Measurement

Question 1

Measurement from a ruler

Answer 1

[mm] or [cm]

for a single measurement record 2 values to measure from each side

uncertainty is the first value ± the uncertainty* minus the second value ± the uncertainty*

• the uncertainty is ± the smallest increment of the device

Question 2

Measurement from a vernier caliper

Answer 2

uncertainty is ± 0.1mm

1. Read from scale on top x._ _
2. Read where vernier scale starts _ . x _
3. Read where lines at scales meet _ . _ x
   l = x.xx ± 0.01cm

Question 3

Measurement from micrometer

Answer 3

uncertainty is ± 0.01mm

1. Read from shaft scale x. x _
2. Read where 2 lines meet _ . xx
   l = x. (x + x) x ± 0.01mm

Question 4

Measurement from a digital scale

Answer 4

mass balance will likely measure in g and the uncertainty is ± 1g

Question 5

Measuring time

Answer 5

with multiple measurements the uncertainty is the range divided by 2

with a single measurement or if the range is too small the uncertainty is ± 0.2 seconds

Question 6

Evaluating measurements

Answer 6

Systematic error: results in all values shifting
can have high precision and low accuracy
Random error: results in scattering of fata
can have high accuracy and low precision

Accuracy: How close the data points are to the theoretical value
Precision: How consistent the data points are

Question 7

Uncertainties

Answer 7

Absolute uncertainty:
used for addition and subtraction
∆c = ∆a + ∆b

Percentage uncertainty:
used for division and multiplication
c = a x b
%c = %a + %b

c ± ∆c = ∆c / c x 100 = %c

Powers:
c = a x b^x
%c = %a + x%b

Question 8

Cathode ray ocsilloscope

Answer 8

for measuring waves

Amplitude of wave to be read directly of screen (y value)

x-axis is in divisions

By rotating voltage/current setting you can zoom in and out of the wave on screen, inc from smaller waves

Time-based setting displayed on x-axis (one division per grid box)

voltage / division shows amplitude

Question 9

Data presentation

Answer 9

Values:
for addition and subtraction results must have same d.p as values used

for multiplication and division results must have number of s.f as value with least s.f

Absolute uncertainty in 1 s.f

Percentage uncertainty in either 2 or 3 s.f

Precision:
compare precisions and change more precise value to match less precise value

final value and uncertainty must have same precision

the last s.f in value must be in the same place as the uncertainty