UNIT OVERVIEW
Practical Skills in Physics II
Unit 6 assesses practical knowledge and understanding developed while studying Units 4 and 5. The focus is not simply on carrying out an experiment, but on understanding how experiments are designed, measured, analysed and evaluated.
A good experimental investigation connects a clear aim, suitable variables, reliable measurements, appropriate analysis and a justified conclusion.
Key areas
- Planning experiments
- Experimental techniques
- Measurements and units
- Uncertainties and errors
- Data processing
- Graphs and gradients
- Logarithmic graphs
- Identifying relationships
- Evaluation and improvements
- Drawing conclusions
TOPIC 01
Planning an Experiment
A successful investigation begins with a clear experimental plan. The plan should allow the relationship between relevant variables to be investigated quantitatively.
Experimental Aim
The aim should clearly state what relationship or physical quantity is being investigated.
Example
Investigate how the period of a pendulum depends on its length.
Independent Variable
The independent variable is the quantity deliberately changed by the experimenter.
Dependent Variable
The dependent variable is the quantity measured in response to the independent variable.
Control Variables
Control variables are quantities that should be kept constant so that they do not affect the relationship being investigated.
When planning, always identify what you change, what you measure and what must remain constant.
TOPIC 02
Variables and Experimental Design
The design of an experiment should allow the effect of one variable on another to be investigated fairly.
Range of Values
The independent variable should normally be varied over a sufficiently large range to make the relationship clear.
Repeated Measurements
Repeating measurements can help identify random variation and improve confidence in the measured value.
Mean Measurements
If repeated measurements are appropriate, a mean can be used to represent the measurements.
Anomalous Results
An anomalous result is a measurement that does not fit the general pattern of the other results.
Anomalies should not automatically be removed. There should be a justified reason for treating a result as anomalous.
TOPIC 03
Measurements and Units
Accurate recording of physical quantities is essential in experimental physics.
SI Units
- Length — metre (m)
- Mass — kilogram (kg)
- Time — second (s)
- Current — ampere (A)
- Temperature — kelvin (K)
Prefixes
Experimental measurements may involve a wide range of scales. Values should be converted consistently when required.
- giga = 10⁹
- mega = 10⁶
- kilo = 10³
- centi = 10⁻²
- milli = 10⁻³
- micro = 10⁻⁶
- nano = 10⁻⁹
Always include units in tables, calculations and graphs where appropriate.
TOPIC 04
Uncertainties
Every experimental measurement has some uncertainty. Understanding uncertainty is essential when evaluating experimental results.
Absolute Uncertainty
Absolute uncertainty expresses the uncertainty in the same units as the measured quantity.
Example
A length is measured as 20.0 cm with an uncertainty of ±0.1 cm.
Percentage Uncertainty
Compound Percentage Uncertainty
When quantities are multiplied, divided or raised to powers, percentage uncertainties can be combined according to the mathematical relationship.
Example
If a quantity is calculated from two measured quantities that are multiplied together, the percentage uncertainties are added.
TOPIC 05
Random and Systematic Errors
Random Errors
Random errors cause measurements to vary unpredictably around a value.
Repeating measurements and calculating a mean can reduce the effect of random variation.
Systematic Errors
Systematic errors produce a consistent shift in measurements.
Repeating the measurement does not necessarily remove a systematic error.
Random errors mainly affect precision, while systematic errors can affect the accuracy of measurements.
TOPIC 06
Accuracy, Precision and Sensitivity
Accuracy
Accuracy describes how close a measurement is to the accepted or true value.
Precision
Precision describes how closely repeated measurements agree with one another.
Sensitivity
Sensitivity describes the ability of an instrument or method to detect small changes in the quantity being measured.
Do not use accuracy and precision as interchangeable terms. They describe different aspects of measurement quality.
TOPIC 07
Experimental Techniques
Unit 6 can draw on practical techniques developed while studying the experimental content of Units 4 and 5.
General Good Practice
- Use suitable measuring instruments.
- Check equipment before taking measurements.
- Record measurements consistently.
- Use an appropriate range of values.
- Repeat measurements where appropriate.
- Control relevant variables.
- Record observations clearly.
- Use appropriate safety precautions.
Improving Measurements
Measurements can often be improved by choosing an appropriate instrument, increasing the scale of the measurement, repeating readings or using a more suitable experimental arrangement.
TOPIC 08
Recording Experimental Data
Experimental results should be recorded in a clear table before detailed analysis is performed.
Good Data Tables
- Give each quantity a clear heading.
- Include units in the headings.
- Use consistent decimal places where appropriate.
- Keep measured and calculated values clearly identifiable.
- Record enough significant figures for the experiment.
Example table structure
Length / m Time / s
0.20 0.91
0.30 1.10
0.40 1.27
TOPIC 09
Drawing and Using Graphs
Graphs are one of the most important tools for analysing experimental relationships.
Choosing Axes
The independent variable is normally placed on the horizontal axis and the dependent variable on the vertical axis.
Graph Requirements
- Label both axes.
- Include units.
- Use an appropriate scale.
- Use the available graph space effectively.
- Plot points accurately.
- Draw a suitable line or curve of best fit.
Gradient
The gradient of a graph can be used to determine a physical constant or establish a mathematical relationship.
When finding a gradient from a best-fit line, use a large triangle rather than a tiny triangle to reduce the effect of drawing and reading uncertainty.
TOPIC 10
Logarithmic Graphs
Log graphs can be used to investigate relationships that are not directly linear.
Power Relationships
Suppose two variables follow a relationship of the form:
Taking logarithms gives:
Therefore, plotting log(y) against log(x) produces a straight line when the power relationship is valid.
Finding the Power
The gradient of the log-log graph gives the power n.
Finding the Constant
The intercept can be used to determine the constant a.
Unit 6 expects students to be comfortable using graphs to determine relationships and constants, including logarithmic graphs.
TOPIC 11
Determining Relationships
Experimental data can be used to determine how one physical quantity depends on another.
Linear Relationship
The gradient gives m and the vertical intercept gives c.
Direct Proportionality
A graph through the origin supports a direct proportional relationship.
Power Relationship
A log-log graph can be used to determine the value of n.
TOPIC 12
Data Analysis
Experimental analysis involves converting raw measurements into useful physical information.
Calculations
Calculations should use appropriate equations and maintain consistent units.
Significant Figures
Final answers should normally be given to an appropriate number of significant figures based on the precision of the measurements.
Patterns and Trends
Experimental data should be examined for patterns such as proportionality, linearity, curves, anomalies and changes in gradient.
Example
If doubling x approximately doubles y, the results may provide evidence for a direct proportional relationship.
TOPIC 13
Evaluating an Experiment
Evaluation requires more than saying that an experiment was "good" or "bad". The evaluation should be connected to evidence from the experiment.
Sources of Error
Identify realistic sources of uncertainty or error that could affect the measurements.
Limitations
Consider limitations of the apparatus, method, measurement range and experimental design.
Improvements
Improvements should directly address an identified limitation.
Weak evaluation
"Use better equipment."
Better evaluation
"Use a digital timer with a smaller measurement uncertainty to reduce uncertainty in the measured period."
TOPIC 14
Drawing Conclusions
A conclusion should answer the original experimental aim using evidence obtained from the data.
A Strong Conclusion
- States the relationship found.
- Uses quantitative evidence where appropriate.
- Refers to the graph or calculated value.
- Addresses the original aim.
- Acknowledges uncertainty where relevant.
A conclusion should be based on the experimental evidence, not simply on what theory predicts.
TOPIC 15
Comparing Experimental and Accepted Values
Experimental results can be compared with accepted or theoretical values.
Percentage Difference
A small percentage difference may indicate good agreement, but the size of experimental uncertainty must also be considered.
Do not claim that an experimental result is wrong merely because it differs slightly from an accepted value. Consider uncertainty.
PRACTICE MODE
Unit 6 Mixed Practice
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The independent variable is deliberately changed, while the dependent variable is measured in response.
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Repeated measurements can reveal random variation, allow a mean to be calculated and increase confidence in the measured value.
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Percentage uncertainty = (0.5 / 50.0) × 100 = 1.0%.
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Accuracy describes how close a measurement is to the accepted value. Precision describes how closely repeated measurements agree with each other.
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A large triangle reduces the relative effect of small uncertainties in reading the coordinates and therefore gives a more reliable gradient.
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Plot log(y) against log(x). The gradient of the straight-line graph gives n.
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Quantities should have clear headings with appropriate units, and measurements should be recorded consistently.
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Repeat measurements and use an appropriate mean.
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A systematic error produces a consistent shift in the measurements, so repeating the same flawed measurement does not remove the underlying bias.
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It should answer the original aim and use quantitative evidence from the experiment, while considering uncertainty where appropriate.
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A control variable is kept constant so that it does not affect the relationship between the independent and dependent variables.
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The gradient represents the exponent n.
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An apparent anomaly may contain useful experimental information. There should be a justified reason for excluding a result rather than removing it simply because it does not fit the expected pattern.
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Random errors cause unpredictable variation between measurements, whereas systematic errors tend to produce a consistent bias or shift.
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A difference between the experimental and accepted values may be consistent with the experimental uncertainty. Therefore, the uncertainty must be considered before deciding whether the results agree.
QUICK REVIEW
Unit 6 Key Ideas
Think like an experimental physicist: every measurement needs a method, every result needs evidence, and every conclusion needs justification.