2nd class

Determining the Range of Uncertainty

1) Analogue scales (rulers,thermometers meters with needles)

± half of the smallest division

2) Digital scales

± the smallest division on the readout

If the digital scale reads 5.052g, then the uncertainty would be ± 0.001g

10

40

30

20

50

Since the smallest division on the cylinder is 10 ml, the reading would be 32 ± 5 ml

Absolute Uncertainty- has units of the measurement

Absolute vs % UncertaintyAbsolute Uncertainty 0.25 ± 0.005 g 100.00 ± 0.05 g

Absolute Uncertainty

%05.0100100

05.0

%210025.0

005.0

100tmeasuremen

yuncertaint absoluteyuncertaint percentage

%

%

=xΔ

=xΔ

=

Or we can write

0.25 g ± 2 % --------- Larger % Uncertainty ------ Less Precise

100.00 g ± 0.05 % --------- Smaller % Uncertainty ------ More Precise

Addition / Subtraction of Uncertainties

● The type of uncertainty seen so far is an absolute uncertainty.– This is often written as Δx if the measurement is x

• If we add or subtract two physical quantities, their maximum uncertainties must be added together

 

 

The mass of block of metal is (11.5 ± 0.5) kg and its volume is (1000 ± 20) cm3. How would you express the density of the metal?

The dimensions of a box are recorded as follows:

Length, l = (5.0 ± 0.2) cm ,Width, b = (4.0 ± 0.1) cm, Height, h = (8.0 ± 0.2) cm

What is the maximum percentage error for the volume of the box?

The diameter of a wire is (0.56 ± 0.01)mm. What is the cross-sectional area of the wire