Hi steemians, I have decided to share some of my physics notes in the hopes that it will help some of you!
Systematic Uncertainties:
This occurs when all the measurements are affected in the same way due to equipment and or method.
Example:
Metre / Meter stick may have shrunk may cause all the measurements to be too small.
Measuring:
As this affects all measurements, it is not usually calculated.
Scale Reading Uncertainty
On an analogue scale like so:
the uncertainty is measured as +- half of the smallest division.
Example:
If a voltmeter has 10 divisions between each 1volt difference the uncertainty would be 0.05 (half of 1/10) expressed as:
1.65 +- 0.05 Volts
On a digital scale:
We take the uncertainty as +- the last digit on the screen.
Example:
Reading 12.88 Volts
Uncertainty is 0.01 Volts
So 12.88 +- 0.01 Volts
Random Uncertainty:
Random fluctuations can affect measurements from reading to reading, for example, some are too big and some are too small.
E.g Timing with a stopwatch as sometimes it starts early and sometimes it starts late.
To work out the random uncertainty you have to repeat the experiment a few times.
Random Uncertainty = (Max Reading - Min Reading) / Number of readings
Example:
Times for a ball to run down a slope:
Times: 1.5, 1.1, 1.6, 1.4 Seconds
Random Uncertainty = (1.6 - 1.1)/ 4
= 0.5/4
= 0.125
= 0.1 to 1dp as original figures are only 1 dp.
Answer = (1.5 + 1.1 + 1.6 + 1.4) / 4 (MEAN AVERAGE)
= 1.4 Seconds
Final Answer: 1.4 +- 0.1 Seconds
Comparison of Uncertainties:
When you have multiple uncertainties you must convert them to percentages by using the formula:
Percent Uncertainty = Uncertainty / Value * 100
and then you take the highest percentage uncertainty as the uncertainty and convert it back to a number.
So say we have:
Distance = 1.5 +- 0.1 Metres (1 Metre = ~3 1/3 Feet)
Time = 1.2 +- 0.1 Seconds
Calculate Speed With Uncertainties:
Distance Uncertainty = 0.1/1.5 = 6.67% (2 Decimal Places)
Time Uncertainty = 0.1 / 1.2 = 8.33% (2Dp)
So Final Uncertainty = 8.33%
v = d/t or s = d/t
v = 1.5/1.2
v = 1.25 Ms^-1 or 1.25 M/s (Metres Per Second)
v = 1.25 +- 8.33% M/s
Uncertainty = 1.25 * 8.33%
Uncertainty = 0.104125
Uncertainty = 0.10 to 2dp
v = 1.25 +- 0.10 M/s