In physics experiments and measurements, it’s impossible to get a perfectly “true” value. There will always be some difference between our measured value and the actual value. This difference is due to errors and uncertainties. Understanding these concepts is crucial for evaluating the quality of your experimental results, especially in your School-Based Assessment (SBA).
What are Errors and Uncertainties?
While sometimes used interchangeably in everyday language, in physics, “error” and “uncertainty” have distinct meanings:
- Error: This refers to the difference between a measured value and the true or accepted value of a quantity. Errors can be caused by various factors and can sometimes be identified and reduced.
- Uncertainty: This represents the doubt about the value of a measurement. It’s a range around a measured value within which the true value is expected to lie. Uncertainty is a measure of the precision of a measurement and can never be completely eliminated.
Think of it this way: an error is about how wrong your measurement might be from the true value, while uncertainty is about how precise your measurement is.
Types of Errors
There are two main types of errors in physics experiments:
1. Random Errors
- Definition: These errors cause measured values to vary unpredictably from one reading to the next. They have an equal chance of being positive or negative, making a measurement slightly higher or lower than the true value.
- Causes: Random errors are often due to factors that are difficult to control or predict, such as:
- Fluctuations in environmental conditions (e.g., slight drafts affecting a balance).
- Difficulty in reading a scale precisely due to limitations of the eye.
- Reaction time when starting or stopping a timer.
- Random variations in the quantity being measured itself (if it’s not perfectly stable).
- Effect on Results: Random errors affect the precision of your measurements, leading to a spread in your readings if you repeat the experiment. They make it harder to get the exact same result each time.
- How to Minimize: The best way to reduce the impact of random errors is by repeating measurements multiple times and calculating the average (mean) of the readings. The more readings you take, the closer your average is likely to be to the true value. Taking an average helps the random high and low values cancel each other out.
Examples of Random Errors in Physics Experiments:
- Timing the swing of a pendulum – your reaction time starting and stopping the stopwatch will introduce random errors.
- Reading the exact position of a pointer on a scale between the markings.
- Measuring the diameter of a slightly irregular object with a ruler – getting a slightly different reading each time depending on where you measure.
2. Systematic Errors
- Definition: These errors cause all measurements to be consistently too high or too low by a fixed amount or proportion. They are not random and will affect all readings in the same way.
- Causes: Systematic errors are usually due to a fault in the measuring instrument or a flaw in the experimental method.
- Zero Error: When a measuring instrument does not read exactly zero when it should (e.g., an ammeter showing a reading when no current is flowing, a scale that doesn’t start at zero).
- Incorrect Calibration: If an instrument is not calibrated correctly, all its readings will be consistently off.
- Parallax Error (if consistently viewed from the same angle): Although sometimes considered random if viewing angle varies, consistently viewing a scale from the same non-perpendicular angle will lead to a systematic error.
- Faulty Equipment: A balance that consistently reads high or low.
- Environmental Factors: A constant external factor affecting the experiment in a consistent way (e.g., a constant magnetic field affecting a current measurement).
- Effect on Results: Systematic errors affect the accuracy of your measurements, meaning your results will be consistently shifted away from the true value. Repeating the experiment with the same faulty instrument or method will not reduce a systematic error.
- How to Minimize: Identifying and eliminating the source of the systematic error is necessary.
- Check for and correct zero errors before taking measurements.
- Ensure instruments are properly calibrated.
- Use the correct technique consistently (e.g., always reading scales at eye level to avoid parallax).
- If possible, use different instruments to see if the results are consistent.
Examples of Systematic Errors in CSEC Experiments:
- Using a ruler that has a worn-down zero mark – all length measurements will be too large.
- An ammeter that shows a reading of 0.1 A when no current is flowing – all current measurements will be 0.1 A too high.
- Not taring an electronic balance before measuring the mass of a substance in a container – the mass of the container will be included in every reading.
Uncertainties
Uncertainty quantifies the range of possible values for a measurement. It’s related to the precision of the measuring instrument.
- Estimating Uncertainty: For a single measurement using an analog scale (like a ruler or thermometer), the uncertainty is typically estimated as ± half of the smallest division on the scale. For example, if a ruler has markings every millimeter (0.1 cm), the uncertainty might be ± 0.5 mm (± 0.05 cm). For digital instruments, the uncertainty is usually taken as ± the value of the last significant digit or as stated by the manufacturer.
- Representing Uncertainty: Uncertainty is usually written with the measured value using the ± symbol.
- Example: If you measure a length as 15.2 cm using a ruler with millimeter markings, you might record it as 15.2±0.05 cm.
Reducing Errors and Improving Accuracy
To conduct good physics experiments and get reliable results for your SBA, you should always aim to:
- Minimize Random Errors: By taking multiple readings and calculating the average.
- Identify and Eliminate Systematic Errors: By carefully checking and calibrating your instruments and using the correct experimental techniques.
- Be Aware of Limitations: Recognize that even with the best efforts, some uncertainty will always remain in your measurements due to the limitations of the instruments and the experimental setup.
By understanding and accounting for errors and uncertainties, you demonstrate a key scientific skill and can better interpret the results of your experiments.