Uncertainty

Question 1

The uncertainty in a measurement using a particular instrument is

Answer 1

plus or minus half of the smallest division or greater. For example, a temperature measured with a thermometer is likely to have an uncertainty of ±0.5 °C if the graduations are 1 °C apart.

Question 2

If measurements are repeated, the uncertainty can be calculated by

Answer 2

finding half the range of the measured values.

Question 3

The percentage uncertainty in a measurement can be calculated using:

Answer 3

uncertainty/value x 100%

Question 4

The percentage uncertainty in a repeated measurement can be calculated using:

Answer 4

uncertainty/mean value x 100%

Question 5

Finding uncertainty when adding or subtracting values

Answer 5

Add the absolute uncertainties Δa = Δb + Δc Absolute uncertainties (denoted by Δ) have the same units as the quantity.

Question 6

Finding uncertainty when multiplying or dividing values

Answer 6

Add the percentage uncertainties εa = εb + εc Percentage uncertainties (denoted by ε) have no units.

Question 7

Object distance, u = (5.0 ± 0.1) cm Image distance, v = (7.2 ± 0.1) cm Find the difference in the distances and the uncertainty

Answer 7

Difference (v – u) = (2.2 ± 0.2) cm

Question 8

Power = voltage*current Voltage = (15.20 ± 0.1) V Current = (0.51 ± 0.01) A Find the uncertainty in the power

Answer 8

Voltage = (15.20 ± 0.1) V Current = (0.51 ± 0.01) A Percentage uncertainty in voltage = 0.7% Percentage uncertainty in current = 1.96 % Power = Voltage x current = 7.75 W Percentage uncertainty in power = 2.66 % Absolute uncertainty in power = ± 0.21 W

Question 9

Density = mass/volume Mass of object = (30.2 ± 0.1) g Volume of object = (18.0 ± 0.5) cm3 Find the uncertainty in the density

Answer 9

Mass of object = (30.2 ± 0.1) g Volume of object = (18.0 ± 0.5) cm3 Percentage uncertainty in mass of object = 0.3 % Percentage uncertainty in volume = 2.8 % Density = 30.2 = 1.68 gcm-3 18.0 Percentage uncertainty in density = 3.1 % Absolute uncertainty in density = + 0.05 gcm-3

Question 10

Uncertainty in graphs

Answer 10

|gradient of line of best fit - gradient of steepest line of best fit| / best gradient x 100%

Question 11

Uncertainty =

Answer 11

resolution/2measurement *100% = absolute uncertainty/ measurement * 100%

Question 12

micrometer gap=

Answer 12

measurement needed in mm

Question 13

move wire closer to scale on ruler to avoid

Answer 13

parallex error

Question 14

Unit

Symbol

Power

Tera

T

Giga

G

Mega

M

Kilo

k

Centi

c

Milli

m

Micro

μ

Nano

n

Pico

p

femto

f

Answer 14

Unit

Symbol

Power

Tera

T

10^12

Giga

G

10^9

Mega

M

10^6

Kilo

k

10^3

Centi

c

10^−2

Milli

m

10^−3

Micro

μ

10^−6

Nano

n

10^−9

Pico

p

10^−12

femto

f

10^−15

Question 15

Combination

Operation

Example

Adding or subtracting values

a = b + c

Multiplying values a = b + c

Dividing values a = b/c

Percentage uncertainties (denoted by ε) have no units.

Power rules a = b^c

Answer 15

Combination

Operation

Example

Adding or subtracting values

a = b + c

Add the absolute uncertainties

Δa = Δb + Δc

Absolute uncertainties (denoted by Δ) have the same units as the quantity.

Multiplying values a = b + c

Dividing values a = b/c

Percentage uncertainties (denoted by ε) have no units.

Add the percentage uncertainties

εa = εb + εc

When you multiply or divide several measurements together, find the percentage uncertainties in each value (uncertainty/value x 100) and add together the percentage uncertainties to find the percentage uncertainty in the final sum – using this total percentage uncertainty, find the actual uncertainty in the total sum.

Power rules a = b^c

Multiply the percentage uncertainty by the power

εa = c × εb

Radius of circle = (6.0 ± 0.1) cm

Percentage uncertainty in radius = 1.6 %

Area of circle = πr² = 20.7 cm²

Percentage uncertainty in area = 3.2 %

Absolute uncertainty = ± 0.7 cm²

(Note – the uncertainty in π is taken to be zero)