Physics Experiment Investigation Validation

Absolute Uncertainty

• digital readings → uncertainty = ➕➖ smallest increment

• Analogue readings → half of the smallest scale e.g. 1.6 ➕➖ 0.25 cm

Uncertainties in averages

• if there are multiple measurements → calculate an average

• Your uncertainty becomes half the differences between the highest and lowest values in the average calculations

• Average = (1.3+1.5+1.0)/2 = 1.25

• Uncertainty = (1.5-1.0)/2 = 0.25

• therefore, 1.27➕➖ 0.25

• *If there is a choice, such as between measurement uncertainty and an average uncertainty, choose the greater of the two (ie bigger number)

Percentage Uncertainty

• Examples of absolute uncertainty

  • r=0/12 ➕➖ 0.01 m

  • uncertainty is in the same units of measurements

• %uncertainty = uncertainty/measurement x 100%

• if number increases by factor of 10, uncertainty decreases by a factor of 10

Uncertainty in calculations - measurements are added or subtracted

add absolute uncertainties

• x1 = 1.4➕➖0.1 cm

• x2 = 0.7 ➕➖0.2cm

• x3 (combined) = 2.1➕➖0.3cm

Uncertainty in calculations - measurements are multiplied/divided

add percentage uncertainties

1. 25.0➕➖0.5 cm (2%) = L

2. 10.0 ➕➖0.5cm (5%) = w

A = lw

= 25.0×10 = 250 cm²

%:

Percentage uncertainty → 7%

Uncertainty in calculations - measurements are raised to a power, you multiply the power by the percentage uncertainty

you multiply the power by the percentage uncertainty

• v = 2.54 ➕➖4%

• v² = 2.54²

• v² = 6.45 ➕➖ 8%

Percentage Error

• how far off the mark you were

• % error = ((measured - theoretical)/theoretical ) x100%
  If % error is smaller than uncertainty that is GOOD