1. Measurement & their errors Flashcards
What are the 6 SI units, and their units?
- Mass (m): kg (kilograms
- Length (l): m (metres)
- Time (t): s (seconds)
- Amount of substance (n): mol (moles
- Temperature (t): K (kelvin)
- Elective current (I): A (amperes)
What are the prefexis that can be dded before any of the SI units with a multiplier that is greater?
Kilo
Mega
Giga
Tera
Pera
What are the prefixes that can be added before any of the SI units with a multiplier smaller than 10
Centi
Milli
Micro
Nano
Pico
Femto
Give newtons in SI unit
kgms^-2
What are the SI units of voltage?
kgm^(2)s^(-3)A^(-1)
What is the relationship between electron volts and joules?
1eV = 1.6x10^(-19)
What is the relationship with between kilowatts and joules
2 kW=1000 J/s
What is a random error?
affects on precision
- they cause differences in measurements which causes a spread about the mean
- can’t get rid of all random errors
How can you reduce random errors?
- take 3 repeats and calculate a mean, also allows anomalies to be identified
- use computers to reduce human error and enable smaller intervals
- use appropriate equipment
What is a systematic error?
affects on accuracy
- can occur dur to apparatus or faults in the experimental method
- systematic errors cause results to be too high or too low by the same amount each time
How can you reduce systematic error?3
- calibrating apparatus by measuring a known value, if the reading is inaccurate then the systematic error is easily identified
- in radiation experiments correct for background radiation by measuring it beforehand and excluding it from final results
- read a meniscus at eye level and use controls in an experiment
What is a precise measurement?
consistent measurements, they fluctuate slightly about a mean value - this doesn’t indicate the value is accurate
What is repeatability?
if the original experimenter can redo the experiment with the same equipment and method then get the same results it is repeatable
What does it mean for an experiment to be reproducible?
if the experiment is redone by a different person or with different techniques and equipment and the same results are found, it is reproducible
What is the resolution of an experiment?
the smallest change in the quantity being measured that gives a recognisable change in reading
What is accuracy
a measurement close to the true value is accurate
What is uncertainty?
the uncertainty of a measurement is the bounds in which the accurate value can be expected to lie
What is the absolute uncertainty?
uncertainty given as a fixed quantity
e.g. 2±1V
What is fractional uncertainty?
uncertainty as a fraction of the measurement
e.e. 7± 3/35 V
What is percentage uncertainty?
uncertainty as a percentage of the measurement
2±1.5%
How can you reduce percentage or fractional uncertainty?
measuring larger quantities
How do you find the uncertainty in a reading?
± half the smallest division
e.g. if reading on a thermometer is 1℃, the uncertainty would be ±0.5℃
How do you find the uncertainty in a measurement?
at lease ±1 smallest division
How is the uncertainty found on a digital reading?
given values will either
- have the uncertainty quoted
- or assumed to be ± the last sigfig
effected by the resolution of the instument
How is the uncertainty measured on repeated data?
uncertainty is half the range (largest - smallest value), shows as mean ± range/2
What are some ways you can reduce an uncertainty?
- fixing one end of a ruler as only the uncertainty in one reading is included
- measuring multiple instances
How many sig figs should uncertainties be measured too?
the same as the data
When do you use the absolute uncertainty?
if the data is being added or subtracted
When do you use the percentage uncertainty?
when the data is being multiplied or divided
A thermometer with an uncertainty of ±0.5K shows the temp of water falling from 298±0.5K to 273±0.5K, what is the difference in temperature?
298-273 = 25K
0.5 + 0.5 = 1K
difference = 25±1K
If raising to a power what happens with the uncertainty?
multiply percentage uncertainty by power
A force of 91±3N is applied to a mass of 7 ±0.2kg, What is the acceleration of the mass?
- a=F/m =91/7 =13m s^(−2)
- percentage uncertainty = uncertainty/value times100
- (3/91 x 100) + (0.2/7 x 100) = 3.3% +2.9% = 6.2%
- so a= 13±6.2%m/s^2
- 6.2% of 13 is 0.8
- a= 13±0.8ms^(-2)
The radius of a circle is 5±0.3cm, what is the percentage uncertainty of the area of the circle?
- area = π x 25 = 78.5cm^2
- area = πr^2
- % uncertainty in radius = 0.3/5 x 100= 6%
- % uncertainty in area = 6 x 2 (2 being from the square) = 12%
- 78.5 ± 12% cm^2
How are uncertainties shown on a graph?
as error bars
How can you find the uncertainty using error bars?
- using error bars to draw a ling of best fit and worst fit.
- the lines must go through all of the error bars
- calculate the gradient of the line of best and worst fit, uncertainty is difference between the best and worst gradients
What is the equation for percentage uncertainties?
percentage uncertainty = uncertainty/ value x 100
What is the equation for the percentage uncertainty using the gradient?
percentage uncertainty = (best gradient-worst gradient)/best gradient x 100
What’s the equation for the percentage uncertainty when the best and worst LOB have different y intercepts
percentage uncertainty = (best y intercept - worst y intercept)/ best y intercept x 100
What’s the equation of the percentage uncertainty when the average of the two maximum and minimum lines can be used to calculate the percentage uncertainty
percentage uncertainty (max gradient - min gradient)/2 x 100
What is the order of magnitude?
powers of ten which describe the size of an object, and which can also be used to compare the sizes of objects
What is estimation?
a skills used to approximate values of physical quantities in order to make comparisons, or to check if a value they’ve calculated is reasonable.
