Welcome to Practical Physics!

In Physics, we don't just guess how the world works—we measure it. But every measurement comes with a story: How was it taken? What tool was used? And how much can we actually trust the result? This chapter focuses on Section 3.1: Measurements and their errors, covering the skills you need to become a precise and accurate experimental scientist. These skills are vital for Paper 2 of your AS exams.

1. SI Units and Prefixes

To talk to each other, scientists use a standard "language" called SI Units. You need to know the six fundamental base units for the AS course:

  • Mass: kilogram (\(kg\))
  • Length: metre (\(m\))
  • Time: second (\(s\))
  • Amount of substance: mole (\(mol\))
  • Temperature: kelvin (\(K\))
  • Electric current: ampere (\(A\))

Note: Any other unit (like Joules, Newtons, or Volts) is called a derived unit because it is made by combining these base units.

Unit Prefixes

Physics deals with things as massive as galaxies and as tiny as quarks. We use prefixes to make these numbers manageable. You must be able to convert between these:

  • Tera (T): \(10^{12}\)
  • Giga (G): \(10^{9}\)
  • Mega (M): \(10^{6}\)
  • kilo (k): \(10^{3}\)
  • milli (m): \(10^{-3}\)
  • micro (\(\mu\)): \(10^{-6}\)
  • nano (n): \(10^{-9}\)
  • pico (p): \(10^{-12}\)
  • femto (f): \(10^{-15}\)

Standard Form and Energy Conversions

Always write your final answers in standard form (e.g., \(6.02 \times 10^{23}\)). You are also expected to convert between Joules (\(J\)) and electron volts (\(eV\)):

\(1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}\)

Quick Tip: To go from \(eV \to J\), multiply by \(1.60 \times 10^{-19}\). To go from \(J \to eV\), divide by it!

2. Estimation of Physical Quantities

Sometimes, you just need a "ballpark" figure. This is called an order of magnitude estimate. If a value is \(1.2 \times 10^{4}\), its order of magnitude is \(10^{4}\).

Why do we do this? It helps you spot if your calculated answer is sensible. If you calculate the mass of a car and get \(10^{-5} \text{ kg}\), you know something went wrong!

3. Limitations of Physical Measurements

No measurement is perfect. We categorize these "imperfections" into two types of errors:

  • Random Errors: These cause readings to be spread about the true value. They vary every time you take a measurement. Fix: Take repeat readings and calculate a mean.
  • Systematic Errors: These cause readings to differ from the true value by a consistent amount each time (e.g., a "zero error" where a scale doesn't start at 0). Fix: Recalibrate the instrument or adjust your data.

Key Definitions (The "Must-Knows")

  • Precision: How close the measurements are to each other (very little spread).
  • Accuracy: How close the measurement is to the "true" value.
  • Resolution: The smallest change in the quantity being measured that gives a perceptible change in the reading (e.g., a standard ruler has a resolution of \(1 \text{ mm}\)).
  • Repeatability: Can you get the same result again using the same method and equipment?
  • Reproducibility: Can someone else (or you using different equipment) get the same result?

4. Working with Uncertainties

Uncertainty is the range within which the true value is expected to lie. It can be expressed in three ways:

  1. Absolute Uncertainty: Expressed in the same units as the measurement (e.g., \(10.0 \pm 0.1 \text{ cm}\)).
  2. Fractional Uncertainty: \(\frac{\text{Absolute Uncertainty}}{\text{Measured Value}}\)
  3. Percentage Uncertainty: \(\text{Fractional Uncertainty} \times 100\%\)

Combining Uncertainties (The Rules)

Don't worry if this seems tricky; just follow these three golden rules:

  • Adding or Subtracting: Add the absolute uncertainties.
    Example: If \(a = 5.0 \pm 0.1\) and \(b = 2.0 \pm 0.1\), then \(a + b = 7.0 \pm 0.2\).
  • Multiplying or Dividing: Add the percentage uncertainties.
  • Raising to a Power: Multiply the percentage uncertainty by the power.
    Example: If the uncertainty in radius \(r\) is \(3\%\), the uncertainty in area (\(A = \pi r^{2}\)) is \(3\% \times 2 = 6\%\).

5. Apparatus and Techniques

The AQA specification expects you to be familiar with specific tools. Here are some highlights:

  • Analogue vs. Digital: Analogue scales (like a thermometer) require interpolation (estimating between the lines). Digital scales (like a multimeter) give a clear number but still have limited resolution.
  • Micrometers and Calipers: These are used for very small distances. A micrometer might have a resolution of \(0.01 \text{ mm}\).
  • Oscilloscopes: Used to "see" waves. You must know how to use the volts/division dial (y-axis) and the time-base dial (x-axis) to calculate voltage and frequency.
  • Accuracy Boosters:
    • Use a fiducial marker (a clear reference point) to help time oscillations.
    • Use a set square to ensure equipment is perfectly vertical or horizontal.
    • Take time for multiple oscillations (e.g., 20 swings of a pendulum) and divide by the number of swings to reduce the impact of reaction time.

6. Uncertainties on Graphs

When you plot data, you represent uncertainty using error bars. These show the possible range of the data point in the x or y direction.

  • Lines of Best Fit: Should pass through all error bars if possible.
  • Uncertainty in Gradient: Draw a "worst" line of best fit (the steepest or shallowest possible line that still passes through the error bars).
    \(\text{Uncertainty} = |\text{Best Gradient} - \text{Worst Gradient}|\)
  • Uncertainty in Intercept: Similarly, compare the y-intercept of your best line and your worst line.

Quick Review:
1. Systematic errors affect accuracy; random errors affect precision.
2. For multiplying/dividing, always convert to percentage uncertainty first.
3. Resolution is the smallest division on your tool.

Note: For details on how to apply these techniques to specific experiments, see the chapter on Required Practical Activities 1-6.