2.1.4
Limitation of Physical Measurements
Physical Measurement Errors
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.
 - Edited-min,h_400,q_80,w_640.png)
 - Edited-min,h_400,q_80,w_640.png)
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
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.
,h_400,q_80,w_640.png)
,h_400,q_80,w_640.png)
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
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.
1Physical Quantities & Units
2Measurement Techniques
3Kinematics
4Dynamics
4.1Momentum & Newton's Laws of Motion
4.2Non-Uniform Motion
4.3Linear Momentum & Conservation
4.4Force, Density & Pressure
4.4.1Fields
4.4.2Force in Uniform Fields
4.4.3Friction
4.4.4Buoyancy
4.4.5Terminal Speed
4.4.6End of Topic Test - Acceleration Due to Gravity
4.4.7Centre of Mass
4.4.8Forces & Equilibrium
4.4.9End of Topic Test - Scalars & Vectors
4.4.10Moments
4.4.11End of Topic Test - Moments & Centre of Mass
4.4.12Density
4.4.13Pressure
4.5Work, Energy & Power
5Gravitational Fields
5.1Gravitational Fields (A2 only)
6Deformation of Solids
7Thermal Physics
7.1Thermal Physics
7.1.1Temperature
7.1.2Measuring Temperature
7.1.3Ideal Gas Law
7.1.4Ideal Gases
7.1.5Boyle's Law & Charles' Law
7.1.6Molecular Kinetic Theory Model
7.1.7Molecular Kinetic Theory Model 2
7.1.8Thermal Energy Transfer
7.1.9Thermal Energy Transfer Experiments
7.1.10End of Topic Test - Thermal Energy & Ideal Gases
7.1.11First Law of Thermodynamics
8Oscillations
8.1Simple Harmonic Motion
8.2Waves
8.2.1Progressive Waves
8.2.2Intensity of Waves
8.2.3Wave Speed & Phase Difference
8.2.4Longitudinal & Transverse Waves
8.2.5End of Topic Test - Progressive Waves
8.2.6Electromagnetic Waves
8.2.7Doppler Effect
8.2.8Sound Waves
8.2.9Measuring Sound Waves
8.2.10End of Topic Test - Waves
8.2.11Ultrasound Imaging
8.2.12Ultrasound Imaging 2
9Communication
9.1Communication Channels
9.2Digital Communication
10Electric Fields
10.1Electric Fields
11Current Electricity
11.1Current Electricity
11.1.1Basics of Electricity
11.1.2Mean Drift Velocity
11.1.3Current-Voltage Characteristics
11.1.4End of Topic Test - Basics of Electricity
11.1.5Resistivity
11.1.6End of Topic Test - Resistivity & Superconductors
11.1.7Power and Conservation
11.1.8Microphones
11.1.9Components
11.1.10Relays
11.1.11Strain Gauges
12Magnetic Fields
12.1Magnetic Fields
13Modern Physics
13.1Quantum Physics
13.1.1The Photoelectric Effect
13.1.2The Photoelectric Effect Explanation
13.1.3End of Topic Test - The Photoelectric Effect
13.1.4Collisions of Electrons with Atoms
13.1.5Energy Levels & Photon Emission
13.1.6Wave-Particle Duality
13.1.7End of Topic Test - Absorption & Emission
13.1.8Band Theory
13.1.9Diagnostic X-Rays
13.1.10X-Ray Image Processing
13.1.11Absorption of X-Rays
13.1.12CT Scanners
13.2Nuclear Physics
13.2.1Rutherford Scattering
13.2.2Atomic Model
13.2.3Isotopes
13.2.4Stable & Unstable Nuclei
13.2.5A-A* (AO3/4) - Stable & Unstable Nuclei
13.2.6Alpha & Beta Radiation
13.2.7Gamma Radiation
13.2.8Particles, Antiparticles & Photons
13.2.9Quarks & Antiquarks
13.2.10Particle Interactions
13.2.11Radioactive Decay
13.2.12Half Life
13.2.13End of Topic Test - Radioactivity
13.2.14Nuclear Instability
13.2.15Mass & Energy
13.2.16Binding Energy
13.2.17A-A* (AO3/4) - Nuclear Fusion
Jump to other topics
1Physical Quantities & Units
2Measurement Techniques
3Kinematics
4Dynamics
4.1Momentum & Newton's Laws of Motion
4.2Non-Uniform Motion
4.3Linear Momentum & Conservation
4.4Force, Density & Pressure
4.4.1Fields
4.4.2Force in Uniform Fields
4.4.3Friction
4.4.4Buoyancy
4.4.5Terminal Speed
4.4.6End of Topic Test - Acceleration Due to Gravity
4.4.7Centre of Mass
4.4.8Forces & Equilibrium
4.4.9End of Topic Test - Scalars & Vectors
4.4.10Moments
4.4.11End of Topic Test - Moments & Centre of Mass
4.4.12Density
4.4.13Pressure
4.5Work, Energy & Power
5Gravitational Fields
5.1Gravitational Fields (A2 only)
6Deformation of Solids
7Thermal Physics
7.1Thermal Physics
7.1.1Temperature
7.1.2Measuring Temperature
7.1.3Ideal Gas Law
7.1.4Ideal Gases
7.1.5Boyle's Law & Charles' Law
7.1.6Molecular Kinetic Theory Model
7.1.7Molecular Kinetic Theory Model 2
7.1.8Thermal Energy Transfer
7.1.9Thermal Energy Transfer Experiments
7.1.10End of Topic Test - Thermal Energy & Ideal Gases
7.1.11First Law of Thermodynamics
8Oscillations
8.1Simple Harmonic Motion
8.2Waves
8.2.1Progressive Waves
8.2.2Intensity of Waves
8.2.3Wave Speed & Phase Difference
8.2.4Longitudinal & Transverse Waves
8.2.5End of Topic Test - Progressive Waves
8.2.6Electromagnetic Waves
8.2.7Doppler Effect
8.2.8Sound Waves
8.2.9Measuring Sound Waves
8.2.10End of Topic Test - Waves
8.2.11Ultrasound Imaging
8.2.12Ultrasound Imaging 2
9Communication
9.1Communication Channels
9.2Digital Communication
10Electric Fields
10.1Electric Fields
11Current Electricity
11.1Current Electricity
11.1.1Basics of Electricity
11.1.2Mean Drift Velocity
11.1.3Current-Voltage Characteristics
11.1.4End of Topic Test - Basics of Electricity
11.1.5Resistivity
11.1.6End of Topic Test - Resistivity & Superconductors
11.1.7Power and Conservation
11.1.8Microphones
11.1.9Components
11.1.10Relays
11.1.11Strain Gauges
12Magnetic Fields
12.1Magnetic Fields
13Modern Physics
13.1Quantum Physics
13.1.1The Photoelectric Effect
13.1.2The Photoelectric Effect Explanation
13.1.3End of Topic Test - The Photoelectric Effect
13.1.4Collisions of Electrons with Atoms
13.1.5Energy Levels & Photon Emission
13.1.6Wave-Particle Duality
13.1.7End of Topic Test - Absorption & Emission
13.1.8Band Theory
13.1.9Diagnostic X-Rays
13.1.10X-Ray Image Processing
13.1.11Absorption of X-Rays
13.1.12CT Scanners
13.2Nuclear Physics
13.2.1Rutherford Scattering
13.2.2Atomic Model
13.2.3Isotopes
13.2.4Stable & Unstable Nuclei
13.2.5A-A* (AO3/4) - Stable & Unstable Nuclei
13.2.6Alpha & Beta Radiation
13.2.7Gamma Radiation
13.2.8Particles, Antiparticles & Photons
13.2.9Quarks & Antiquarks
13.2.10Particle Interactions
13.2.11Radioactive Decay
13.2.12Half Life
13.2.13End of Topic Test - Radioactivity
13.2.14Nuclear Instability
13.2.15Mass & Energy
13.2.16Binding Energy
13.2.17A-A* (AO3/4) - Nuclear Fusion
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