Measurements and their errors

Question 1

combing uncertainties: multiplying/dividing data

Answer 1

ADD PERCENTAGE uncertainties

Question 2

combing uncertainties: adding/subtracting data

Answer 2

ADD ABSOLUTE uncertainties

Question 3

combing uncertainties: raising to a power

Answer 3

MULTIPLY PERCENTAGE uncertainty by the power

Question 4

define precision

Answer 4

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

Question 5

define accuracy

Answer 5

A measurement close to the true value is accurate

Question 6

define repeatability

Answer 6

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

Question 7

define reproducability

Answer 7

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 8

define resolution

Answer 8

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

For example, the resolution of a wristwatch is 1 s, whereas the resolution of a digital stop-clock is typically 10 ms (0.01 s)

Question 9

Fento

Answer 9

10^-15

Question 10

Giga

Answer 10

10^9

Question 11

how are uncertainties shown on a graph

Answer 11

error bars

e.g. if uncertainty is 5mm, then 5 squares of error bars on either side of the point

line of best fit should go thru all error bars

Question 12

how can SI units of quantities be derived

Answer 12

using their equations

e.g. F = ma ———–> kgms-2 which is N

Question 13

how many sig figs to give uncertainty to

Answer 13

same number of sig figs as the data

Question 14

how to find uncertainty in y intercepts

Answer 14

best y-intercept - worst y-intercept (using libnes of best and worst fit)

Question 15

how to find uncertainty of a gradient

Answer 15

To calculate the uncertainty in a gradient, two lines of best fit should be drawn on the graph:
* The ‘best’ line of best fit, which passes as close to the points as possible
* The ‘worst’ line of best fit, either the steepest possible or the shallowest possible line which fits within all the error bars

the uncertainty is the difference between gradients

Question 16

how to reduce random errors

Answer 16

take at least 3 repeats and calculate a mean - allows you to identify anomalies

use computers/data loggers to reduce human error

use appropriate equipment e.g. higher resolution

Question 17

how to reduce systematic error

Answer 17

calibrate apparatus by measuring a known value - can identify innacuraccies

if radiation experiement - correct for background radiation

read at eye level to reduce parallax error

use controls in experiments

Question 18

how to reduce uncertainty

Answer 18

reduce no. readings in a measurement e.g. fixing one end of a ruler

measuring multiple instances, e.g. taking 10 and dividing by 10 to find 1 (uncertainty is also divided by 10)

Question 19

mega

Answer 19

M 10^6

Question 20

micro

Answer 20

mu 10^-6

Question 21

Nano

Answer 21

n 10^-9

Question 22

Pico

Answer 22

p 10^-12

Question 23

Tera

Answer 23

T 10^12

Question 24

Peta

Answer 24

P 10^15

Question 25

kilo

Answer 25

K 10^3

Question 26

deca

Answer 26

da 10^1

Question 27

hecto

Answer 27

h 10^2

Question 28

deci

Answer 28

d 10^-1

Question 29

milli

Answer 29

m 10^-3

Question 30

centi

Answer 30

c 10^-2

Question 31

uncertainty

Answer 31

0.5 * range % uncertainty = uncertainty / mean * 100 if all data is the same the uncertainty is the resolution

Question 32

uncertainty for digital readings

Answer 32

+ or - the last significant digit

Question 33

what are systematic errors

Answer 33

cause all results to be too high/low by the same maount each time e.g. zero error or parallax error usually occur due to apparatus or faults in method

Question 34

what are the SI units

Answer 34

fundamental units: Mass (m): kg (kilograms) Length (I): m (metres) Time (t): s (seconds) Amount of substance (n): mol (moles) Temperature (t): K (kelvin) Electric current (I): A (amperes)

Question 35

what do random errors effect

Answer 35

Random errors cause unpredictable fluctuations in an instrument’s readings as a result of uncontrollable factors, such as environmental conditions This affects the precision of the measurements taken, causing a wider spread of results about the mean value

Question 36

what do systematic errors effect

Answer 36

* Systematic errors arise from the use of faulty instruments used or from flaws in the experimental method * This type of error is repeated consistently every time the instrument is used or the method is followed, which affects the accuracy of all readings obtained

Question 37

Zero error

Answer 37

This is a type of systematic error which occurs when an instrument gives a reading when the true reading is zero. This introduces a fixed error into readings which must be accounted for when the results are recorded

Question 38

what is uncertainty

Answer 38

The uncertainty is a range of values around a measurement within which the true value is expected to lie, and is an estimate.

Question 39

uncertainties can be represented in 3 ways

Answer 39

Absolute Uncertainty: where uncertainty is given as a fixed quantity Fractional Uncertainty: where uncertainty is given as a fraction of the measurement Percentage Uncertainty: where uncertainty is given as a percentage of the measurement

Question 40

How to find uncertainties in different situations

Answer 40

* The uncertainty in a reading: ± half the smallest division * The uncertainty in a measurement: at least ±1 smallest division * The uncertainty in repeated data: half the range i.e. ± ½ (largest - smallest value) * The uncertainty in digital readings: ± the last significant digit unless otherwise quoted

Question 41

1 kW h =

Answer 41

1 kW h = 3600 kW s (since 1 hour = 3600 s) 3600 kW s = 3 600 000 W s (since 1 kW = 1000 W) 3 600 000 W s = 3 600 000 J = 3.6 MJ (since power = energy / time or 1 W = 1 J s–1)

Question 42

Orders of Magnitude of of 3 × 10^8

Answer 42

10^8