1. Measurement & their errors

Question 1

What are the 6 SI units, and their units?

Answer 1

• 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)

Question 2

What are the prefexis that can be dded before any of the SI units with a multiplier that is greater?

Answer 2

Kilo
Mega
Giga
Tera
Pera

Question 3

What are the prefixes that can be added before any of the SI units with a multiplier smaller than 10

Answer 3

Centi
Milli
Micro
Nano
Pico
Femto

Question 4

Give newtons in SI unit

Answer 4

kgms^-2

Question 5

What are the SI units of voltage?

Answer 5

kgm^(2)s^(-3)A^(-1)

Question 6

What is the relationship between electron volts and joules?

Answer 6

1eV = 1.6x10^(-19)

Question 7

What is the relationship with between kilowatts and joules

Answer 7

2 kW=1000 J/s

Question 8

What is a random error?

Answer 8

affects on precision
- they cause differences in measurements which causes a spread about the mean
- can’t get rid of all random errors

Question 9

How can you reduce random errors?

Answer 9

• 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

Question 10

What is a systematic error?

Answer 10

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

Question 11

How can you reduce systematic error?3

Answer 11

• 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

Question 12

What is a precise measurement?

Answer 12

consistent measurements, they fluctuate slightly about a mean value - this doesn’t indicate the value is accurate

Question 13

What is repeatability?

Answer 13

if the original experimenter can redo the experiment with the same equipment and method then get the same results it is repeatable

Question 14

What does it mean for an experiment to be reproducible?

Answer 14

if the experiment is redone by a different person or with different techniques and equipment and the same results are found, it is reproducible

Question 15

What is the resolution of an experiment?

Answer 15

the smallest change in the quantity being measured that gives a recognisable change in reading

Question 16

What is accuracy

Answer 16

a measurement close to the true value is accurate

Question 17

What is uncertainty?

Answer 17

the uncertainty of a measurement is the bounds in which the accurate value can be expected to lie

Question 18

What is the absolute uncertainty?

Answer 18

uncertainty given as a fixed quantity
e.g. 2±1V

Question 19

What is fractional uncertainty?

Answer 19

uncertainty as a fraction of the measurement
e.e. 7± 3/35 V

Question 20

What is percentage uncertainty?

Answer 20

uncertainty as a percentage of the measurement
2±1.5%

Question 21

How can you reduce percentage or fractional uncertainty?

Answer 21

measuring larger quantities

Question 22

How do you find the uncertainty in a reading?

Answer 22

± half the smallest division
e.g. if reading on a thermometer is 1℃, the uncertainty would be ±0.5℃

Question 23

How do you find the uncertainty in a measurement?

Answer 23

at lease ±1 smallest division

Question 24

How is the uncertainty found on a digital reading?

Answer 24

given values will either
- have the uncertainty quoted
- or assumed to be ± the last sigfig
effected by the resolution of the instument

Question 25

How is the uncertainty measured on repeated data?

Answer 25

uncertainty is half the range (largest - smallest value), shows as mean ± range/2

Question 26

What are some ways you can reduce an uncertainty?

Answer 26

• fixing one end of a ruler as only the uncertainty in one reading is included
• measuring multiple instances

Question 27

How many sig figs should uncertainties be measured too?

Answer 27

the same as the data

Question 28

When do you use the absolute uncertainty?

Answer 28

if the data is being added or subtracted

Question 29

When do you use the percentage uncertainty?

Answer 29

when the data is being multiplied or divided

Question 30

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?

Answer 30

298-273 = 25K
0.5 + 0.5 = 1K
difference = 25±1K

Question 31

If raising to a power what happens with the uncertainty?

Answer 31

multiply percentage uncertainty by power

Question 32

A force of 91±3N is applied to a mass of 7 ±0.2kg, What is the acceleration of the mass?

Answer 32

• 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)

Question 33

The radius of a circle is 5±0.3cm, what is the percentage uncertainty of the area of the circle?

Answer 33

• 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

Question 34

How are uncertainties shown on a graph?

Answer 34

as error bars

Question 35

How can you find the uncertainty using error bars?

Answer 35

• 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

Question 36

What is the equation for percentage uncertainties?

Answer 36

percentage uncertainty = uncertainty/ value x 100

Question 37

What is the equation for the percentage uncertainty using the gradient?

Answer 37

percentage uncertainty = (best gradient-worst gradient)/best gradient x 100

Question 38

What’s the equation for the percentage uncertainty when the best and worst LOB have different y intercepts

Answer 38

percentage uncertainty = (best y intercept - worst y intercept)/ best y intercept x 100

Question 39

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

Answer 39

percentage uncertainty (max gradient - min gradient)/2 x 100

Question 40

What is the order of magnitude?

Answer 40

powers of ten which describe the size of an object, and which can also be used to compare the sizes of objects

Question 41

What is estimation?

Answer 41

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.