6.2.1

Limitation of Physical Measurements

Test yourself

Physical Measurement Errors

All measurement has an associated uncertainty. We call this uncertainty "error".

Illustrative background for Measurement modelIllustrative background for Measurement model ?? "content

Measurement model

  • We can model a measurement you make as two parts.
    • The measurement you make is called the "observed value".
    • What value the measurement should be is called the "true value".
  • The uncertainty we have about our measurement is called the "error". So the model is:
    • Observed value = true value + error
Illustrative background for ErrorIllustrative background for Error ?? "content

Error

  • The error in our measurement model is made up of two parts:
    • Random error.
    • Systematic error.
Illustrative background for Measurement model revisitedIllustrative background for Measurement model revisited ?? "content

Measurement model revisited

  • We can now rewrite our measurement model as:
    • Observed value = true value + random error + systematic error
Illustrative background for The model in practiceIllustrative background for The model in practice ?? "content

The model in practice

  • Normally, the model always has a positive error.
  • In practice, we know that the error could make our observed value look larger or smaller than the true value.
  • One example of this is measuring the temperature of a cup of tea.
    • To show our uncertainty, we might say that the tea has a temperature of 95 ± 3oC.
    • This means our true value is likely to be between 92oC and 98oC.

Systematic and Random Errors

A systematic error is an error that follows a set pattern. A random error follows no set pattern.

Illustrative background for Systematic errorIllustrative background for Systematic error ?? "content

Systematic error

  • A systematic error is an error that follows a set pattern.
    • E.g. If you were taking the mass of some flour and forgot to zero your mass balance, all your measurements would be off by a set amount. This type of systematic error is called zero error.
  • It is hard to avoid systematic error.
    • To avoid systematic error, you should use the measuring equipment to measure a known value.
    • This process is called calibration.
Illustrative background for Systematic error cont.Illustrative background for Systematic error cont. ?? "content

Systematic error cont.

  • Let's say you knew a mass of flour was 500g, and the mass balance read differently, you would then know you have a systematic error.
  • You would also have an estimate of the size of the systematic error.
  • You can then either subtract this systematic error from all of your incorrect readings or you could redo the experiment with the equipment correctly calibrated.
Illustrative background for Random errorIllustrative background for Random error ?? "content

Random error

  • Random error is error that follows no set pattern.
  • Random error could be due to reading the measuring equipment in different ways.
  • The error could be because the measuring equipment is changing slightly in different ways.
Illustrative background for Random error cont.Illustrative background for Random error cont. ?? "content

Random error cont.

  • If an experiment was carried out a large number of times, we would expect to see these random errors mostly cancel each other out.
  • Doing lots of repeats is the one way to reduce random error.
  • If there was no systematic error, we assume that the observed value we get after lots of repeats is the true value.

Describing Measurements

You will need to know the following terms for describing measurements:

Illustrative background for AccuracyIllustrative background for Accuracy ?? "content

Accuracy

  • Accuracy is how close a measurement is to the correct value for that measurement.
    • This image shows accurate shots at the target.
Illustrative background for PrecisionIllustrative background for Precision ?? "content

Precision

  • The precision of a measurement system refers to how close to each other the repeated measurements are.
    • It is independent of the "true" value of the measurement.
    • This image shows precise (but not accurate) shots at the target.
Illustrative background for RepeatabilityIllustrative background for Repeatability ?? "content

Repeatability

  • A measurement is repeatable if the same person performing the same experiment with the same apparatus gives the same results (within random errors).
Illustrative background for ReproducibilityIllustrative background for Reproducibility ?? "content

Reproducibility

  • A measurement is reproducible if a different person can perform the same experiment with the same apparatus and get the same results (within errors).
Illustrative background for ResolutionIllustrative background for Resolution ?? "content

Resolution

  • The resolution of a measuring instrument describes its maximum precision.
    • A higher resolution TV screen will have a sharper (more detailed) image.
    • A higher resolution telescope will be able to separate points of light more easily than a lower resolution one.

Jump to other topics

1Space, Time & Motion

1.1Motion

1.1.1Motion Basics

1.1.2Graphs of Motion

1.1.3Uniform Acceleration Equations

1.1.4Projectile Motion

1.1.5Bouncing Ball Example

1.2Forces

1.2.1Friction

1.2.2Terminal Speed

1.2.3Newton's Laws

1.2.4Exam-Style Question - Forces

1.2.5End of Topic Test - Newton's Third Law

1.3Momentum & Impulse

1.3.1Momentum

1.3.2Momentum 2

1.3.3End of Topic Test - Newton's Laws & Momentum

1.4Work, Energy & Power

1.4.1Work & Energy

1.4.2Conservation of Energy

1.4.3Power & Efficiency

1.4.4IB Multiple Choice- Work, Energy & Power

2The Particulate Nature of Matter

2.1Thermal Concepts

2.1.1Molecular Kinetic Theory Model

2.1.2Molecular Kinetic Theory Model 2

2.1.3Thermal Energy Transfer

2.1.4Thermal Energy Transfer Experiments

2.1.5Thermal Equilibrium

2.1.6Thermal Conductivity

2.1.7Heat Energy Transfer

2.2Modelling a Gas

2.2.1Ideal Gases

2.2.2Ideal Gases 2

2.2.3End of Topic Test - Thermal Energy & Ideal Gases

2.2.4Exam-Style Question - Ideal Gases

3Wave Behaviour

3.1Oscillations

3.1.1Progressive Waves

3.1.2Simple Harmonic Motion

3.2Travelling Waves

3.2.1Wave Speed & Phase Difference

3.2.2Longitudinal & Transverse Waves

3.2.3Electromagnetic Waves

3.2.4Electromagnetic Waves 2

3.2.5Sound Waves

3.3Wave Characteristics

3.3.1Polarisation

3.4Wave Behaviour

3.4.1Reflection & Absorption

3.4.2Reflection of Light

3.4.3Refraction

3.4.4Refractive index

3.5Standing Waves

3.5.1Standing Waves

3.5.2Standing Waves 2

3.5.3End of Topic Test - Standing Waves

3.5.4IB Multiple Choice - Waves

3.6Simple Harmonic Motion

3.6.1Simple Harmonic Motion

3.6.2Simple Harmonic Systems

3.6.3Energy in Simple Harmonic Motion

3.6.4End of Topic Test - Simple Harmonic Motion

3.6.5End of Topic Test - Simple Harmonic Motion

3.7Single Slit Diffraction

3.7.1Diffraction

3.8Interference

3.8.1Interference

3.8.2Interference 2

3.8.3Diffraction Gratings

3.8.4End of Topic Test - Diffraction

3.9Doppler Effect

3.9.1Doppler Effect

4Fields

4.1Circular Motion

4.1.1Circular Motion

4.1.2Centripetal Force

4.1.3IB Multiple Choice - Circular Motion

4.2Newton's Law of Gravitation

4.2.1Newton's Law

4.2.2Orbits of Planets & Satellites

4.2.3Escape Velocity & Synchronous Orbits

4.2.4End of Topic Test - Gravitational Fields

4.3Fields

4.3.1Fields

4.3.2Gravitational Field Strength

4.3.3Gravitational Potential

4.3.4Electric Field Strength

4.3.5Electrostatic & Gravitational Forces

4.3.6Electric Potential

4.3.7IB Multiple Choice - Gravitational Fields

4.4Fields at Work

4.4.1Radial Field Strength

4.4.2Orbits of Planets & Satellites

4.4.3Escape Velocity & Synchronous Orbits

4.4.4End of Topic Test - Gravitational Fields

4.4.5Uniform Electric Fields

4.4.6IB Multiple Choice - Electric Field & Potential

4.5Electric Fields

4.5.1Electric Charge

4.5.2Conservation of Charge

4.5.3Coulomb's Law

4.5.4Current

4.5.5Potential Difference

4.5.6IB Multiple Choice - Electric Charge

4.6Magnetic Effect of Electric Currents

4.6.1Magnetism

4.6.2Magnetic Field

4.6.3Magnetic Force

4.6.4Moving Charges in a Magnetic Field

4.6.5IB Multiple Choice - Magnetism

4.7Heating Effect of Currents

4.7.1Circuits

4.7.2Resistance

4.7.3Power and Conservation

4.7.4IB Multiple Choice - DC Circuits

4.8Electromagnetic Induction

4.8.1Electromagnetic Induction

4.8.2Electromagnetic Induction 2

4.8.3Magnetic Flux & Flux Linkage

4.8.4End of Topic Test - Electromagnetic Induction

4.9Power Generation & Transmission

4.9.1Alternating Currents

4.9.2Operation of a Transformer

4.10Capacitance

4.10.1Capacitance

4.10.2Parallel Plate Capacitor

4.10.3Energy Stored by a Capacitor

4.10.4Capacitor Discharge

4.10.5Capacitor Charge

4.10.6Magnetic Flux Density

4.10.7End of Topic Test - Capacitance & Flux Density

5Nuclear & Quantum Physics

5.1Discrete Energy & Radioactivity

5.1.1Atomic Spectra

5.1.2Atomic Structure

5.1.3Photons

5.1.4Discrete Energy Levels

5.1.5Alpha, Beta & Gamma Radiation

5.1.6Scientific Practices - Unstable Nuclei

5.1.7Radioactive Decay

5.1.8IB Multiple Choice - Atomic Physics

5.2Nuclear Reactions

5.2.1Mass & Energy

5.2.2Nuclear Fission

5.3The Interaction of Matter with Radiation

5.3.1Particles, Antiparticles & Photons

5.3.2Particle Interactions

5.3.3Classification of Particles

5.3.4Wave-Particle Duality

5.3.5Wave Functions & Probability

5.3.6IB Multiple Choice - Quantum Physics

5.4Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay

5.4.2Nuclear Radius

5.4.3IB Multiple Choice - Nuclear Physics

6Measurements

6.1Measurements & Errors

6.1.1Fundamental Units

6.1.2SI Prefixes, Standard Form & Converting Units

6.1.3End of Topic Test - Units & Prefixes

6.2Uncertainties & Errors

6.2.1Limitation of Physical Measurements

6.2.2Uncertainty

6.2.3Estimation

6.2.4End of Topic Test - Measurements & Errors

6.3Vectors & Scalars

6.3.1Scalars & Vectors

6.3.2Vector Problems

Unlock your full potential with Seneca Premium

  • Unlimited access to 10,000+ open-ended exam questions

  • Mini-mock exams based on your study history

  • Unlock 800+ premium courses & e-books

Get started with Seneca Premium

End of Topic Test - Units & Prefixes

Uncertainty