 0.25%
Percentage error of length is 0.14%
Percentage error of depth is 10%

Total area measured: 18056 cm^2 with 0.39% error
Total volume measured: 45140 cm^3 with 10.39% error

$s=\frac{1}{2} at^{2}$

$v=\frac{s}{t}$
$a=\frac{v}{t}$

$a=\frac{\frac{s}{t}}{t}$

$s=at^2$