1.2.4

Limitation of Physical Measurements

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Physical Measurement Errors

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

Measurement model

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
Error

Error

  • The error in our measurement model is made up of two parts:
    • Random error.
    • Systematic error.
Measurement model revisited

Measurement model revisited

  • We can now rewrite our measurement model as:
    • Observed value = true value + random error + systematic error
The model in practice

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.

Systematic error

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.
Systematic error cont.

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.
Random error

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.
Random error cont.

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:

Accuracy

Accuracy

  • Accuracy is how close a measurement is to the correct value for that measurement.
    • This image shows accurate shots at the target.
Precision

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.
Repeatability

Repeatability

  • A measurement is repeatable if the same person performing the same experiment with the same apparatus gives the same results (within random errors).
Reproducibility

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).
Resolution

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
1

Physical Quantities & Units

1.1

Physical Quantities & Units

1.1.1Use of SI Units1.1.2SI Prefixes, Standard Form & Converting Units1.1.3End of Topic Test - Units & Prefixes1.1.4Avogadro's Constant1.1.5Scalars & Vectors
1.2

Errors & Uncertainty

1.2.1Measuring Length, Time & Volume1.2.2Measuring Temperature1.2.3Circuit Measurements1.2.4Limitation of Physical Measurements1.2.5Uncertainty1.2.6Estimation1.2.7Displaying Data1.2.8End of Topic Test - Measurements & Errors
2

Kinematics

2.1

Equations of Motion

2.1.1Motion in a Straight Line2.1.2Graphs of Motion2.1.3Bouncing Ball Example2.1.4End of Topic Test - Motion in a Straight Line2.1.5Acceleration Due to Gravity
3

Dynamics

3.1

Momentum & Newton's Laws of Motion

3.1.1Mass & Inertia3.1.2Newton's Laws3.1.3Momentum3.1.4End of Topic Test - Newton's Laws & Momentum3.1.5A-A* (AO3/4) - Newton's Third Law
3.2

Non-Uniform Motion

3.2.1Projectile Motion
3.3

Linear Momentum & Conservation

3.3.1Conservation of Momentum
4

Force, Density & Pressure

4.1

Force, Density & Pressure

4.1.1Fields4.1.2Force in Uniform Fields4.1.3Friction4.1.4Buoyancy4.1.5Terminal Speed4.1.6End of Topic Test - Acceleration Due to Gravity4.1.7Centre of Mass4.1.8Forces & Equilibrium4.1.9End of Topic Test - Scalars & Vectors4.1.10Moments4.1.11End of Topic Test - Moments & Centre of Mass4.1.12Density4.1.13Pressure
5

Work, Energy & Power

5.1

Work, Energy & Power

5.1.1Work & Energy5.1.2Power & Efficiency5.1.3Conservation of Energy5.1.4End of Topic Test - Work, Energy & Power
5.2

Gravitational Fields

5.2.1Newton's Law5.2.2Gravitational Field Strength5.2.3Gravitational Potential
6

Deformation of Solids

6.1

Materials

6.1.1Bulk Properties of Solids6.1.2Energy in Materials6.1.3Young Modulus6.1.4End of Topic Test - Materials
7

Waves

7.1

Simple Harmonic Motion

7.1.1Simple Harmonic Motion7.1.2Simple Harmonic Systems7.1.3Energy in Simple Harmonic Motion7.1.4Resonance7.1.5End of Topic Test - Simple Harmonic Motion7.1.6A-A* (AO3/4) - Simple Harmonic Motion7.1.7End of Topic Test - Gravitational Fields
7.2

Waves

7.2.1Progressive Waves7.2.2Intensity of Waves7.2.3Wave Speed & Phase Difference7.2.4Longitudinal & Transverse Waves7.2.5End of Topic Test - Progressive Waves7.2.6Electromagnetic Waves7.2.7Doppler Effect7.2.8Sound Waves7.2.9Measuring Sound Waves7.2.10End of Topic Test - Waves7.2.11Ultrasound Imaging7.2.12Ultrasound Imaging 2
8

Superposition

8.1

Superposition

8.1.1Stationary Waves8.1.2Stationary Waves 28.1.3End of Topic Test - Stationary Waves8.1.4A-A* (AO3/4) - Stationary Waves8.1.5Interference8.1.6Interference 28.1.7End of Topic Test - Interference8.1.8Diffraction8.1.9Diffraction Gratings8.1.10End of Topic Test - Diffraction
9

Thermal Physics

9.1

Circular Motion

9.1.1Circular Motion9.1.2Circular Motion 29.1.3End of Topic Test - Circular Motion
9.2

Thermal Physics

9.2.1Temperature9.2.2Measuring Temperature9.2.3Ideal Gas Law9.2.4Ideal Gases9.2.5Boyle's Law & Charles' Law9.2.6Molecular Kinetic Theory Model9.2.7Molecular Kinetic Theory Model 29.2.8Thermal Energy Transfer9.2.9Thermal Energy Transfer Experiments9.2.10End of Topic Test - Thermal Energy & Ideal Gases9.2.11First Law of Thermodynamics
10

Communication

10.1

Communication Channels

10.1.1Communication Channels10.1.2Modulation10.1.3Attenuation
10.2

Digital Communication

10.2.1Digital & Analogue Signals10.2.2Representing Sound
11

Electric Fields

11.1

Electric Fields

11.1.1Coulomb's Law11.1.2Electric Field Strength11.1.3Electric Field Strength 211.1.4Electric Potential11.1.5End of Topic Test - Electric Fields11.1.6A-A* (AO3/4) - Electric and Gravitational Field
11.2

Capacitance

11.2.1Capacitance11.2.2Parallel Plate Capacitor11.2.3Energy Stored by a Capacitor11.2.4Capacitor Discharge11.2.5Capacitor Charge
12

Current Electricity

12.1

Current Electricity

12.1.1Basics of Electricity12.1.2Mean Drift Velocity12.1.3Current-Voltage Characteristics12.1.4End of Topic Test - Basics of Electricity12.1.5Resistivity12.1.6End of Topic Test - Resistivity & Superconductors12.1.7Power and Conservation12.1.8Microphones12.1.9Components12.1.10Relays12.1.11Strain Gauges
12.2

DC Circuits

12.2.1Circuits12.2.2Potential Divider12.2.3Emf & Internal Resistance12.2.4End of Topic Test - Power & Potential
13

Magnetic Fields

13.1

Magnetic Fields

13.1.1Magnetic Flux Density13.1.2End of Topic Test - Capacitance & Flux Density13.1.3Moving Charges in a Magnetic Field13.1.4Magnetic Flux & Flux Linkage13.1.5Electromagnetic Induction13.1.6Electromagnetic Induction 213.1.7Magnetic Flux Density13.1.8Magnetic Resonance Scanning
13.2

Alternating Currents

13.2.1Alternating Currents13.2.2Operation of a Transformer13.2.3End of Topic Test - Electromagnetic Induction & AC13.2.4Rectification
14

Modern Physics

14.1

Quantum Physics

14.1.1The Photoelectric Effect14.1.2The Photoelectric Effect Explanation14.1.3End of Topic Test - The Photoelectric Effect14.1.4Collisions of Electrons with Atoms14.1.5Energy Levels & Photon Emission14.1.6Wave-Particle Duality14.1.7End of Topic Test - Absorption & Emission14.1.8Band Theory14.1.9Diagnostic X-Rays14.1.10X-Ray Image Processing14.1.11Absorption of X-Rays14.1.12CT Scanners
14.2

Nuclear Physics

14.2.1Rutherford Scattering14.2.2Atomic Model14.2.3Isotopes14.2.4Stable & Unstable Nuclei14.2.5A-A* (AO3/4) - Stable & Unstable Nuclei14.2.6Alpha & Beta Radiation14.2.7Gamma Radiation14.2.8Particles, Antiparticles & Photons14.2.9Quarks & Antiquarks14.2.10Particle Interactions14.2.11Radioactive Decay14.2.12Half Life14.2.13End of Topic Test - Radioactivity14.2.14Nuclear Instability14.2.15Mass & Energy14.2.16Binding Energy14.2.17A-A* (AO3/4) - Nuclear Fusion

Practice questions on Limitation of Physical Measurements

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    A measurement of the length of a table is 140 cm ± 5 cm. What is the maximum possible true length of the table?Multiple choice
  2. 2
    Which statements are true about errors?True / false
  3. 3
    What do we call an error that follows a set pattern?Multiple choice
  4. 4
    What do we call an error that does NOT follow a pattern?Multiple choice
  5. 5
    Two types of error:Fill in the list
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Circuit Measurements

Uncertainty